Diffusion in coronas around clinopyroxene: modelling with local equilibrium and steady state, and a non-steady-state modification to account for zoned actinolite-hornblende

NASA Astrophysics Data System (ADS)

Ashworth, J. R.; Birdi, J. J.; Emmett, T. F.

1992-01-01

Retrograde coronas of Caledonian age, between clinopyroxene and plagioclase in the Jotun Nappe Complex, Norway, illustrate the effects of diffusion kinetics on mineral distributions among layers and on the compositions of hornblende-actinolite. One corona type comprises a symplectite of epidote + quartz adjacent to plagioclase, and a less well-organized intergrowth of amphibole + quartz replacing clinopyroxene. The observed mineral proportions imply an open-system reaction, but the similarity of Al/Si ratios in reactant plagioclase and product symplectite indicates approximate conservation of Al2O3 and SiO2. The largest inferred open-system flux is a loss of CaO, mostly derived from consumption of clinopyroxene. The approximate layer structure, Pl|Ep + Qtz|Hbl + Qtz|Act±Hbl + Qtz|Cpx, is modelled using the theory of steady-state diffusion-controlled growth with local equilibrium. To obtain a solution, it is necessary to use a reactant plagioclase composition which takes into account aluminous (epidote) inclusions. The results indicate that, in terms of Onsager diffusion coefficients L ii , Ca is more mobile than AL ( L CaCa/ L AlAl≳3.) (where ≳ means greater than or approximately equal to). This behaviour of Ca is comparable with that of Mg in previously studied coronas around olivine. Si is non-diffusing in the present modelling, because of silica saturation. Oxidation of some Fe2+ to Fe3+ occurs within the corona. Mg diffuses towards its source (clinopyroxene) to maintain local equilibrium. Other coronas consist of two layers, hornblende adjacent to plagioclase and zoned amphibole + quartz adjacent to clinopyroxene. In the zoned layer, actinolitic hornblende forms relict patches, separated from quartz blebs by more aluminous hornblende. A preliminary steady-state, local-equilibrium model of grain-boundary diffusion explains the formation of low-Al and high-Al layers as due to Al immobility. Zoning and replacement are qualitatively explained in terms of evolution of actinolite to more stable aluminous compositions. This is modelled by a non-steady-state modification of the theory, retaining local equilibrium in grain boundaries while relatively steep zoning profiles develop in grain interiors through slow intracrystalline diffusion. Replacement of actinolite by hornblende does not require a change in P- T conditions if actinolite is a kinetically determined, non-equilibrium product. The common preservation of a sharp contact between hornblende and actionolite layers may be explained by ineffectiveness of intracrystalline diffusion: according to the theory, given sufficient grain-boundary Al flux, a metastable actinolite + quartz layer in contact with hornblende may be diffusionally stable and may continue to grow in a steady state.

Conceptual model analysis of interaction at a concrete-Boom Clay interface

NASA Astrophysics Data System (ADS)

Liu, Sanheng; Jacques, Diederik; Govaerts, Joan; Wang, Lian

In many concepts for deep disposal of high-level radioactive waste, cementitious materials are used in the engineered barriers. For example, in Belgium the engineered barrier system is based on a considerable amount of cementitious materials as buffer and backfill in the so-called supercontainer embedded in the hosting geological formation. A potential hosting formation is Boom Clay. Insight in the interaction between the high-pH pore water of the cementitious materials and neutral-pH Boom Clay pore water is required. Two problems are quite common for modeling of such a system. The first one is the computational cost due to the long timescale model assessments envisaged for the deep disposal system. Also a very fine grid (in sub-millimeter), especially at interfaces has to be used in order to accurately predict the evolution of the system. The second one is whether to use equilibrium or kinetic reaction models. The objectives of this paper are twofold. First, we develop an efficient coupled reactive transport code for this diffusion-dominated system by making full use of multi-processors/cores computers. Second, we investigate how sensitive the system is to chemical reaction models especially when pore clogging due to mineral precipitation is considered within the cementitious system. To do this, we selected two portlandite dissolution models, i.e., equilibrium (fastest) and diffusion-controlled model with precipitation of a calcite layer around portlandite particles (diffusion-controlled dissolution). The results show that with shrinking core model portlandite dissolution and calcite precipitation are much slower than with the equilibrium model. Also diffusion-controlled dissolution smooths out dissolution fronts compared to the equilibrium model. However, only a slight difference with respect to the clogging time can be found even though we use a very small diffusion coefficient (10-20 m2/s) in the precipitated calcite layer.

Dependence of growth of the phases of multiphase binary systems on the diffusion parameters

NASA Astrophysics Data System (ADS)

Molokhina, L. A.; Rogalin, V. E.; Filin, S. A.; Kaplunov, I. A.

2017-12-01

A mathematical model of the diffusion interaction of a binary system with several phases on the equilibrium phase diagram is presented. The theoretical and calculated dependences of the layer thickness of each phase in the multiphase diffusion zone on the isothermal annealing time and the ratio of the diffusion parameters in the neighboring phases with an unlimited supply of both components were constructed. The phase formation and growth in the diffusion zone during "reactive" diffusion corresponds to the equilibrium state diagram for two components, and the order of their appearance in the diffusion zone depends only on the ratio of the diffusion parameters in the phases themselves and on the duration of the incubation periods. The dependence of phase appearance on the incubation periods, annealing time, and difference in the movement rates of the components across the interface boundaries was obtained. An example of the application of the model for processing the experimental data on phase growth in a two-component three-phase system was given.

Design-for-manufacture of gradient-index optical systems using time-varying boundary condition diffusion

NASA Astrophysics Data System (ADS)

Harkrider, Curtis Jason

2000-08-01

The incorporation of gradient-index (GRIN) material into optical systems offers novel and practical solutions to lens design problems. However, widespread use of gradient-index optics has been limited by poor correlation between gradient-index designs and the refractive index profiles produced by ion exchange between glass and molten salt. Previously, a design-for- manufacture model was introduced that connected the design and fabrication processes through use of diffusion modeling linked with lens design software. This project extends the design-for-manufacture model into a time- varying boundary condition (TVBC) diffusion model. TVBC incorporates the time-dependent phenomenon of melt poisoning and introduces a new index profile control method, multiple-step diffusion. The ions displaced from the glass during the ion exchange fabrication process can reduce the total change in refractive index (Δn). Chemical equilibrium is used to model this melt poisoning process. Equilibrium experiments are performed in a titania silicate glass and chemically analyzed. The equilibrium model is fit to ion concentration data that is used to calculate ion exchange boundary conditions. The boundary conditions are changed purposely to control the refractive index profile in multiple-step TVBC diffusion. The glass sample is alternated between ion exchange with a molten salt bath and annealing. The time of each diffusion step can be used to exert control on the index profile. The TVBC computer model is experimentally verified and incorporated into the design- for-manufacture subroutine that runs in lens design software. The TVBC design-for-manufacture model is useful for fabrication-based tolerance analysis of gradient-index lenses and for the design of manufactureable GRIN lenses. Several optical elements are designed and fabricated using multiple-step diffusion, verifying the accuracy of the model. The strength of multiple-step diffusion process lies in its versatility. An axicon, imaging lens, and curved radial lens, all with different index profile requirements, are designed out of a single glass composition.

Diffusion of a particle in the spatially correlated exponential random energy landscape: Transition from normal to anomalous diffusion.

PubMed

Novikov, S V

2018-01-14

Diffusive transport of a particle in a spatially correlated random energy landscape having exponential density of states has been considered. We exactly calculate the diffusivity in the nondispersive quasi-equilibrium transport regime for the 1D transport model and found that for slow decaying correlation functions the diffusivity becomes singular at some particular temperature higher than the temperature of the transition to the true non-equilibrium dispersive transport regime. It means that the diffusion becomes anomalous and does not follow the usual ∝ t 1/2 law. In such situation, the fully developed non-equilibrium regime emerges in two stages: first, at some temperature there is the transition from the normal to anomalous diffusion, and then at lower temperature the average velocity for the infinite medium goes to zero, thus indicating the development of the true dispersive regime. Validity of the Einstein relation is discussed for the situation where the diffusivity does exist. We provide also some arguments in favor of conservation of the major features of the new transition scenario in higher dimensions.

Competitive adsorption of textile dyes using peat: adsorption equilibrium and kinetic studies in monosolute and bisolute systems.

PubMed

Sepulveda, L; Troncoso, F; Contreras, E; Palma, C

2008-09-01

The purpose of this study is to investigate the adsorption by peat of four reactive textile dyes with the following commercial names: Yellow CIBA WR 200% (Y), Dark Blue CIBA WR (DB), Navy CIBA WB (N), and Red CIBA WB 150% (R), used in a cotton-polyester fabric finishing plant. The decolorization levels obtained varied between 5% and 30%, and the most significant variables were pH and ionic strength. Equilibrium studies were carried out at pH 2.8 and temperature of 25 degrees C. Maximum adsorption capacities were between 15 and 20 mg g(-1). Experimental data were fitted to the models of Langmuir. The equilibrium studies for bisolute systems were DB-R and Y-N mixtures. The Langmuir extended model indicated that there is competition for adsorption sites and without interaction between dyes. The results of the kinetic adsorption studies on monosolute and bisolute systems were fitted to the film-pore diffusion, variable diffusivity and quasi-stationary models. They showed that the diffusivity coefficients obtained varied between 2.0 x 10(-8) and 8.5 x 10(-8) cm2s(-1) when the variable diffusivity mass transfer model (VDM) was used and effective diffusion coefficient was fitted between 3.3 x 10(-7) and 56.0 x 10(-7) cm2s(-1) for the film-pore diffusion model (FPDM). The root of average of squares relative error obtained varied between 0.8% and 47.0% for the VDM and FPDM models, respectively.

A structured population model with diffusion in structure space.

PubMed

Pugliese, Andrea; Milner, Fabio

2018-05-09

A structured population model is described and analyzed, in which individual dynamics is stochastic. The model consists of a PDE of advection-diffusion type in the structure variable. The population may represent, for example, the density of infected individuals structured by pathogen density x, [Formula: see text]. The individuals with density [Formula: see text] are not infected, but rather susceptible or recovered. Their dynamics is described by an ODE with a source term that is the exact flux from the diffusion and advection as [Formula: see text]. Infection/reinfection is then modeled moving a fraction of these individuals into the infected class by distributing them in the structure variable through a probability density function. Existence of a global-in-time solution is proven, as well as a classical bifurcation result about equilibrium solutions: a net reproduction number [Formula: see text] is defined that separates the case of only the trivial equilibrium existing when [Formula: see text] from the existence of another-nontrivial-equilibrium when [Formula: see text]. Numerical simulation results are provided to show the stabilization towards the positive equilibrium when [Formula: see text] and towards the trivial one when [Formula: see text], result that is not proven analytically. Simulations are also provided to show the Allee effect that helps boost population sizes at low densities.

Modelling cointegration and Granger causality network to detect long-term equilibrium and diffusion paths in the financial system.

PubMed

Gao, Xiangyun; Huang, Shupei; Sun, Xiaoqi; Hao, Xiaoqing; An, Feng

2018-03-01

Microscopic factors are the basis of macroscopic phenomena. We proposed a network analysis paradigm to study the macroscopic financial system from a microstructure perspective. We built the cointegration network model and the Granger causality network model based on econometrics and complex network theory and chose stock price time series of the real estate industry and its upstream and downstream industries as empirical sample data. Then, we analysed the cointegration network for understanding the steady long-term equilibrium relationships and analysed the Granger causality network for identifying the diffusion paths of the potential risks in the system. The results showed that the influence from a few key stocks can spread conveniently in the system. The cointegration network and Granger causality network are helpful to detect the diffusion path between the industries. We can also identify and intervene in the transmission medium to curb risk diffusion.

Modelling cointegration and Granger causality network to detect long-term equilibrium and diffusion paths in the financial system

PubMed Central

Huang, Shupei; Sun, Xiaoqi; Hao, Xiaoqing; An, Feng

2018-01-01

Microscopic factors are the basis of macroscopic phenomena. We proposed a network analysis paradigm to study the macroscopic financial system from a microstructure perspective. We built the cointegration network model and the Granger causality network model based on econometrics and complex network theory and chose stock price time series of the real estate industry and its upstream and downstream industries as empirical sample data. Then, we analysed the cointegration network for understanding the steady long-term equilibrium relationships and analysed the Granger causality network for identifying the diffusion paths of the potential risks in the system. The results showed that the influence from a few key stocks can spread conveniently in the system. The cointegration network and Granger causality network are helpful to detect the diffusion path between the industries. We can also identify and intervene in the transmission medium to curb risk diffusion. PMID:29657804

The NEUF-DIX space project - Non-EquilibriUm Fluctuations during DIffusion in compleX liquids.

PubMed

Baaske, Philipp; Bataller, Henri; Braibanti, Marco; Carpineti, Marina; Cerbino, Roberto; Croccolo, Fabrizio; Donev, Aleksandar; Köhler, Werner; Ortiz de Zárate, José M; Vailati, Alberto

2016-12-01

Diffusion and thermal diffusion processes in a liquid mixture are accompanied by long-range non-equilibrium fluctuations, whose amplitude is orders of magnitude larger than that of equilibrium fluctuations. The mean-square amplitude of the non-equilibrium fluctuations presents a scale-free power law behavior q -4 as a function of the wave vector q, but the divergence of the amplitude of the fluctuations at small wave vectors is prevented by the presence of gravity. In microgravity conditions the non-equilibrium fluctuations are fully developed and span all the available length scales up to the macroscopic size of the systems in the direction parallel to the applied gradient. Available theoretical models are based on linearized hydrodynamics and provide an adequate description of the statics and dynamics of the fluctuations in the presence of small temperature/concentration gradients and under stationary or quasi-stationary conditions. We describe a project aimed at the investigation of Non-EquilibriUm Fluctuations during DIffusion in compleX liquids (NEUF-DIX). The focus of the project is on the investigation in micro-gravity conditions of the non-equilibrium fluctuations in complex liquids, trying to tackle several challenging problems that emerged during the latest years, such as the theoretical predictions of Casimir-like forces induced by non-equilibrium fluctuations; the understanding of the non-equilibrium fluctuations in multi-component mixtures including a polymer, both in relation to the transport coefficients and to their behavior close to a glass transition; the understanding of the non-equilibrium fluctuations in concentrated colloidal suspensions, a problem closely related with the detection of Casimir forces; and the investigation of the development of fluctuations during transient diffusion. We envision to parallel these experiments with state-of-the-art multi-scale simulations.

Mixed-order phase transition in a minimal, diffusion-based spin model.

PubMed

Fronczak, Agata; Fronczak, Piotr

2016-07-01

In this paper we exactly solve, within the grand canonical ensemble, a minimal spin model with the hybrid phase transition. We call the model diffusion based because its Hamiltonian can be recovered from a simple dynamic procedure, which can be seen as an equilibrium statistical mechanics representation of a biased random walk. We outline the derivation of the phase diagram of the model, in which the triple point has the hallmarks of the hybrid transition: discontinuity in the average magnetization and algebraically diverging susceptibilities. At this point, two second-order transition curves meet in equilibrium with the first-order curve, resulting in a prototypical mixed-order behavior.

Convergence to equilibrium of renormalised solutions to nonlinear chemical reaction–diffusion systems

NASA Astrophysics Data System (ADS)

Fellner, Klemens; Tang, Bao Quoc

2018-06-01

The convergence to equilibrium for renormalised solutions to nonlinear reaction-diffusion systems is studied. The considered reaction-diffusion systems arise from chemical reaction networks with mass action kinetics and satisfy the complex balanced condition. By applying the so-called entropy method, we show that if the system does not have boundary equilibria, i.e. equilibrium states lying on the boundary of R_+^N, then any renormalised solution converges exponentially to the complex balanced equilibrium with a rate, which can be computed explicitly up to a finite-dimensional inequality. This inequality is proven via a contradiction argument and thus not explicitly. An explicit method of proof, however, is provided for a specific application modelling a reversible enzyme reaction by exploiting the specific structure of the conservation laws. Our approach is also useful to study the trend to equilibrium for systems possessing boundary equilibria. More precisely, to show the convergence to equilibrium for systems with boundary equilibria, we establish a sufficient condition in terms of a modified finite-dimensional inequality along trajectories of the system. By assuming this condition, which roughly means that the system produces too much entropy to stay close to a boundary equilibrium for infinite time, the entropy method shows exponential convergence to equilibrium for renormalised solutions to complex balanced systems with boundary equilibria.

Competitive adsorption of furfural and phenolic compounds onto activated carbon in fixed bed column.

PubMed

Sulaymon, Abbas H; Ahmed, Kawther W

2008-01-15

For a multicomponent competitive adsorption of furfural and phenolic compounds, a mathematical model was builtto describe the mass transfer kinetics in a fixed bed column with activated carbon. The effects of competitive adsorption equilibrium constant, axial dispersion, external mass transfer, and intraparticle diffusion resistance on the breakthrough curve were studied for weakly adsorbed compound (furfural) and strongly adsorbed compounds (parachlorophenol and phenol). Experiments were carried out to remove the furfural and phenolic compound from aqueous solution. The equilibrium data and intraparticle diffusion coefficients obtained from separate experiments in a batch adsorber, by fitting the experimental data with theoretical model. The results show that the mathematical model includes external mass transfer and pore diffusion using nonlinear isotherms and provides a good description of the adsorption process for furfural and phenolic compounds in a fixed bed adsorber.

Transport properties of interacting magnetic islands in tokamak plasmas

DOE Office of Scientific and Technical Information (OSTI.GOV)

Gianakon, T.A.; Callen, J.D.; Hegna, C.C.

1993-10-01

This paper explores the equilibrium and transient transport properties of a mixed magnetic topology model for tokamak equilibria. The magnetic topology is composed of a discrete set of mostly non-overlapping magnetic islands centered on the low-order rational surfaces. Transport across the island regions is fast due to parallel transport along the stochastic magnetic field lines about the separatrix of each island. Transport between island regions is assumed to be slow due to a low residual cross-field transport. In equilibrium, such a model leads to: a nonlinear dependence of the heat flux on the pressure gradient; a power balance diffusion coefficientmore » which increases from core to edge; and profile resiliency. Transiently, such a model also exhibits a heat pulse diffusion coefficient larger than the power balance diffusion coefficient.« less

Development of a model using the MATLAB System identification toolbox to estimate (222)Rn equilibrium factor from CR-39 based passive measurements.

PubMed

Abo-Elmagd, M; Sadek, A M

2014-12-01

Can and Bare method is a widely used passive method for measuring the equilibrium factor F through the determination of the track density ratio between bare (D) and filtered (Do) detectors. The dimensions of the used diffusion chamber are altering the deposition ratios of Po-isotopes on the chamber walls as well as the ratios of the existing alpha emitters in air. Then the measured filtered track density and therefore the resultant equilibrium factor is changed according to the diffusion chamber dimensions. For this reason, high uncertainty was expected in the measured F using different diffusion chambers. In the present work, F is derived as a function of both track density ratio (D/Do) and the dimensions of the used diffusion chambers (its volume to the total internal surface area; V/A). The accuracy of the derived formula was verified using the black-box modeling technique via the MATLAB System identification toolbox. The results show that the uncertainty of the calculated F by using the derived formula of F (D/Do, V/A) is only 5%. The obtained uncertainty ensures the quality of the derived function to calculate F using diffusion chambers with wide range of dimensions. Copyright © 2014 Elsevier Ltd. All rights reserved.

Transport of polar and non-polar volatile compounds in polystyrene foam and oriented strand board

NASA Astrophysics Data System (ADS)

Yuan, Huali; Little, John C.; Hodgson, Alfred T.

Transport of hexanal and styrene in polystyrene foam (PSF) and oriented strand board (OSB) was characterized. A microbalance was used to measure sorption/desorption kinetics and equilibrium data. While styrene transport in PSF can be described by Fickian diffusion with a symmetrical and reversible sorption/desorption process, hexanal transport in both PSF and OSB exhibited significant hysteresis, with desorption being much slower than sorption. A porous media diffusion model that assumes instantaneous local equilibrium governed by a nonlinear Freundlich isotherm was found to explain the hysteresis in hexanal transport. A new nonlinear sorption and porous diffusion emissions model was, therefore, developed and partially validated using independent chamber data. The results were also compared to the more conventional linear Fickian-diffusion emissions model. While the linear emissions model predicts styrene emissions from PSF with reasonable accuracy, it substantially underestimates the rate of hexanal emissions from OSB. Although further research and more rigorous validation is needed, the new nonlinear emissions model holds promise for predicting emissions of polar VOCs such as hexanal from porous building materials.

Modeling cesium ion exchange on fixed-bed columns of crystalline silicotitanate granules

DOE Office of Scientific and Technical Information (OSTI.GOV)

Latheef, I.M.; Huckman, M.E.; Anthony, R.G.

2000-05-01

A mathematical model is presented to simulate Cs exchange in fixed-bed columns of a novel crystalline silicotitanate (CST) material, UOP IONSIV IE-911. A local equilibrium is assumed between the macropores and the solid crystals for the particle material balance. Axial dispersed flow and film mass-transfer resistance are incorporated into the column model. Cs equilibrium isotherms and diffusion coefficients were measured experimentally, and dispersion and film mass-transfer coefficients were estimated from correlations. Cs exchange column experiments were conducted in 5--5.7 M Na solutions and simulated using the proposed model. Best-fit diffusion coefficients from column simulations were compared with previously reported batchmore » values of Gu et al. and Huckman. Cs diffusion coefficients for the column were between 2.5 and 5.0 x 10{sup {minus}11} m{sup 2}/s for 5--5.7 M Na solutions. The effect of the isotherm shape on the Cs diffusion coefficient was investigated. The proposed model provides good fits to experimental data and may be utilized in designing commercial-scale units.« less

Continuum models of cohesive stochastic swarms: The effect of motility on aggregation patterns

NASA Astrophysics Data System (ADS)

Hughes, Barry D.; Fellner, Klemens

2013-10-01

Mathematical models of swarms of moving agents with non-local interactions have many applications and have been the subject of considerable recent interest. For modest numbers of agents, cellular automata or related algorithms can be used to study such systems, but in the present work, instead of considering discrete agents, we discuss a class of one-dimensional continuum models, in which the agents possess a density ρ(x,t) at location x at time t. The agents are subject to a stochastic motility mechanism and to a global cohesive inter-agent force. The motility mechanisms covered include classical diffusion, nonlinear diffusion (which may be used to model, in a phenomenological way, volume exclusion or other short-range local interactions), and a family of linear redistribution operators related to fractional diffusion equations. A variety of exact analytic results are discussed, including equilibrium solutions and criteria for unimodality of equilibrium distributions, full time-dependent solutions, and transitions between asymptotic collapse and asymptotic escape. We address the behaviour of the system for diffusive motility in the low-diffusivity limit for both smooth and singular interaction potentials and show how this elucidates puzzling behaviour in fully deterministic non-local particle interaction models. We conclude with speculative remarks about extensions and applications of the models.

On the kinetics of the pack - Aluminization process

NASA Technical Reports Server (NTRS)

Sivakumar, R.; Seigle, L. L.

1976-01-01

An investigation has been made of the aluminization of unalloyed Ni in fluoride-activated packs of varying Al activity. In packs of low Al activity, in which the ratio of Al to Ni was less than 50 at. pct, the specimen surface quickly came to equilibrium with the pack and remained close to equilibrium for the duration of normal coating runs. In these packs the kinetics of aluminization was controlled by diffusion in the solid. In packs of higher Al activity the surface of the specimen did not come to equilibrium with the pack and the kinetics of the process was governed by a combination of solid and gas diffusion rates. Under most conditions however, the surface composition was time-invariant and a steady-state appeared to exist at the pack-coating interface. By combining Levine and Caves' model for gaseous diffusion in pure-Al packs with calculations of solid diffusion rates some success has been achieved in explaining the results.

Rethinking pattern formation in reaction-diffusion systems

NASA Astrophysics Data System (ADS)

Halatek, J.; Frey, E.

2018-05-01

The present theoretical framework for the analysis of pattern formation in complex systems is mostly limited to the vicinity of fixed (global) equilibria. Here we present a new theoretical approach to characterize dynamical states arbitrarily far from (global) equilibrium. We show that reaction-diffusion systems that are driven by locally mass-conserving interactions can be understood in terms of local equilibria of diffusively coupled compartments. Diffusive coupling generically induces lateral redistribution of the globally conserved quantities, and the variable local amounts of these quantities determine the local equilibria in each compartment. We find that, even far from global equilibrium, the system is well characterized by its moving local equilibria. We apply this framework to in vitro Min protein pattern formation, a paradigmatic model for biological pattern formation. Within our framework we can predict and explain transitions between chemical turbulence and order arbitrarily far from global equilibrium. Our results reveal conceptually new principles of self-organized pattern formation that may well govern diverse dynamical systems.

Calculation of Transport Coefficients in Dense Plasma Mixtures

NASA Astrophysics Data System (ADS)

Haxhimali, T.; Cabot, W. H.; Caspersen, K. J.; Greenough, J.; Miller, P. L.; Rudd, R. E.; Schwegler, E. R.

2011-10-01

We use classical molecular dynamics (MD) to estimate species diffusivity and viscosity in mixed dense plasmas. The Yukawa potential is used to describe the screened Coulomb interaction between the ions. This potential has been used widely, providing the basis for models of dense stellar materials, inertial confined plasmas, and colloidal particles in electrolytes. We calculate transport coefficients in equilibrium simulations using the Green- Kubo relation over a range of thermodynamic conditions including the viscosity and the self - diffusivity for each component of the mixture. The interdiffusivity (or mutual diffusivity) can then be related to the self-diffusivities by using a generalization of the Darken equation. We have also employed non-equilibrium MD to estimate interdiffusivity during the broadening of the interface between two regions each with a high concentration of either species. Here we present results for an asymmetric mixture between Ar and H. These can easily be extended to other plasma mixtures. A main motivation for this study is to develop accurate transport models that can be incorporated into the hydrodynamic codes to study hydrodynamic instabilities. We use classical molecular dynamics (MD) to estimate species diffusivity and viscosity in mixed dense plasmas. The Yukawa potential is used to describe the screened Coulomb interaction between the ions. This potential has been used widely, providing the basis for models of dense stellar materials, inertial confined plasmas, and colloidal particles in electrolytes. We calculate transport coefficients in equilibrium simulations using the Green- Kubo relation over a range of thermodynamic conditions including the viscosity and the self - diffusivity for each component of the mixture. The interdiffusivity (or mutual diffusivity) can then be related to the self-diffusivities by using a generalization of the Darken equation. We have also employed non-equilibrium MD to estimate interdiffusivity during the broadening of the interface between two regions each with a high concentration of either species. Here we present results for an asymmetric mixture between Ar and H. These can easily be extended to other plasma mixtures. A main motivation for this study is to develop accurate transport models that can be incorporated into the hydrodynamic codes to study hydrodynamic instabilities. This work was performed under the auspices of the US Dept. of Energy by Lawrence Livermore National Security, LLC under Contract DE-AC52-07NA27344.

Plasma diffusion at the magnetopause? The case of lower hybrid drift waves

NASA Technical Reports Server (NTRS)

Treumann, R. A.; Labelle, J.; Pottelette, R.; Gary, S. P.

1990-01-01

The diffusion expected from the quasilinear theory of the lower hybrid drift instability at the Earth's magnetopause is recalculated. The resulting diffusion coefficient is in principle just marginally large enough to explain the thickness of the boundary layer under quiet conditions, based on observational upper limits for the wave intensities. Thus, one possible model for the boundary layer could involve equilibrium between the diffusion arising from lower hybrid waves and various low processes. However, some recent data and simulations seems to indicate that the magnetopause is not consistent with such a soft diffusive equilibrium model. Furthermore, investigation of the nonlinear equations for the lower hybrid waves for magnetopause parameters indicates that the quasilinear state may never arise because coalescence to large wavelengths, followed by collapse once a critical wavelengths is reached, occur on a time scale faster than the quasilinear diffusion. In this case, an inhomogeneous boundary layer is to be expected. More simulations are required over longer time periods to explore whether this nonlinear evolution really takes place at the magnetopause.

Bulk diffusion in a kinetically constrained lattice gas

NASA Astrophysics Data System (ADS)

Arita, Chikashi; Krapivsky, P. L.; Mallick, Kirone

2018-03-01

In the hydrodynamic regime, the evolution of a stochastic lattice gas with symmetric hopping rules is described by a diffusion equation with density-dependent diffusion coefficient encapsulating all microscopic details of the dynamics. This diffusion coefficient is, in principle, determined by a Green-Kubo formula. In practice, even when the equilibrium properties of a lattice gas are analytically known, the diffusion coefficient cannot be computed except when a lattice gas additionally satisfies the gradient condition. We develop a procedure to systematically obtain analytical approximations for the diffusion coefficient for non-gradient lattice gases with known equilibrium. The method relies on a variational formula found by Varadhan and Spohn which is a version of the Green-Kubo formula particularly suitable for diffusive lattice gases. Restricting the variational formula to finite-dimensional sub-spaces allows one to perform the minimization and gives upper bounds for the diffusion coefficient. We apply this approach to a kinetically constrained non-gradient lattice gas in two dimensions, viz. to the Kob-Andersen model on the square lattice.

Determination of equilibrium and rate constants for complex formation by fluorescence correlation spectroscopy supplemented by dynamic light scattering and Taylor dispersion analysis.

PubMed

Zhang, Xuzhu; Poniewierski, Andrzej; Jelińska, Aldona; Zagożdżon, Anna; Wisniewska, Agnieszka; Hou, Sen; Hołyst, Robert

2016-10-04

The equilibrium and rate constants of molecular complex formation are of great interest both in the field of chemistry and biology. Here, we use fluorescence correlation spectroscopy (FCS), supplemented by dynamic light scattering (DLS) and Taylor dispersion analysis (TDA), to study the complex formation in model systems of dye-micelle interactions. In our case, dyes rhodamine 110 and ATTO-488 interact with three differently charged surfactant micelles: octaethylene glycol monododecyl ether C 12 E 8 (neutral), cetyltrimethylammonium chloride CTAC (positive) and sodium dodecyl sulfate SDS (negative). To determine the rate constants for the dye-micelle complex formation we fit the experimental data obtained by FCS with a new form of the autocorrelation function, derived in the accompanying paper. Our results show that the association rate constants for the model systems are roughly two orders of magnitude smaller than those in the case of the diffusion-controlled limit. Because the complex stability is determined by the dissociation rate constant, a two-step reaction mechanism, including the diffusion-controlled and reaction-controlled rates, is used to explain the dye-micelle interaction. In the limit of fast reaction, we apply FCS to determine the equilibrium constant from the effective diffusion coefficient of the fluorescent components. Depending on the value of the equilibrium constant, we distinguish three types of interaction in the studied systems: weak, intermediate and strong. The values of the equilibrium constant obtained from the FCS and TDA experiments are very close to each other, which supports the theoretical model used to interpret the FCS data.

Evaluation of diffusivity in the anterior lobe of the pituitary gland: 3D turbo field echo with diffusion-sensitized driven-equilibrium preparation.

PubMed

Hiwatashi, A; Yoshiura, T; Togao, O; Yamashita, K; Kikuchi, K; Kobayashi, K; Ohga, M; Sonoda, S; Honda, H; Obara, M

2014-01-01

3D turbo field echo with diffusion-sensitized driven-equilibrium preparation is a non-echo-planar technique for DWI, which enables high-resolution DWI without field inhomogeneity-related image distortion. The purpose of this study was to evaluate the feasibility of diffusion-sensitized driven-equilibrium turbo field echo in evaluating diffusivity in the normal pituitary gland. First, validation of diffusion-sensitized driven-equilibrium turbo field echo was attempted by comparing it with echo-planar DWI. Five healthy volunteers were imaged by using diffusion-sensitized driven-equilibrium turbo field echo and echo-planar DWI. The imaging voxel size was 1.5 × 1.5 × 1.5 mm(3) for diffusion-sensitized driven-equilibrium turbo field echo and 1.5 × 1.9 × 3.0 mm(3) for echo-planar DWI. ADCs measured by the 2 methods in 15 regions of interests (6 in gray matter and 9 in white matter) were compared by using the Pearson correlation coefficient. The ADC in the pituitary anterior lobe was then measured in 10 volunteers by using diffusion-sensitized driven-equilibrium turbo field echo, and the results were compared with those in the pons and vermis by using a paired t test. The ADCs from the 2 methods showed a strong correlation (r = 0.79; P < .0001), confirming the accuracy of the ADC measurement with the diffusion-sensitized driven-equilibrium sequence. The ADCs in the normal pituitary gland were 1.37 ± 0.13 × 10(-3) mm(2)/s, which were significantly higher than those in the pons (1.01 ± 0.24 × 10(-3) mm(2)/s) and the vermis (0.89 ± 0.25 × 10(-3) mm(2)/s, P < .01). We demonstrated that diffusion-sensitized driven-equilibrium turbo field echo is feasible in assessing ADC in the pituitary gland.

Equilibrium and kinetic adsorption study of a cationic dye by a natural adsorbent--silkworm pupa.

PubMed

Noroozi, B; Sorial, G A; Bahrami, H; Arami, M

2007-01-02

In this work the use of silkworm pupa, which is the waste of silk spinning industries has been investigated as an adsorbent for the removal of C.I. Basic Blue 41. The amino acid nature of the pupa provided a reasonable capability for dye removal. Equilibrium adsorption isotherms and kinetics were investigated. The adsorption equilibrium data were analyzed by using various adsorption isotherm models and the results have shown that adsorption behavior of the dye could be described reasonably well by either Langmuir or Freundlich models. The characteristic parameters for each isotherm have been determined. The monolayer adsorption capacity was determined to be 555 mg/g. Kinetic studies indicated that the adsorption follows pseudo-second-order kinetics with a rate constant of 0.0434 and 0.0572 g/min mg for initial dye concentration of 200 mg/l at 20 and 40 degrees C, respectively. Kinetic studies showed that film diffusion and intra-particle diffusion were simultaneously operating during the adsorption process. The rate constant for intra-particle diffusion was estimated to be 1.985 mg/g min(0.5).

Diffusion mediated localization on membrane surfaces

NASA Technical Reports Server (NTRS)

Weaver, D. L.

1982-01-01

Using the model of a cell membrane of a spherical surface in which membrane components may diffuse, the rate of localization due to trapping under diffusion control has been estimated by computing an analytical expression for the mean trapping time including the possibilities of a trapping probability less than one and/or the establishment of an equilibrium at the trap boundary.

Asymptotic analysis of discrete schemes for non-equilibrium radiation diffusion

DOE Office of Scientific and Technical Information (OSTI.GOV)

Cui, Xia, E-mail: cui_xia@iapcm.ac.cn; Yuan, Guang-wei; Shen, Zhi-jun

Motivated by providing well-behaved fully discrete schemes in practice, this paper extends the asymptotic analysis on time integration methods for non-equilibrium radiation diffusion in [2] to space discretizations. Therein studies were carried out on a two-temperature model with Larsen's flux-limited diffusion operator, both the implicitly balanced (IB) and linearly implicit (LI) methods were shown asymptotic-preserving. In this paper, we focus on asymptotic analysis for space discrete schemes in dimensions one and two. First, in construction of the schemes, in contrast to traditional first-order approximations, asymmetric second-order accurate spatial approximations are devised for flux-limiters on boundary, and discrete schemes with second-ordermore » accuracy on global spatial domain are acquired consequently. Then by employing formal asymptotic analysis, the first-order asymptotic-preserving property for these schemes and furthermore for the fully discrete schemes is shown. Finally, with the help of manufactured solutions, numerical tests are performed, which demonstrate quantitatively the fully discrete schemes with IB time evolution indeed have the accuracy and asymptotic convergence as theory predicts, hence are well qualified for both non-equilibrium and equilibrium radiation diffusion. - Highlights: • Provide AP fully discrete schemes for non-equilibrium radiation diffusion. • Propose second order accurate schemes by asymmetric approach for boundary flux-limiter. • Show first order AP property of spatially and fully discrete schemes with IB evolution. • Devise subtle artificial solutions; verify accuracy and AP property quantitatively. • Ideas can be generalized to 3-dimensional problems and higher order implicit schemes.« less

Mesoscale modeling of vacancy-mediated Si segregation near an edge dislocation in Ni under irradiation

NASA Astrophysics Data System (ADS)

Li, Zebo; Trinkle, Dallas R.

2017-04-01

We use a continuum method informed by transport coefficients computed using self-consistent mean field theory to model vacancy-mediated diffusion of substitutional Si solutes in FCC Ni near an a/2 [1 1 ¯0 ] (111 ) edge dislocation. We perform two sequential simulations: first under equilibrium boundary conditions and then under irradiation. The strain field around the dislocation induces heterogeneity and anisotropy in the defect transport properties and determines the steady-state vacancy and Si distributions. At equilibrium both vacancies and Si solutes diffuse to form Cottrell atmospheres with vacancies accumulating in the compressive region above the dislocation core while Si segregates to the tensile region below the core. Irradiation raises the bulk vacancy concentration, driving vacancies to flow into the dislocation core. The out-of-equilibrium vacancy fluxes drag Si atoms towards the core, causing segregation to the compressive region, despite Si being an oversized solute in Ni.

Monolayers of hard rods on planar substrates. II. Growth

NASA Astrophysics Data System (ADS)

Klopotek, M.; Hansen-Goos, H.; Dixit, M.; Schilling, T.; Schreiber, F.; Oettel, M.

2017-02-01

Growth of hard-rod monolayers via deposition is studied in a lattice model using rods with discrete orientations and in a continuum model with hard spherocylinders. The lattice model is treated with kinetic Monte Carlo simulations and dynamic density functional theory while the continuum model is studied by dynamic Monte Carlo simulations equivalent to diffusive dynamics. The evolution of nematic order (excess of upright particles, "standing-up" transition) is an entropic effect and is mainly governed by the equilibrium solution, rendering a continuous transition [Paper I, M. Oettel et al., J. Chem. Phys. 145, 074902 (2016)]. Strong non-equilibrium effects (e.g., a noticeable dependence on the ratio of rates for translational and rotational moves) are found for attractive substrate potentials favoring lying rods. Results from the lattice and the continuum models agree qualitatively if the relevant characteristic times for diffusion, relaxation of nematic order, and deposition are matched properly. Applicability of these monolayer results to multilayer growth is discussed for a continuum-model realization in three dimensions where spherocylinders are deposited continuously onto a substrate via diffusion.

Thermodynamics of viscoelastic rate-type fluids with stress diffusion

NASA Astrophysics Data System (ADS)

Málek, Josef; Průša, Vít; Skřivan, Tomáš; Süli, Endre

2018-02-01

We propose thermodynamically consistent models for viscoelastic fluids with a stress diffusion term. In particular, we derive variants of compressible/incompressible Maxwell/Oldroyd-B models with a stress diffusion term in the evolution equation for the extra stress tensor. It is shown that the stress diffusion term can be interpreted either as a consequence of a nonlocal energy storage mechanism or as a consequence of a nonlocal entropy production mechanism, while different interpretations of the stress diffusion mechanism lead to different evolution equations for the temperature. The benefits of the knowledge of the thermodynamical background of the derived models are documented in the study of nonlinear stability of equilibrium rest states. The derived models open up the possibility to study fully coupled thermomechanical problems involving viscoelastic rate-type fluids with stress diffusion.

Plasma diffusion at the magnetopause - The case of lower hybrid drift waves

NASA Technical Reports Server (NTRS)

Treumann, R. A.; Labelle, J.; Pottelette, R.

1991-01-01

The diffusion expected from the quasi-linear theory of the lower hybrid drift instability at the earth's magnetopause is recalculated. The resulting diffusion coefficient is marginally large enough to explain the thickness of the boundary layer under quiet conditions, based on observational upper limits for the wave intensities. Thus, one possible model for the boundary layer could involve equilibrium between the diffusion arising from lower hybrid waves and various loss processes.

Dynamical influences on thermospheric composition: implications for semi-empirical models

NASA Astrophysics Data System (ADS)

Sutton, E. K.; Solomon, S. C.

2014-12-01

The TIE-GCM was recently augmented to include helium and argon, two approximately inert species that can be used as tracers of dynamics in the thermosphere. The former species is treated as a major species due to its large abundance near the upper boundary. The effects of exospheric transport are also included in order to simulate realistic seasonal and latitudinal helium distributions. The latter species is treated as a classical minor species, imparting absolutely no forces on the background atmosphere. In this study, we examine the interplay of the various dynamical terms - i.e. background circulation, molecular and Eddy diffusion - as they drive departures from the distributions that would be expected under the assumption of diffusive equilibrium. As this has implications on the formulation of all empirical thermospheric models, we use this understanding to address the following questions: (1) how do errors caused by the assumption of diffusive equilibrium manifest within empirical models of the thermosphere? and (2) where and when does an empirical model's output disagree with its underlying datasets due to the inherent limitations of said model's formulation?

Numerical Experiments Based on the Catastrophe Model of Solar Eruptions

NASA Astrophysics Data System (ADS)

Xie, X. Y.; Ziegler, U.; Mei, Z. X.; Wu, N.; Lin, J.

2017-11-01

On the basis of the catastrophe model developed by Isenberg et al., we use the NIRVANA code to perform the magnetohydrodynamics (MHD) numerical experiments to look into various behaviors of the coronal magnetic configuration that includes a current-carrying flux rope used to model the prominence levitating in the corona. These behaviors include the evolution in equilibrium heights of the flux rope versus the change in the background magnetic field, the corresponding internal equilibrium of the flux rope, dynamic properties of the flux rope after the system loses equilibrium, as well as the impact of the referential radius on the equilibrium heights of the flux rope. In our calculations, an empirical model of the coronal density distribution given by Sittler & Guhathakurta is used, and the physical diffusion is included. Our experiments show that the deviation of simulations in the equilibrium heights from the theoretical results exists, but is not apparent, and the evolutionary features of the two results are similar. If the flux rope is initially locate at the stable branch of the theoretical equilibrium curve, the flux rope will quickly reach the equilibrium position in the simulation after several rounds of oscillations as a result of the self-adjustment of the system; and the flux rope lose the equilibrium if the initial location of the flux rope is set at the critical point on the theoretical equilibrium curve. Correspondingly, the internal equilibrium of the flux rope can be reached as well, and the deviation from the theoretical results is somewhat apparent since the approximation of the small radius of the flux rope is lifted in our experiments, but such deviation does not affect the global equilibrium in the system. The impact of the referential radius on the equilibrium heights of the flux rope is consistent with the prediction of the theory. Our calculations indicate that the motion of the flux rope after the loss of equilibrium is consistent with which is predicted by the Lin-Forbes model and observations. Formation of the fast mode shock ahead of the flux rope is observed in our experiments. Outward motions of the flux rope are smooth, and magnetic energy is continuously converted into the other types of energy because both the diffusions are considered in calculations, and magnetic reconnection is allowed to occur successively in the current sheet behind the flux rope.

Static SPME sampling of VOCs emitted from indoor building materials: prediction of calibration curves of single compounds for two different emission cells.

PubMed

Mocho, Pierre; Desauziers, Valérie

2011-05-01

Solid-phase microextraction (SPME) is a powerful technique, easy to implement for on-site static sampling of indoor VOCs emitted by building materials. However, a major constraint lies in the establishment of calibration curves which requires complex generation of standard atmospheres. Thus, the purpose of this paper is to propose a model to predict adsorption kinetics (i.e., calibration curves) of four model VOCs. The model is based on Fick's laws for the gas phase and on the equilibrium or the solid diffusion model for the adsorptive phase. Two samplers (the FLEC® and a home-made cylindrical emission cell), coupled to SPME for static sampling of material emissions, were studied. A good agreement between modeling and experimental data is observed and results show the influence of sampling rate on mass transfer mode in function of sample volume. The equilibrium model is adapted to quite large volume sampler (cylindrical cell) while the solid diffusion model is dedicated to small volume sampler (FLEC®). The limiting steps of mass transfer are the diffusion in gas phase for the cylindrical cell and the pore surface diffusion for the FLEC®. In the future, this modeling approach could be a useful tool for time-saving development of SPME to study building material emission in static mode sampling.

Mathematical modelling of the Phloem: the importance of diffusion on sugar transport at osmotic equilibrium.

PubMed

Payvandi, S; Daly, K R; Zygalakis, K C; Roose, T

2014-11-01

Plants rely on the conducting vessels of the phloem to transport the products of photosynthesis from the leaves to the roots, or to any other organs, for growth, metabolism, and storage. Transport within the phloem is due to an osmotically-generated pressure gradient and is hence inherently nonlinear. Since convection dominates over diffusion in the main bulk flow, the effects of diffusive transport have generally been neglected by previous authors. However, diffusion is important due to boundary layers that form at the ends of the phloem, and at the leaf-stem and stem-root boundaries. We present a mathematical model of transport which includes the effects of diffusion. We solve the system analytically in the limit of high Münch number which corresponds to osmotic equilibrium and numerically for all parameter values. We find that the bulk solution is dependent on the diffusion-dominated boundary layers. Hence, even for large Péclet number, it is not always correct to neglect diffusion. We consider the cases of passive and active sugar loading and unloading. We show that for active unloading, the solutions diverge with increasing Péclet. For passive unloading, the convergence of the solutions is dependent on the magnitude of loading. Diffusion also permits the modelling of an axial efflux of sugar in the root zone which may be important for the growing root tip and for promoting symbiotic biological interactions in the soil. Therefore, diffusion is an essential mechanism for transport in the phloem and must be included to accurately predict flow.

Modeling packed bed sorbent systems with the Pore Surface Diffusion Model: Evidence of facilitated surface diffusion of arsenate in nano-metal (hydr)oxide hybrid ion exchange media.

PubMed

Dale, Sachie; Markovski, Jasmina; Hristovski, Kiril D

2016-09-01

This study explores the possibility of employing the Pore Surface Diffusion Model (PSDM) to predict the arsenic breakthrough curve of a packed bed system operated under continuous flow conditions with realistic groundwater, and consequently minimize the need to conduct pilot scale tests. To provide the nano-metal (hydr)oxide hybrid ion exchange media's performance in realistic water matrices without engaging in taxing pilot scale testing, the multi-point equilibrium batch sorption tests under pseudo-equilibrium conditions were performed; arsenate breakthrough curve of short bed column (SBC) was predicted by the PSDM in the continuous flow experiments; SBC tests were conducted under the same conditions to validate the model. The overlapping Freundlich isotherms suggested that the water matrix and competing ions did not have any denoting effect on sorption capacity of the media when the matrix was changed from arsenic-only model water to real groundwater. As expected, the PSDM provided a relatively good prediction of the breakthrough profile for arsenic-only model water limited by intraparticle mass transports. In contrast, the groundwater breakthrough curve demonstrated significantly faster intraparticle mass transport suggesting to a surface diffusion process, which occurs in parallel to the pore diffusion. A simple selection of DS=1/2 DP appears to be sufficient when describing the facilitated surface diffusion of arsenate inside metal (hydr)oxide nano-enabled hybrid ion-exchange media in presence of sulfate, however, quantification of the factors determining the surface diffusion coefficient's magnitude under different treatment scenarios remained unexplored. Copyright © 2015 Elsevier B.V. All rights reserved.

Load-dependent surface diffusion model for analyzing the kinetics of protein adsorption onto mesoporous materials.

PubMed

Marbán, Gregorio; Ramírez-Montoya, Luis A; García, Héctor; Menéndez, J Ángel; Arenillas, Ana; Montes-Morán, Miguel A

2018-02-01

The adsorption of cytochrome c in water onto organic and carbon xerogels with narrow pore size distributions has been studied by carrying out transient and equilibrium batch adsorption experiments. It was found that equilibrium adsorption exhibits a quasi-Langmuirian behavior (a g coefficient in the Redlich-Peterson isotherms of over 0.95) involving the formation of a monolayer of cyt c with a depth of ∼4nm on the surface of all xerogels for a packing density of the protein inside the pores of 0.29gcm -3 . A load-dependent surface diffusion model (LDSDM) has been developed and numerically solved to fit the experimental kinetic adsorption curves. The results of the LDSDM show better fittings than the standard homogeneous surface diffusion model. The value of the external mass transfer coefficient obtained by numerical optimization confirms that the process is controlled by the intraparticle surface diffusion of cyt c. The surface diffusion coefficients decrease with increasing protein load down to zero for the maximum possible load. The decrease is steeper in the case of the xerogels with the smallest average pore diameter (∼15nm), the limit at which the zero-load diffusion coefficient of cyt c also begins to be negatively affected by interactions with the opposite wall of the pore. Copyright © 2017 Elsevier Inc. All rights reserved.

A novel model for smectic liquid crystals: Elastic anisotropy and response to a steady-state flow.

PubMed

Püschel-Schlotthauer, Sergej; Meiwes Turrión, Victor; Stieger, Tillmann; Grotjahn, Robin; Hall, Carol K; Mazza, Marco G; Schoen, Martin

2016-10-28

By means of a combination of equilibrium Monte Carlo and molecular dynamics simulations and nonequilibrium molecular dynamics we investigate the ordered, uniaxial phases (i.e., nematic and smectic A) of a model liquid crystal. We characterize equilibrium behavior through their diffusive behavior and elastic properties. As one approaches the equilibrium isotropic-nematic phase transition, diffusion becomes anisotropic in that self-diffusion D ⊥ in the direction orthogonal to a molecule's long axis is more hindered than self-diffusion D ∥ in the direction parallel to that axis. Close to nematic-smectic A phase transition the opposite is true, D ∥ < D ⊥ . The Frank elastic constants K 1 , K 2 , and K 3 for the respective splay, twist, and bend deformations of the director field n̂ are no longer equal and exhibit a temperature dependence observed experimentally for cyanobiphenyls. Under nonequilibrium conditions, a pressure gradient applied to the smectic A phase generates Poiseuille-like or plug flow depending on whether the convective velocity is parallel or orthogonal to the plane of smectic layers. We find that in Poiseuille-like flow the viscosity of the smectic A phase is higher than in plug flow. This can be rationalized via the velocity-field component in the direction of the flow. In a sufficiently strong flow these smectic layers are not destroyed but significantly bent.

Self-diffusion of magnesium in spinel and in equilibrium melts - Constraints on flash heating of silicates

NASA Technical Reports Server (NTRS)

Sheng, Y. J.; Wasserburg, G. J.; Hutcheon, I. D.

1992-01-01

An isotopic tracer is used to measure Mg self-diffusion in spinel and coexisting melt at bulk chemical equilibrium. The diffusion coefficients were calculated from the measured isotope profiles using a model that includes the complementary diffusion of Mg-24, Mg-25, and Mg-26 in both phases with the constraint that the Mg content of each phase is constant. The activation energy and preexponential factor for Mg self-diffusion in spinel are, respectively, 384 +/- 7 kJ and 74.6 +/- 1.1 sq cm/s. These data indicate Mg diffusion in spinel is much slower than previous estimates. The activation energy for Mg self-diffusion in coexisting melt is 343 +/- 25 kJ and the preexponential factor is 7791.9 +/- 1.3 sq cm/s. These results are used to evaluate cooling rates of plagioclase-olivine inclusions (POIs) in the Allende meteorite. Given a maximum melting temperature for POIs of about 1500 C, these results show that a 1-micron radius spinel would equilibrate isotopically with a melt within about 60 min.

Use of Excel ion exchange equilibrium solver with WinGEMS to model and predict NPE distribution in the Mead/Westvaco Evandale, TX, hardwood bleach plant

Treesearch

Christopher Litvay; Alan Rudie; Peter Hart

2003-01-01

An Excel spreadsheet developed to solve the ion-exchange equilibrium in wood pulps has been linked by dynamic data exchange to WinGEMS and used to model the non-process elements in the hardwood bleach plant of the Mead/Westvaco Evandale mill. Pulp and filtrate samples were collected from the diffusion washers and final wash press of the bleach plant. A WinGEMS model of...

Diffusion-weighted magnetic resonance imaging of extraocular muscles in patients with Grave's ophthalmopathy using turbo field echo with diffusion-sensitized driven-equilibrium preparation.

PubMed

Hiwatashi, A; Togao, O; Yamashita, K; Kikuchi, K; Momosaka, D; Honda, H

2018-03-20

The purpose of this study was to correlate diffusivity of extraocular muscles, measured by three-dimensional turbo field echo (3DTFE) magnetic resonance (MR) imaging using diffusion-sensitized driven-equilibrium preparation, with their size and activity in patients with Grave's ophthalmopathy. Twenty-three patients with Grave's ophthalmopathy were included. There were 17 women and 6 men with a mean age of 55.8±12.6 (SD) years (range: 26-83 years). 3DTFE with diffusion-sensitized driven-equilibrium MR images were obtained with b-values of 0 and 500s/mm 2 . The apparent diffusion coefficient (ADC) of extraocular muscles was measured on coronal reformatted MR images. Signal intensities of extraocular muscles on conventional MR images were compared to those of normal-appearing white matter, and cross-sectional areas of the muscles were also measured. The clinical activity score was also evaluated. Statistical analyses were performed with Pearson correlation and Mann-Whitney U tests. On 3DTFE with diffusion-sensitized driven-equilibrium preparation, the mean ADC of the extraocular muscles was 2.23±0.37 (SD)×10 -3 mm2/s (range: 1.70×10 -3 -3.11×10 -3 mm 2 /s). There was a statistically significant moderate correlation between ADC and the size of the muscles (r=0.61). There were no statistically significant correlations between ADC and signal intensity on conventional MR and the clinical activity score. 3DTFE with diffusion-sensitized driven-equilibrium preparation technique allows quantifying diffusivity of extraocular muscles in patients with Grave's ophthalmopathy. The diffusivity of the extraocular muscles on 3DTFE with diffusion-sensitized driven-equilibrium preparation MR images moderately correlates with their size. Copyright © 2018. Published by Elsevier Masson SAS.

Sorption kinetics and isotherm studies of a cationic dye using agricultural waste: broad bean peels.

PubMed

Hameed, B H; El-Khaiary, M I

2008-06-15

In this paper, broad bean peels (BBP), an agricultural waste, was evaluated for its ability to remove cationic dye (methylene blue) from aqueous solutions. Batch mode experiments were conducted at 30 degrees C. Equilibrium sorption isotherms and kinetics were investigated. The kinetic data obtained at different concentrations have been analyzed using pseudo-first-order, pseudo-second-order and intraparticle diffusion equations. The experimental data fitted very well the pseudo-first-order kinetic model. Analysis of the temportal change of q indicates that at the beginning of the process the overall rate of adsorption is controlled by film-diffusion, then at later stage intraparticle-diffusion controls the rate. Diffusion coefficients and times of transition from film to pore-diffusion control were estimated by piecewise linear regression. The experimental data were analyzed by the Langmuir and Freundlich models. The sorption isotherm data fitted well to Langmuir isotherm and the monolayer adsorption capacity was found to be 192.7 mg/g and the equilibrium adsorption constant Ka is 0.07145 l/mg at 30 degrees C. The results revealed that BBP was a promising sorbent for the removal of methylene blue from aqueous solutions.

Laser Raman Diagnostics in Subsonic and Supersonic Turbulent Jet Diffusion Flames.

NASA Astrophysics Data System (ADS)

Cheng, Tsarng-Sheng

1991-02-01

UV spontaneous vibrational Raman scattering combined with laser-induced predissociative fluorescence (LIPF) is developed for temperature and multi-species concentration measurements. For the first time, simultaneous measurements of temperature, major species (H_2, O_2, N_2, H_2O), and minor species (OH) concentrations are made with a "single" narrowband KrF excimer laser in subsonic and supersonic lifted turbulent hydrogen-air diffusion flames. The UV Raman system is calibrated with a flat -flame diffusion burner operated at several known equivalence ratios from fuel-lean to fuel-rich. Temperature measurements made by the ratio of Stokes/anti-Stokes signal and by the ideal gas law are compared. Single-shot uncertainties for temperature and concentration measurements are analyzed with photon statistics. Calibration constants and bandwidth factors are used in the data reduction program to arrive at temperature and species concentration measurements. UV Raman measurements in the subsonic lifted turbulent diffusion flame indicate that fuel and oxidizer are in rich, premixed, and unignited conditions in the center core of the lifted flame base. The unignited mixtures are due to rapid turbulent mixing that affects chemical reaction. Combustion occurs in an intermittent annular turbulent flame brush with strong finite-rate chemistry effects. The OH radical exists in sub-equilibrium and super-equilibrium concentrations. Major species and temperature are found with non-equilibrium values. Further downstream the super-equilibrium OH radicals decay toward equilibrium through slow three-body recombination reactions. In the supersonic lifted flame, a little reaction occurs upstream of the flame base, due to shock wave interactions and mixing with hot vitiated air. The strong turbulent mixing and total enthalpy fluctuations lead to temperature, major, and minor species concentrations with non-equilibrium values. Combustion occurs farther downstream of the lifted region. Slow three-body recombination reactions result in super-equilibrium OH concentrations that depress temperature below the equilibrium values. Near the equilibrium region, ambient air entrainment contaminates flame properties. These simultaneous measurements of temperature and multi-species concentrations allow a better understanding of the complex turbulence-chemistry interactions and provide information for the input and validation of CFD models.

Reaction rates of oxygen with hemoglobin measured by non-equilibrium facilitated oxygen diffusion through hemoglobin solutions.

PubMed

Bouwer, S T; Hoofd, L; Kreuzer, F

2001-02-16

The purpose of this study was to verify the concept of non-equilibrium facilitated oxygen diffusion. This work succeeds our previous study, where facilitated oxygen diffusion by hemoglobin was measured at conditions of chemical equilibrium, and which yielded diffusion coefficients of hemoglobin and of oxygen. In the present work chemical non-equilibrium was induced using very thin diffusion layers. As a result, facilitation was decreased as predicted by theory. Thus, this work presents the first experimental demonstration of non-equilibrium facilitated oxygen diffusion. In addition, association and dissociation rate parameters of the reaction between oxygen and bovine and human hemoglobin were calculated and the effect of the homotropic and heterotropic interactions on each rate parameter was demonstrated. The results indicate that the homotropic interaction--which leads to increasing oxygen affinity with increasing oxygenation--is predominantly due to an increase in the association rate. The heterotropic interaction--which leads to decreasing oxygen affinity by anionic ligands--appears to be effected in two ways. Cl- increases the dissociation rate. In contrast, 2,3-diphosphoglycerate decreases the association rate.

Phase diagram for a two-dimensional, two-temperature, diffusive XY model.

PubMed

Reichl, Matthew D; Del Genio, Charo I; Bassler, Kevin E

2010-10-01

Using Monte Carlo simulations, we determine the phase diagram of a diffusive two-temperature conserved order parameter XY model. When the two temperatures are equal the system becomes the equilibrium XY model with the continuous Kosterlitz-Thouless (KT) vortex-antivortex unbinding phase transition. When the two temperatures are unequal the system is driven by an energy flow from the higher temperature heat-bath to the lower temperature one and reaches a far-from-equilibrium steady state. We show that the nonequilibrium phase diagram contains three phases: A homogenous disordered phase and two phases with long range, spin texture order. Two critical lines, representing continuous phase transitions from a homogenous disordered phase to two phases of long range order, meet at the equilibrium KT point. The shape of the nonequilibrium critical lines as they approach the KT point is described by a crossover exponent φ=2.52±0.05. Finally, we suggest that the transition between the two phases with long-range order is first-order, making the KT-point where all three phases meet a bicritical point.

Simulating 3D Stellar Winds and Diffuse X-ray Emissions from Gases in Non-equilibrium Ionization State

NASA Astrophysics Data System (ADS)

Long, Min; Sun, Wei; Niu, Shu; Zhou, Xin; Ji, Li

2017-08-01

We investigate the physical properties of stellar winds launched in super stellar clusters (SSCs). Chandra observations have detected the presence of diffuse X-ray emission caused by hot gas from such winds in SSCs, and provide the best probe for understanding interactions between the stellar winds and the complex nursery regions. However, the details of the origin of cluster winds, the mass and energy ejection, the formation of diffuse X-ray emission, the fraction of winds contribution to the distribution of diffuse X-ray emission still remain unclear. We developed a multiphysics hydrodynamic model including self-gravity, head conduction and performed 3D simulations with an unprecedented grid resolution due to adaptive mesh refinement (AMR) capability in a case study of NGC 3603, as a supplement to the analysis of the archived 500 ks Chandra observations. The synthetic emission will be computed by assuming the gas in a non-equilibrium ionization (NEI) state indicated by Chandra observation, not coronal ionization equilibrium (CIE) that most works assumed, by using a customized NEI calculation module based on AtomDB. The results will be compared to the Chandra observations.

Adsorption Processes of Lead Ions on the Mixture Surface of Bentonite and Bottom Sediments.

PubMed

Hegedűsová, Alžbeta; Hegedűs, Ondrej; Tóth, Tomáš; Vollmannová, Alena; Andrejiová, Alena; Šlosár, Miroslav; Mezeyová, Ivana; Pernyeszi, Tímea

2016-12-01

The adsorption of contaminants plays an important role in the process of their elimination from a polluted environment. This work describes the issue of loading environment with lead Pb(II) and the resulting negative impact it has on plants and living organisms. It also focuses on bentonite as a natural adsorbent and on the adsorption process of Pb(II) ions on the mixture of bentonite and bottom sediment from the water reservoir in Kolíňany (SR). The equilibrium and kinetic experimental data were evaluated using Langmuir isotherm kinetic pseudo-first and pseudo-second-order rate equations the intraparticle and surface diffusion models. Langmuir isotherm model was successfully used to characterize the lead ions adsorption equilibrium on the mixture of bentonite and bottom sediment. The pseudo second-order model, the intraparticle and surface (film) diffusion models could be simultaneously fitted the experimental kinetic data.

A facilitated diffusion model constrained by the probability isotherm: a pedagogical exercise in intuitive non-equilibrium thermodynamics.

PubMed

Chapman, Brian

2017-06-01

This paper seeks to develop a more thermodynamically sound pedagogy for students of biological transport than is currently available from either of the competing schools of linear non-equilibrium thermodynamics (LNET) or Michaelis-Menten kinetics (MMK). To this end, a minimal model of facilitated diffusion was constructed comprising four reversible steps: cis- substrate binding, cis → trans bound enzyme shuttling, trans -substrate dissociation and trans → cis free enzyme shuttling. All model parameters were subject to the second law constraint of the probability isotherm, which determined the unidirectional and net rates for each step and for the overall reaction through the law of mass action. Rapid equilibration scenarios require sensitive 'tuning' of the thermodynamic binding parameters to the equilibrium substrate concentration. All non-equilibrium scenarios show sigmoidal force-flux relations, with only a minority of cases having their quasi -linear portions close to equilibrium. Few cases fulfil the expectations of MMK relating reaction rates to enzyme saturation. This new approach illuminates and extends the concept of rate-limiting steps by focusing on the free energy dissipation associated with each reaction step and thereby deducing its respective relative chemical impedance. The crucial importance of an enzyme's being thermodynamically 'tuned' to its particular task, dependent on the cis- and trans- substrate concentrations with which it deals, is consistent with the occurrence of numerous isoforms for enzymes that transport a given substrate in physiologically different circumstances. This approach to kinetic modelling, being aligned with neither MMK nor LNET, is best described as intuitive non-equilibrium thermodynamics, and is recommended as a useful adjunct to the design and interpretation of experiments in biotransport.

A facilitated diffusion model constrained by the probability isotherm: a pedagogical exercise in intuitive non-equilibrium thermodynamics

PubMed Central

2017-01-01

This paper seeks to develop a more thermodynamically sound pedagogy for students of biological transport than is currently available from either of the competing schools of linear non-equilibrium thermodynamics (LNET) or Michaelis–Menten kinetics (MMK). To this end, a minimal model of facilitated diffusion was constructed comprising four reversible steps: cis-substrate binding, cis→trans bound enzyme shuttling, trans-substrate dissociation and trans→cis free enzyme shuttling. All model parameters were subject to the second law constraint of the probability isotherm, which determined the unidirectional and net rates for each step and for the overall reaction through the law of mass action. Rapid equilibration scenarios require sensitive ‘tuning’ of the thermodynamic binding parameters to the equilibrium substrate concentration. All non-equilibrium scenarios show sigmoidal force–flux relations, with only a minority of cases having their quasi-linear portions close to equilibrium. Few cases fulfil the expectations of MMK relating reaction rates to enzyme saturation. This new approach illuminates and extends the concept of rate-limiting steps by focusing on the free energy dissipation associated with each reaction step and thereby deducing its respective relative chemical impedance. The crucial importance of an enzyme's being thermodynamically ‘tuned’ to its particular task, dependent on the cis- and trans-substrate concentrations with which it deals, is consistent with the occurrence of numerous isoforms for enzymes that transport a given substrate in physiologically different circumstances. This approach to kinetic modelling, being aligned with neither MMK nor LNET, is best described as intuitive non-equilibrium thermodynamics, and is recommended as a useful adjunct to the design and interpretation of experiments in biotransport. PMID:28680687

Generalized Cahn-Hilliard equation for solutions with drastically different diffusion coefficients. Application to exsolution in ternary feldspar

NASA Astrophysics Data System (ADS)

Petrishcheva, E.; Abart, R.

2012-04-01

We address mathematical modeling and computer simulations of phase decomposition in a multicomponent system. As opposed to binary alloys with one common diffusion parameter, our main concern is phase decomposition in real geological systems under influence of strongly different interdiffusion coefficients, as it is frequently encountered in mineral solid solutions with coupled diffusion on different sub-lattices. Our goal is to explain deviations from equilibrium element partitioning which are often observed in nature, e.g., in a cooled ternary feldspar. To this end we first adopt the standard Cahn-Hilliard model to the multicomponent diffusion problem and account for arbitrary diffusion coefficients. This is done by using Onsager's approach such that flux of each component results from the combined action of chemical potentials of all components. In a second step the generalized Cahn-Hilliard equation is solved numerically using finite-elements approach. We introduce and investigate several decomposition scenarios that may produce systematic deviations from the equilibrium element partitioning. Both ideal solutions and ternary feldspar are considered. Typically, the slowest component is initially "frozen" and the decomposition effectively takes place only for two "fast" components. At this stage the deviations from the equilibrium element partitioning are indeed observed. These deviations may became "frozen" under conditions of cooling. The final equilibration of the system occurs on a considerably slower time scale. Therefore the system may indeed remain unaccomplished at the observation point. Our approach reveals the intrinsic reasons for the specific phase separation path and rigorously describes it by direct numerical solution of the generalized Cahn-Hilliard equation.

Self-Organized Percolation and Critical Sales Fluctuations

NASA Astrophysics Data System (ADS)

Weisbuch, Gérard; Solomon, Sorin

There is a discrepancy between the standard view of equilibrium through price adjustment in economics and the observation of large fluctuations in stock markets. We study here a simple model where agents decisions not only depend upon their individual preferences but also upon information obtained from their neighbors in a social network. The model shows that information diffusion coupled to the adjustment process drives the system to criticality with large fluctuations rather than converging smoothly to equilibrium.

Adsorption of leather dye onto activated carbon prepared from bottle gourd: equilibrium, kinetic and mechanism studies.

PubMed

Foletto, Edson Luiz; Weber, Caroline Trevisan; Paz, Diego Silva; Mazutti, Marcio Antonio; Meili, Lucas; Bassaco, Mariana Moro; Collazzo, Gabriela Carvalho

2013-01-01

Activated carbon prepared from bottle gourd has been used as adsorbent for removal of leather dye (Direct Black 38) from aqueous solution. The activated carbon obtained showed a mesoporous texture, with surface area of 556.16 m(2) g(-1), and a surface free of organic functional groups. The initial dye concentration, contact time and pH significantly influenced the adsorption capacity. In the acid region (pH 2.5) the adsorption of dye was more favorable. The adsorption equilibrium was attained after 60 min. Equilibrium data were analyzed by the Langmuir, Freundlich, Dubinin-Radushkevich and Temkin isotherm models. The equilibrium data were best described by the Langmuir isotherm, with maximum adsorption capacity of 94.9 mg g(-1). Adsorption kinetic data were fitted using the pseudo-first-order, pseudo-second-order, Elovich and intraparticle diffusion models. The adsorption kinetic was best described by the second-order kinetic equation. The adsorption process was controlled by both external mass transfer and intraparticle diffusion. Activated carbon prepared from bottle gourd was shown to be a promising material for adsorption of Direct Black 38 from aqueous solution.

Quasi-equilibria in reduced Liouville spaces.

PubMed

Halse, Meghan E; Dumez, Jean-Nicolas; Emsley, Lyndon

2012-06-14

The quasi-equilibrium behaviour of isolated nuclear spin systems in full and reduced Liouville spaces is discussed. We focus in particular on the reduced Liouville spaces used in the low-order correlations in Liouville space (LCL) simulation method, a restricted-spin-space approach to efficiently modelling the dynamics of large networks of strongly coupled spins. General numerical methods for the calculation of quasi-equilibrium expectation values of observables in Liouville space are presented. In particular, we treat the cases of a time-independent Hamiltonian, a time-periodic Hamiltonian (with and without stroboscopic sampling) and powder averaging. These quasi-equilibrium calculation methods are applied to the example case of spin diffusion in solid-state nuclear magnetic resonance. We show that there are marked differences between the quasi-equilibrium behaviour of spin systems in the full and reduced spaces. These differences are particularly interesting in the time-periodic-Hamiltonian case, where simulations carried out in the reduced space demonstrate ergodic behaviour even for small spins systems (as few as five homonuclei). The implications of this ergodic property on the success of the LCL method in modelling the dynamics of spin diffusion in magic-angle spinning experiments of powders is discussed.

A theoretical model of grain boundary self-diffusion in metals with phase transitions (case study into titanium and zirconium)

NASA Astrophysics Data System (ADS)

Semenycheva, Alexandra V.; Chuvil'deev, Vladimir N.; Nokhrin, Aleksey V.

2018-05-01

The paper offers a model describing the process of grain boundary self-diffusion in metals with phase transitions in the solid state. The model is based on ideas and approaches found in the theory of non-equilibrium grain boundaries. The range of application of basic relations contained in this theory is shown to expand, as they can be used to calculate the parameters of grain boundary self-diffusion in high-temperature and low-temperature phases of metals with a phase transition. The model constructed is used to calculate grain boundary self-diffusion activation energy in titanium and zirconium and an explanation is provided as to their abnormally low values in the low-temperature phase. The values of grain boundary self-diffusion activation energy are in good agreement with the experiment.

A survey of upwind methods for flows with equilibrium and non-equilibrium chemistry and thermodynamics

NASA Technical Reports Server (NTRS)

Grossman, B.; Garrett, J.; Cinnella, P.

1989-01-01

Several versions of flux-vector split and flux-difference split algorithms were compared with regard to general applicability and complexity. Test computations were performed using curve-fit equilibrium air chemistry for an M = 5 high-temperature inviscid flow over a wedge, and an M = 24.5 inviscid flow over a blunt cylinder for test computations; for these cases, little difference in accuracy was found among the versions of the same flux-split algorithm. For flows with nonequilibrium chemistry, the effects of the thermodynamic model on the development of flux-vector split and flux-difference split algorithms were investigated using an equilibrium model, a general nonequilibrium model, and a simplified model based on vibrational relaxation. Several numerical examples are presented, including nonequilibrium air chemistry in a high-temperature shock tube and nonequilibrium hydrogen-air chemistry in a supersonic diffuser.

Efficient reactive Brownian dynamics

DOE PAGES

Donev, Aleksandar; Yang, Chiao-Yu; Kim, Changho

2018-01-21

We develop a Split Reactive Brownian Dynamics (SRBD) algorithm for particle simulations of reaction-diffusion systems based on the Doi or volume reactivity model, in which pairs of particles react with a specified Poisson rate if they are closer than a chosen reactive distance. In our Doi model, we ensure that the microscopic reaction rules for various association and dissociation reactions are consistent with detailed balance (time reversibility) at thermodynamic equilibrium. The SRBD algorithm uses Strang splitting in time to separate reaction and diffusion and solves both the diffusion-only and reaction-only subproblems exactly, even at high packing densities. To efficiently processmore » reactions without uncontrolled approximations, SRBD employs an event-driven algorithm that processes reactions in a time-ordered sequence over the duration of the time step. A grid of cells with size larger than all of the reactive distances is used to schedule and process the reactions, but unlike traditional grid-based methods such as reaction-diffusion master equation algorithms, the results of SRBD are statistically independent of the size of the grid used to accelerate the processing of reactions. We use the SRBD algorithm to compute the effective macroscopic reaction rate for both reaction-limited and diffusion-limited irreversible association in three dimensions and compare to existing theoretical predictions at low and moderate densities. We also study long-time tails in the time correlation functions for reversible association at thermodynamic equilibrium and compare to recent theoretical predictions. Finally, we compare different particle and continuum methods on a model exhibiting a Turing-like instability and pattern formation. Our studies reinforce the common finding that microscopic mechanisms and correlations matter for diffusion-limited systems, making continuum and even mesoscopic modeling of such systems difficult or impossible. We also find that for models in which particles diffuse off lattice, such as the Doi model, reactions lead to a spurious enhancement of the effective diffusion coefficients.« less

Efficient reactive Brownian dynamics

NASA Astrophysics Data System (ADS)

Donev, Aleksandar; Yang, Chiao-Yu; Kim, Changho

2018-01-01

We develop a Split Reactive Brownian Dynamics (SRBD) algorithm for particle simulations of reaction-diffusion systems based on the Doi or volume reactivity model, in which pairs of particles react with a specified Poisson rate if they are closer than a chosen reactive distance. In our Doi model, we ensure that the microscopic reaction rules for various association and dissociation reactions are consistent with detailed balance (time reversibility) at thermodynamic equilibrium. The SRBD algorithm uses Strang splitting in time to separate reaction and diffusion and solves both the diffusion-only and reaction-only subproblems exactly, even at high packing densities. To efficiently process reactions without uncontrolled approximations, SRBD employs an event-driven algorithm that processes reactions in a time-ordered sequence over the duration of the time step. A grid of cells with size larger than all of the reactive distances is used to schedule and process the reactions, but unlike traditional grid-based methods such as reaction-diffusion master equation algorithms, the results of SRBD are statistically independent of the size of the grid used to accelerate the processing of reactions. We use the SRBD algorithm to compute the effective macroscopic reaction rate for both reaction-limited and diffusion-limited irreversible association in three dimensions and compare to existing theoretical predictions at low and moderate densities. We also study long-time tails in the time correlation functions for reversible association at thermodynamic equilibrium and compare to recent theoretical predictions. Finally, we compare different particle and continuum methods on a model exhibiting a Turing-like instability and pattern formation. Our studies reinforce the common finding that microscopic mechanisms and correlations matter for diffusion-limited systems, making continuum and even mesoscopic modeling of such systems difficult or impossible. We also find that for models in which particles diffuse off lattice, such as the Doi model, reactions lead to a spurious enhancement of the effective diffusion coefficients.

Efficient reactive Brownian dynamics

DOE Office of Scientific and Technical Information (OSTI.GOV)

Donev, Aleksandar; Yang, Chiao-Yu; Kim, Changho

We develop a Split Reactive Brownian Dynamics (SRBD) algorithm for particle simulations of reaction-diffusion systems based on the Doi or volume reactivity model, in which pairs of particles react with a specified Poisson rate if they are closer than a chosen reactive distance. In our Doi model, we ensure that the microscopic reaction rules for various association and dissociation reactions are consistent with detailed balance (time reversibility) at thermodynamic equilibrium. The SRBD algorithm uses Strang splitting in time to separate reaction and diffusion and solves both the diffusion-only and reaction-only subproblems exactly, even at high packing densities. To efficiently processmore » reactions without uncontrolled approximations, SRBD employs an event-driven algorithm that processes reactions in a time-ordered sequence over the duration of the time step. A grid of cells with size larger than all of the reactive distances is used to schedule and process the reactions, but unlike traditional grid-based methods such as reaction-diffusion master equation algorithms, the results of SRBD are statistically independent of the size of the grid used to accelerate the processing of reactions. We use the SRBD algorithm to compute the effective macroscopic reaction rate for both reaction-limited and diffusion-limited irreversible association in three dimensions and compare to existing theoretical predictions at low and moderate densities. We also study long-time tails in the time correlation functions for reversible association at thermodynamic equilibrium and compare to recent theoretical predictions. Finally, we compare different particle and continuum methods on a model exhibiting a Turing-like instability and pattern formation. Our studies reinforce the common finding that microscopic mechanisms and correlations matter for diffusion-limited systems, making continuum and even mesoscopic modeling of such systems difficult or impossible. We also find that for models in which particles diffuse off lattice, such as the Doi model, reactions lead to a spurious enhancement of the effective diffusion coefficients.« less

Equilibrium distribution of heavy quarks in fokker-planck dynamics

PubMed

Walton; Rafelski

2000-01-03

We obtain an explicit generalization, within Fokker-Planck dynamics, of Einstein's relation between drag, diffusion, and the equilibrium distribution for a spatially homogeneous system, considering both the transverse and longitudinal diffusion for dimension n>1. We provide a complete characterization of the equilibrium distribution in terms of the drag and diffusion transport coefficients. We apply this analysis to charm quark dynamics in a thermal quark-gluon plasma for the case of collisional equilibration.

From Vulcanian explosions to sustained explosive eruptions: The role of diffusive mass transfer in conduit flow dynamics

NASA Astrophysics Data System (ADS)

Mason, R. M.; Starostin, A. B.; Melnik, O. E.; Sparks, R. S. J.

2006-05-01

Magmatic explosive eruptions are influenced by mass transfer processes of gas diffusion into bubbles caused by decompression. Melnik and Sparks [Melnik, O.E., Sparks, R.S.J. 2002, Modelling of conduit flow dynamic during explosive activity at Soufriere Hills Volcano, Montserrat. In: Druitt, T.H., Kokelaar, B.P. (eds). The Eruption of Soufriere Hills Volcano, Montserrat, from 1995 to 1999. Geological Society, London, Memoirs, 21, 307-317] proposed two end member cases corresponding to complete equilibrium and complete disequilibrium. In the first case, diffusion is fast enough to maintain the system near equilibrium and a long-lived explosive eruption develops. In the latter case, pre-existing bubbles expand under conditions of explosive eruption and decompression, but diffusive gas transfer is negligible. This leads to a much shorter eruption. Here we develop this model to consider the role of mass transfer by investigating transient flows at the start of an explosive eruption triggered by a sudden decompression. The simulations reveal a spectrum of behaviours from sustained to short-lived highly non-equilibrium Vulcanian-style explosions lasting a few tens of seconds, through longer lasting eruptions that can be sustained for tens of minutes and finally to eruptions that can last hours or even days. Behaviour is controlled by a mass-transfer parameter, ω, which equals n*2/3D, where n* is the bubble number density and D is the diffusivity. The parameter ω is expected to vary between 10 - 5 and 1 s - 1 in nature and reflects a time-scale for efficient diffusion. The spectrum of model behaviours is consistent with variations in styles of explosive eruptions of silicic volcanoes. In the initial stages peak discharges occur over 10-20 s and then decline to low discharges. If a critical bubble overpressure is assumed to be the criterion for fragmentation then fragmentation may stop and start several times in the declining period causing several pulses of high-intensity discharge. For the cases of strong disequilibria, the fluxes can decrease to negligible values where other processes, such as gas escape through permeable magma, prevents explosive conditions becoming re-established so that explosive activity stops and dome growth can start. For cases closer to the equilibrium the eruption can evolve towards a quasi-steady sustained flow, never declining sufficiently for gas escape to become dominant.

Interactions of lysozyme in concentrated electrolyte solutions from dynamic light-scattering measurements.

PubMed Central

Kuehner, D E; Heyer, C; Rämsch, C; Fornefeld, U M; Blanch, H W; Prausnitz, J M

1997-01-01

The diffusion of hen egg-white lysozyme has been studied by dynamic light scattering in aqueous solutions of ammonium sulfate as a function of protein concentration to 30 g/liter. Experiments were conducted under the following conditions: pH 4-7 and ionic strength 0.05-5.0 M. Diffusivity data for ionic strengths up to 0.5 M were interpreted in the context of a two-body interaction model for monomers. From this analysis, two potential-of-mean-force parameters, the effective monomer charge, and the Hamaker constant were obtained. At higher ionic strength, the data were analyzed using a model that describes the diffusion coefficient of a polydisperse system of interacting protein aggregates in terms of an isodesmic, indefinite aggregation equilibrium constant. Data analysis incorporated multicomponent virial and hydrodynamic effects. The resulting equilibrium constants indicate that lysozyme does not aggregate significantly as ionic strength increases, even at salt concentrations near the point of salting-out precipitation. PMID:9414232

Climate warming due to increasing atmospheric CO2 - Simulations with a multilayer coupled atmosphere-ocean seasonal energy balance model

NASA Technical Reports Server (NTRS)

Li, Peng; Chou, Ming-Dah; Arking, Albert

1987-01-01

The transient response of the climate to increasing CO2 is studied using a modified version of the multilayer energy balance model of Peng et al. (1982). The main characteristics of the model are described. Latitudinal and seasonal distributions of planetary albedo, latitude-time distributions of zonal mean temperatures, and latitudinal distributions of evaporation, water vapor transport, and snow cover generated from the model and derived from actual observations are analyzed and compared. It is observed that in response to an atmospheric doubling of CO2, the model reaches within 1/e of the equilibrium response of global mean surface temperature in 9-35 years for the probable range of vertical heat diffusivity in the ocean. For CO2 increases projected by the National Research Council (1983), the model's transient response in annually and globally averaged surface temperatures is 60-75 percent of the corresponding equilibrium response, and the disequilibrium increases with increasing heat diffusivity of the ocean.

Numerical simulation of plagioclase rim growth during magma ascent at Bezymianny Volcano, Kamchatka

NASA Astrophysics Data System (ADS)

Gorokhova, N. V.; Melnik, O. E.; Plechov, P. Yu.; Shcherbakov, V. D.

2013-08-01

Slow CaAl-NaSi interdiffusion in plagioclase crystals preserves chemical zoning of plagioclase in detail, which, along with strong dependence of anorthite content in plagioclase on melt composition, pressure, and temperature, make this mineral an important source of information on magma processes. A numerical model of zoned crystal growth is developed in the paper. The model is based on equations of multicomponent diffusion with diagonal cross-component diffusion terms and accounts for mass conservation on the melt-crystal interface and growth rate controlled by undercooling. The model is applied to the data of plagioclase rim zoning from several recent Bezymianny Volcano (Kamchatka) eruptions. We show that an equilibrium growth model cannot explain crystallization of naturally observed plagioclase during magma ascent. The developed non-equilibrium model reproduced natural plagioclase zoning and allowed magma ascent rates to be constrained. Matching of natural and simulated zoning suggests ascent from 100 to 50 MPa during 15-20 days. Magma ascent rate from 50 MPa to the surface varies from eruption to eruption: plagioclase zoning from the December 2006 eruption suggests ascent to the surface in less than 1 day, whereas plagioclase zoning from March 2000 and May 2007 eruptions are better explained by magma ascent over periods of more than 30 days). Based on comparison of diffusion coefficients for individual elements a mechanism of atomic diffusion during plagioclase crystallization is proposed.

Communication: A method to compute the transport coefficient of pure fluids diffusing through planar interfaces from equilibrium molecular dynamics simulations.

PubMed

Vermorel, Romain; Oulebsir, Fouad; Galliero, Guillaume

2017-09-14

The computation of diffusion coefficients in molecular systems ranks among the most useful applications of equilibrium molecular dynamics simulations. However, when dealing with the problem of fluid diffusion through vanishingly thin interfaces, classical techniques are not applicable. This is because the volume of space in which molecules diffuse is ill-defined. In such conditions, non-equilibrium techniques allow for the computation of transport coefficients per unit interface width, but their weak point lies in their inability to isolate the contribution of the different physical mechanisms prone to impact the flux of permeating molecules. In this work, we propose a simple and accurate method to compute the diffusional transport coefficient of a pure fluid through a planar interface from equilibrium molecular dynamics simulations, in the form of a diffusion coefficient per unit interface width. In order to demonstrate its validity and accuracy, we apply our method to the case study of a dilute gas diffusing through a smoothly repulsive single-layer porous solid. We believe this complementary technique can benefit to the interpretation of the results obtained on single-layer membranes by means of complex non-equilibrium methods.

Radiation-enhanced self- and boron diffusion in germanium

NASA Astrophysics Data System (ADS)

Schneider, S.; Bracht, H.; Klug, J. N.; Hansen, J. Lundsgaard; Larsen, A. Nylandsted; Bougeard, D.; Haller, E. E.

2013-03-01

We report experiments on proton radiation-enhanced self- and boron (B) diffusion in germanium (Ge) for temperatures between 515 ∘C and 720 ∘C. Modeling of the experimental diffusion profiles measured by means of secondary ion mass spectrometry is achieved on the basis of the Frenkel pair reaction and the interstitialcy and dissociative diffusion mechanisms. The numerical simulations ascertain concentrations of Ge interstitials and B-interstitial pairs that deviate by several orders of magnitude from their thermal equilibrium values. The dominance of self-interstitial related defects under irradiation leads to an enhanced self- and B diffusion in Ge. Analysis of the experimental profiles yields data for the diffusion of self-interstitials (I) and the thermal equilibrium concentration of BI pairs in Ge. The temperature dependence of these quantities provides the migration enthalpy of I and formation enthalpy of BI that are compared with recent results of atomistic calculations. The behavior of self- and B diffusion in Ge under concurrent annealing and irradiation is strongly affected by the property of the Ge surface to hinder the annihilation of self-interstitials. The limited annihilation efficiency of the Ge surface can be caused by donor-type surface states favored under vacuum annealing, but the physical origin remains unsolved.

Experimental characterization and modelization of ion exchange kinetics for a carboxylic resin in infinite solution volume conditions. Application to monovalent-trivalent cations exchange.

PubMed

Picart, Sébastien; Ramière, Isabelle; Mokhtari, Hamid; Jobelin, Isabelle

2010-09-02

This study is devoted to the characterization of ion exchange inside a microsphere of carboxylic resin. It aims at describing the kinetics of this exchange reaction which is known to be controlled by interdiffusion in the particle. The fractional attainment of equilibrium function of time depends on the concentration of the cations in the resin which can be modelized by the Nernst-Planck equation. A powerful approach for the numerical resolution of this equation is introduced in this paper. This modeling is based on the work of Helfferich but involves an implicit numerical scheme which reduces the computational cost. Knowing the diffusion coefficients of the cations in the resin and the radius of the spherical exchanger, the kinetics can be hence completely determined. When those diffusion parameters are missing, they can be deduced by fitting experimental data of fractional attainment of equilibrium. An efficient optimization tool coupled with the implicit resolution has been developed for this purpose. A monovalent/trivalent cation exchange had been experimentally characterized for a carboxylic resin. Diffusion coefficients and concentration profiles in the resin were then deduced through this new model.

Plasma transport in the Io torus - The importance of microscopic diffusion

NASA Technical Reports Server (NTRS)

Mei, YI; Thorne, Richard M.

1991-01-01

This paper considers the question of whether the distribution of mass in the Io plasma torus is consistent with the concept of interchange eddy transport. Specifically, the flux tube content exhibits a gradual decrease with increasing radial distance from the source near Io without any evidence for substantial density irregularity associated with the plasma source or loss. Using a simple one-dimensional numerical model to simulate macroscopic interchange eddy transport, it is demonstrated that this smooth equilibrium distribution of mass can occur but only with the inclusion of a minimal level of small scale microscopic mixing at a rate approaching Bohm diffusion. Otherwise, the system exhibits a chaotic appearance which never approaches an equilibrium distribution. Various physical mechanisms for the microscopic diffusion process which is required to provide a sufficiently rapid mixing of material between the macroscopic eddies are discussed.

A Diffuse Interface Model with Immiscibility Preservation

PubMed Central

Tiwari, Arpit; Freund, Jonathan B.; Pantano, Carlos

2013-01-01

A new, simple, and computationally efficient interface capturing scheme based on a diffuse interface approach is presented for simulation of compressible multiphase flows. Multi-fluid interfaces are represented using field variables (interface functions) with associated transport equations that are augmented, with respect to an established formulation, to enforce a selected interface thickness. The resulting interface region can be set just thick enough to be resolved by the underlying mesh and numerical method, yet thin enough to provide an efficient model for dynamics of well-resolved scales. A key advance in the present method is that the interface regularization is asymptotically compatible with the thermodynamic mixture laws of the mixture model upon which it is constructed. It incorporates first-order pressure and velocity non-equilibrium effects while preserving interface conditions for equilibrium flows, even within the thin diffused mixture region. We first quantify the improved convergence of this formulation in some widely used one-dimensional configurations, then show that it enables fundamentally better simulations of bubble dynamics. Demonstrations include both a spherical bubble collapse, which is shown to maintain excellent symmetry despite the Cartesian mesh, and a jetting bubble collapse adjacent a wall. Comparisons show that without the new formulation the jet is suppressed by numerical diffusion leading to qualitatively incorrect results. PMID:24058207

Modeling growth kinetics of thin films made by atomic layer deposition in lateral high-aspect-ratio structures

NASA Astrophysics Data System (ADS)

Ylilammi, Markku; Ylivaara, Oili M. E.; Puurunen, Riikka L.

2018-05-01

The conformality of thin films grown by atomic layer deposition (ALD) is studied using all-silicon test structures with long narrow lateral channels. A diffusion model, developed in this work, is used for studying the propagation of ALD growth in narrow channels. The diffusion model takes into account the gas transportation at low pressures, the dynamic Langmuir adsorption model for the film growth and the effect of channel narrowing due to film growth. The film growth is calculated by solving the diffusion equation with surface reactions. An efficient analytic approximate solution of the diffusion equation is developed for fitting the model to the measured thickness profile. The fitting gives the equilibrium constant of adsorption and the sticking coefficient. This model and Gordon's plug flow model are compared. The simulations predict the experimental measurement results quite well for Al2O3 and TiO2 ALD processes.

Preliminary study: Moisture-polymer interaction. Stuby objectives

NASA Technical Reports Server (NTRS)

Wen, L. C.

1985-01-01

The problems associated with mathematically modeling water-module interaction phenomena, including sorption and desorption, diffusion, and permeation are discussed. With reliable analytical models, an extensive materials data base, and solar radiation surface meteorological observations (SOLMET) weather data, predicting module lifetimes in realistic environments can become a practical reality. The status of the present techniques of simulating the various transport mechanisms was reported. The Dent model (a modified Brunauer-Emmet-Teller) approach represented polyvinyl butyral (PVB) sorption data. A 100-layer material model and Fick's diffusion model gave diffusivity values exhibiting adequate agreement with those measured for PVB. Diffusivity of PVB is concentration dependent, decreasing as the water content in PVB increases. The temperature dependence of diffusion in PVB is well modeled by the Arrhenius rate equation. Equilibrium conductivity and leakage current data are well represented by Hearle's model for bulk ionic conductivity. A nodal network analysis using the Systems Improved Numerical Differencing Analyzer (SINDA) Thermal Analyzer gave reasonable correlation with measurable data. It is concluded that realistic lifetime predictions seem to be feasible.

Phonon cross-plane transport and thermal boundary resistance: effect of heat source size and thermal boundary resistance on phonon characteristics

NASA Astrophysics Data System (ADS)

Ali, H.; Yilbas, B. S.

2016-09-01

Phonon cross-plane transport across silicon and diamond thin films pair is considered, and thermal boundary resistance across the films pair interface is examined incorporating the cut-off mismatch and diffusive mismatch models. In the cut-off mismatch model, phonon frequency mismatch for each acoustic branch is incorporated across the interface of the silicon and diamond films pair in line with the dispersion relations of both films. The frequency-dependent and transient solution of the Boltzmann transport equation is presented, and the equilibrium phonon intensity ratios at the silicon and diamond film edges are predicted across the interface for each phonon acoustic branch. Temperature disturbance across the edges of the films pair is incorporated to assess the phonon transport characteristics due to cut-off and diffusive mismatch models across the interface. The effect of heat source size, which is allocated at high-temperature (301 K) edge of the silicon film, on the phonon transport characteristics at the films pair interface is also investigated. It is found that cut-off mismatch model predicts higher values of the thermal boundary resistance across the films pair interface as compared to that of the diffusive mismatch model. The ratio of equilibrium phonon intensity due to the cut-off mismatch over the diffusive mismatch models remains >1 at the silicon edge, while it becomes <1 at the diamond edge for all acoustic branches.

Adsorption of anionic and cationic dyes on activated carbon from aqueous solutions: equilibrium and kinetics.

PubMed

Rodríguez, Araceli; García, Juan; Ovejero, Gabriel; Mestanza, María

2009-12-30

Activated carbon was utilized as adsorbent to remove anionic dye, Orange II (OII), and cationic dye, Methylene blue (MB), from aqueous solutions by adsorption. Batch experiments were conducted to study the effects of temperature (30-65 degrees C), initial concentration of adsorbate (300-500 mg L(-1)) and pH (3.0-9.0) on dyes adsorption. Equilibrium adsorption isotherms and kinetics were investigated. The equilibrium experimental data were analyzed by the Langmuir, Freundlich, Toth and Redlich-Peterson models. The kinetic data obtained with different carbon mass were analyzed using a pseudo-first order, pseudo-second order, intraparticle diffusion, Bangham and Chien-Clayton equations. The best results were achieved with the Langmuir isotherm equilibrium model and with the pseudo-second order kinetic model. The activated carbon was found to be very effective as adsorbent for MB and OII from aqueous solutions.

Patchy reaction-diffusion and population abundance: the relative importance of habitat amount and arrangement

Treesearch

Curtis H. Flather; Michael Bevers

2002-01-01

A discrete reaction-diffusion model was used to estimate long-term equilibrium populations of a hypothetical species inhabiting patchy landscapes to examine the relative importance of habitat amount and arrangement in explaining population size. When examined over a broad range of habitat amounts and arrangements, population size was largely determined by a pure amount...

Modeling Bimolecular Reactive Transport With Mixing-Limitation: Theory and Application to Column Experiments

NASA Astrophysics Data System (ADS)

Ginn, T. R.

2018-01-01

The challenge of determining mixing extent of solutions undergoing advective-dispersive-diffusive transport is well known. In particular, reaction extent between displacing and displaced solutes depends on mixing at the pore scale, that is, generally smaller than continuum scale quantification that relies on dispersive fluxes. Here a novel mobile-mobile mass transfer approach is developed to distinguish diffusive mixing from dispersive spreading in one-dimensional transport involving small-scale velocity variations with some correlation, such as occurs in hydrodynamic dispersion, in which short-range ballistic transports give rise to dispersed but not mixed segregation zones, termed here ballisticules. When considering transport of a single solution, this approach distinguishes self-diffusive mixing from spreading, and in the case of displacement of one solution by another, each containing a participant reactant of an irreversible bimolecular reaction, this results in time-delayed diffusive mixing of reactants. The approach generates models for both kinetically controlled and equilibrium irreversible reaction cases, while honoring independently measured reaction rates and dispersivities. The mathematical solution for the equilibrium case is a simple analytical expression. The approach is applied to published experimental data on bimolecular reactions for homogeneous porous media under postasymptotic dispersive conditions with good results.

Characteristic power spectrum of diffusive interface dynamics in the two-dimensional Ising model

NASA Astrophysics Data System (ADS)

Masumoto, Yusuke; Takesue, Shinji

2018-05-01

We investigate properties of the diffusive motion of an interface in the two-dimensional Ising model in equilibrium or nonequilibrium situations. We focused on the relation between the power spectrum of a time sequence of spins and diffusive motion of an interface which was already clarified in one-dimensional systems with a nonequilibrium phase transition like the asymmetric simple exclusion process. It is clarified that the interface motion is a diffusion process with a drift force toward the higher-temperature side when the system is in contact with heat reservoirs at different temperatures and heat transfers through the system. Effects of the width of the interface are also discussed.

Laminar flamelet modeling of turbulent diffusion flames

NASA Technical Reports Server (NTRS)

Mell, W. E.; Kosaly, G.; Planche, O.; Poinsot, T.; Ferziger, J. H.

1990-01-01

In modeling turbulent combustion, decoupling the chemistry from the turbulence is of great practical significance. In cases in which the equilibrium chemistry model breaks down, laminar flamelet modeling (LFM) is a promising approach to decoupling. Here, the validity of this approach is investigated using direct numerical simulation of a simple chemical reaction in two-dimensional turbulence.

Non-Equilibrium Properties from Equilibrium Free Energy Calculations

NASA Technical Reports Server (NTRS)

Pohorille, Andrew; Wilson, Michael A.

2012-01-01

Calculating free energy in computer simulations is of central importance in statistical mechanics of condensed media and its applications to chemistry and biology not only because it is the most comprehensive and informative quantity that characterizes the eqUilibrium state, but also because it often provides an efficient route to access dynamic and kinetic properties of a system. Most of applications of equilibrium free energy calculations to non-equilibrium processes rely on a description in which a molecule or an ion diffuses in the potential of mean force. In general case this description is a simplification, but it might be satisfactorily accurate in many instances of practical interest. This hypothesis has been tested in the example of the electrodiffusion equation . Conductance of model ion channels has been calculated directly through counting the number of ion crossing events observed during long molecular dynamics simulations and has been compared with the conductance obtained from solving the generalized Nernst-Plank equation. It has been shown that under relatively modest conditions the agreement between these two approaches is excellent, thus demonstrating the assumptions underlying the diffusion equation are fulfilled. Under these conditions the electrodiffusion equation provides an efficient approach to calculating the full voltage-current dependence routinely measured in electrophysiological experiments.

Stability Analysis of an Encapsulated Microbubble against Gas Diffusion

PubMed Central

Katiyar, Amit; Sarkar, Kausik

2009-01-01

Linear stability analysis is performed for a mathematical model of diffusion of gases from an encapsulated microbubble. It is an Epstein-Plesset model modified to account for encapsulation elasticity and finite gas permeability. Although, bubbles, containing gases other than air is considered, the final stable bubble, if any, contains only air, and stability is achieved only when the surrounding medium is saturated or oversaturated with air. In absence of encapsulation elasticity, only a neutral stability is achieved for zero surface tension, the other solution being unstable. For an elastic encapsulation, different equilibrium solutions are obtained depending on the saturation level and whether the surface tension is smaller or higher than the elasticity. For an elastic encapsulation, elasticity can stabilize the bubble. However, imposing a non-negativity condition on the effective surface tension (consisting of reference surface tension and the elastic stress) leads to an equilibrium radius which is only neutrally stable. If the encapsulation can support net compressive stress, it achieves actual stability. The linear stability results are consistent with our recent numerical findings. Physical mechanisms for the stability or instability of various equilibriums are provided. PMID:20005522

Atomistic simulations of carbon diffusion and segregation in liquid silicon

NASA Astrophysics Data System (ADS)

Luo, Jinping; Alateeqi, Abdullah; Liu, Lijun; Sinno, Talid

2017-12-01

The diffusivity of carbon atoms in liquid silicon and their equilibrium distribution between the silicon melt and crystal phases are key, but unfortunately not precisely known parameters for the global models of silicon solidification processes. In this study, we apply a suite of molecular simulation tools, driven by multiple empirical potential models, to compute diffusion and segregation coefficients of carbon at the silicon melting temperature. We generally find good consistency across the potential model predictions, although some exceptions are identified and discussed. We also find good agreement with the range of available experimental measurements of segregation coefficients. However, the carbon diffusion coefficients we compute are significantly lower than the values typically assumed in continuum models of impurity distribution. Overall, we show that currently available empirical potential models may be useful, at least semi-quantitatively, for studying carbon (and possibly other impurity) transport in silicon solidification, especially if a multi-model approach is taken.

Adsorption-Coupled Diffusion of Gold Nanoclusters within a Large-Pore Protein Crystal Scaffold.

PubMed

Hartje, Luke F; Munsky, Brian; Ni, Thomas W; Ackerson, Christopher J; Snow, Christopher D

2017-08-17

Large-pore protein crystals (LPCs) are ordered biologically derived nanoporous materials exhibiting pore diameters greater than 8 nm. These substantial pores distinguish LPCs from typical nanoporous scaffolds, enabling engineered LPC materials to readily uptake, immobilize, and release macromolecular guests. In this study, macromolecular transport within an LPC environment was experimentally and computationally investigated by studying adsorption-coupled diffusion of Au 25 (glutathione) 18 nanoclusters within a cross-linked LPC scaffold via time-lapse confocal microscopy, bulk equilibrium adsorption, and hindered diffusion simulation. Equilibrium adsorption data is congruent with a Langmuir adsorption model, exhibiting strong binding behavior between nanoclusters and the scaffold. The standard Gibbs free energy of binding is equivalent to -37.2 kJ/mol, and the maximum binding capacity of 1.25 × 10 3 mg/g corresponds to approximately 29 nanoclusters per LPC unit cell. The hindered diffusion model showed good agreement with experimental data, revealing a pore diffusion coefficient of 3.7 × 10 -7 cm 2 /s under low nanocluster concentration. Furthermore, the model was sufficient to determine adsorption and desorption kinetic values for k a and k d equal to 13 cm 3 /mol·s and 1.7 × 10 -7 s -1 , respectively. At higher nanocluster concentrations, the simulated pore diffusion coefficient could be reduced by 3 orders of magnitude to 3.4 × 10 -10 cm 2 /s due to the effects of pore occlusion. This study demonstrates a strategy to analyze adsorption-coupled diffusion data to better understand complex transport of fluorescent macromolecules into LPCs. This approach fits the observable fluorescence data to the key molecular details and will benefit downstream efforts to engineer LPC-based nanoporous materials.

Modeling the migration of platinum nanoparticles on surfaces using a kinetic Monte Carlo approach

DOE PAGES

Li, Lin; Plessow, Philipp N.; Rieger, Michael; ...

2017-02-15

We propose a kinetic Monte Carlo (kMC) model for simulating the movement of platinum particles on supports, based on atom-by-atom diffusion on the surface of the particle. The proposed model was able to reproduce equilibrium cluster shapes predicted using Wulff-construction. The diffusivity of platinum particles was simulated both purely based on random motion and assisted using an external field that causes a drift velocity. The overall particle diffusivity increases with temperature; however, the extracted activation barrier appears to be temperature independent. Additionally, this barrier was found to increase with particle size, as well as, with the adhesion between the particlemore » and the support.« less

The Effect of Limited Diffusion and Wet-Dry Cycling on Reversible Polymerization Reactions: Implications for Prebiotic Synthesis of Nucleic Acids.

PubMed

Higgs, Paul G

2016-06-08

A long-standing problem for the origins of life is that polymerization of many biopolymers, including nucleic acids and peptides, is thermodynamically unfavourable in aqueous solution. If bond making and breaking is reversible, monomers and very short oligomers predominate. Recent experiments have shown that wetting and drying cycles can overcome this problem and drive the formation of longer polymers. In the dry phase, bond formation is favourable, but diffusion is restricted, and bonds only form between monomers that are initially close together. In the wet phase, some of the bonds are hydrolyzed. However, repositioning of the molecules allows new bonds to form in the next dry phase, leading to an increase in mean polymer length. Here, we consider a simple theoretical model that explains the effect of cycling. There is an equilibrium length distribution with a high mean length that could be achieved if diffusion occurred freely in the dry phase. This equilibrium is inaccessible without diffusion. A single dry cycle without diffusion leads to mean lengths much shorter than this. Repeated cycling leads to a significant increase in polymerization relative to a single cycle. In the most favourable case, cycling leads to the same equilibrium length distribution as would be achieved if free diffusion were possible in the dry phase. These results support the RNA World scenario by explaining a potential route to synthesis of long RNAs; however, they also imply that cycling would be beneficial to the synthesis of other kinds of polymers, including peptides, where bond formation involves a condensation reaction.

The Effect of Limited Diffusion and Wet–Dry Cycling on Reversible Polymerization Reactions: Implications for Prebiotic Synthesis of Nucleic Acids

PubMed Central

Higgs, Paul G.

2016-01-01

A long-standing problem for the origins of life is that polymerization of many biopolymers, including nucleic acids and peptides, is thermodynamically unfavourable in aqueous solution. If bond making and breaking is reversible, monomers and very short oligomers predominate. Recent experiments have shown that wetting and drying cycles can overcome this problem and drive the formation of longer polymers. In the dry phase, bond formation is favourable, but diffusion is restricted, and bonds only form between monomers that are initially close together. In the wet phase, some of the bonds are hydrolyzed. However, repositioning of the molecules allows new bonds to form in the next dry phase, leading to an increase in mean polymer length. Here, we consider a simple theoretical model that explains the effect of cycling. There is an equilibrium length distribution with a high mean length that could be achieved if diffusion occurred freely in the dry phase. This equilibrium is inaccessible without diffusion. A single dry cycle without diffusion leads to mean lengths much shorter than this. Repeated cycling leads to a significant increase in polymerization relative to a single cycle. In the most favourable case, cycling leads to the same equilibrium length distribution as would be achieved if free diffusion were possible in the dry phase. These results support the RNA World scenario by explaining a potential route to synthesis of long RNAs; however, they also imply that cycling would be beneficial to the synthesis of other kinds of polymers, including peptides, where bond formation involves a condensation reaction. PMID:27338479

Computation of the unsteady facilitated transport of oxygen in hemoglobin

NASA Technical Reports Server (NTRS)

Davis, Sanford

1990-01-01

The transport of a reacting permeant diffusing through a thin membrane is extended to more realistic dissociation models. A new nonlinear analysis of the reaction-diffusion equations, using implicit finite-difference methods and direct block solvers, is used to study the limits of linearized and equilibrium theories. Computed curves of molecular oxygen permeating through hemoglobin solution are used to illustrate higher-order reaction models, the effect of concentration boundary layers at the membrane interfaces, and the transient buildup of oxygen flux.

Multicomponent lattice Boltzmann model from continuum kinetic theory.

PubMed

Shan, Xiaowen

2010-04-01

We derive from the continuum kinetic theory a multicomponent lattice Boltzmann model with intermolecular interaction. The resulting model is found to be consistent with the model previously derived from a lattice-gas cellular automaton [X. Shan and H. Chen, Phys. Rev. E 47, 1815 (1993)] but applies in a much broader domain. A number of important insights are gained from the kinetic theory perspective. First, it is shown that even in the isothermal case, the energy equipartition principle dictates the form of the equilibrium distribution function. Second, thermal diffusion is shown to exist and the corresponding diffusivities are given in terms of macroscopic parameters. Third, the ordinary diffusion is shown to satisfy the Maxwell-Stefan equation at the ideal-gas limit.

Laboratory longitudinal diffusion tests: 1. Dimensionless formulations and validity of simplified solutions

NASA Astrophysics Data System (ADS)

Takeda, M.; Nakajima, H.; Zhang, M.; Hiratsuka, T.

2008-04-01

To obtain reliable diffusion parameters for diffusion testing, multiple experiments should not only be cross-checked but the internal consistency of each experiment should also be verified. In the through- and in-diffusion tests with solution reservoirs, test interpretation of different phases often makes use of simplified analytical solutions. This study explores the feasibility of steady, quasi-steady, equilibrium and transient-state analyses using simplified analytical solutions with respect to (i) valid conditions for each analytical solution, (ii) potential error, and (iii) experimental time. For increased generality, a series of numerical analyses are performed using unified dimensionless parameters and the results are all related to dimensionless reservoir volume (DRV) which includes only the sorptive parameter as an unknown. This means the above factors can be investigated on the basis of the sorption properties of the testing material and/or tracer. The main findings are that steady, quasi-steady and equilibrium-state analyses are applicable when the tracer is not highly sorptive. However, quasi-steady and equilibrium-state analyses become inefficient or impractical compared to steady state analysis when the tracer is non-sorbing and material porosity is significantly low. Systematic and comprehensive reformulation of analytical models enables the comparison of experimental times between different test methods. The applicability and potential error of each test interpretation can also be studied. These can be applied in designing, performing, and interpreting diffusion experiments by deducing DRV from the available information for the target material and tracer, combined with the results of this study.

In Silico Determination of Gas Permeabilities by Non-Equilibrium Molecular Dynamics: CO2 and He through PIM-1

PubMed Central

Frentrup, Hendrik; Hart, Kyle E.; Colina, Coray M.; Müller, Erich A.

2015-01-01

We study the permeation dynamics of helium and carbon dioxide through an atomistically detailed model of a polymer of intrinsic microporosity, PIM-1, via non-equilibrium molecular dynamics (NEMD) simulations. This work presents the first explicit molecular modeling of gas permeation through a high free-volume polymer sample, and it demonstrates how permeability and solubility can be obtained coherently from a single simulation. Solubilities in particular can be obtained to a very high degree of confidence and within experimental inaccuracies. Furthermore, the simulations make it possible to obtain very specific information on the diffusion dynamics of penetrant molecules and yield detailed maps of gas occupancy, which are akin to a digital tomographic scan of the polymer network. In addition to determining permeability and solubility directly from NEMD simulations, the results shed light on the permeation mechanism of the penetrant gases, suggesting that the relative openness of the microporous topology promotes the anomalous diffusion of penetrant gases, which entails a deviation from the pore hopping mechanism usually observed in gas diffusion in polymers. PMID:25764366

Nonequilibrium two-dimensional Ising model with stationary uphill diffusion.

PubMed

Colangeli, Matteo; Giardinà, Cristian; Giberti, Claudio; Vernia, Cecilia

2018-03-01

Usually, in a nonequilibrium setting, a current brings mass from the highest density regions to the lowest density ones. Although rare, the opposite phenomenon (known as "uphill diffusion") has also been observed in multicomponent systems, where it appears as an artificial effect of the interaction among components. We show here that uphill diffusion can be a substantial effect, i.e., it may occur even in single component systems as a consequence of some external work. To this aim we consider the two-dimensional ferromagnetic Ising model in contact with two reservoirs that fix, at the left and the right boundaries, magnetizations of the same magnitude but of opposite signs.We provide numerical evidence that a class of nonequilibrium steady states exists in which, by tuning the reservoir magnetizations, the current in the system changes from "downhill" to "uphill". Moreover, we also show that, in such nonequilibrium setup, the current vanishes when the reservoir magnetization attains a value approaching, in the large volume limit, the magnetization of the equilibrium dynamics, thus establishing a relation between equilibrium and nonequilibrium properties.

Nonequilibrium two-dimensional Ising model with stationary uphill diffusion

NASA Astrophysics Data System (ADS)

Colangeli, Matteo; Giardinà, Cristian; Giberti, Claudio; Vernia, Cecilia

2018-03-01

Usually, in a nonequilibrium setting, a current brings mass from the highest density regions to the lowest density ones. Although rare, the opposite phenomenon (known as "uphill diffusion") has also been observed in multicomponent systems, where it appears as an artificial effect of the interaction among components. We show here that uphill diffusion can be a substantial effect, i.e., it may occur even in single component systems as a consequence of some external work. To this aim we consider the two-dimensional ferromagnetic Ising model in contact with two reservoirs that fix, at the left and the right boundaries, magnetizations of the same magnitude but of opposite signs.We provide numerical evidence that a class of nonequilibrium steady states exists in which, by tuning the reservoir magnetizations, the current in the system changes from "downhill" to "uphill". Moreover, we also show that, in such nonequilibrium setup, the current vanishes when the reservoir magnetization attains a value approaching, in the large volume limit, the magnetization of the equilibrium dynamics, thus establishing a relation between equilibrium and nonequilibrium properties.

Reaction-diffusion systems coupled at the boundary and the Morse-Smale property

NASA Astrophysics Data System (ADS)

Broche, Rita de Cássia D. S.; de Oliveira, Luiz Augusto F.

We study an one-dimensional nonlinear reaction-diffusion system coupled on the boundary. Such system comes from modeling problems of temperature distribution on two bars of same length, jointed together, with different diffusion coefficients. We prove the transversality property of unstable and stable manifolds assuming all equilibrium points are hyperbolic. To this end, we write the system as an equation with noncontinuous diffusion coefficient. We then study the nonincreasing property of the number of zeros of a linearized nonautonomous equation as well as the Sturm-Liouville properties of the solutions of a linear elliptic problem.

Tracking Water Diffusion Fronts in a Highly Viscous Aerosol Particle

NASA Astrophysics Data System (ADS)

Bastelberger, Sandra; Krieger, Ulrich; Peter, Thomas

2016-04-01

Field measurements indicate that atmospheric secondary aerosol particles can be present in a highly viscous, glassy state [1]. In contrast to liquid state particles, the gas phase equilibration is kinetically limited and governed by condensed phase diffusion. In recent water diffusion experiments on highly viscous single aerosol particles levitated in an electrodynamic balance (EDB) we observed a characteristic shift behavior of the Mie whispering gallery modes (WGM) indicative of the changing radial structure of the particle, thus providing us with an experimental method to track the diffusion process inside the particle. When a highly viscous, homogeneous particle is exposed to an abrupt increase in relative humidity, the rapid gas phase diffusion and strong concentration dependence of the diffusion coefficient in the condensed phase lead to extremely steep water concentration gradients inside the particle, reminiscent of diffusion fronts. The resulting quasi step-like concentration profile motivates the introduction of a simple core-shell model describing the morphology of the non-equilibrium particle during humidification. The subsequent particle growth and reduction of the shell refractive index can be observed as red and blueshift behavior of the WGM, respectively. The shift pattern can be attributed to a core-shell radius ratio and particle radius derived from model calculations [2]. If supplemented with growth information obtained from the WGM redshift and thermodynamic equilibrium data, we can infer a comprehensive picture of the time evolution of the diffusion fronts in the framework of our core-shell model. The measured time dependent concentration profile is then compared with simulations solving the non-linear diffusion equation [3] [1] Virtanen, A., et al., Nature, 467, 824-827, 2010 [2] Kaiser, T., Schweiger, G., Computers in Physics, Vol. 7, No. 6, 682-686, Nov/Dec 1993 [3] Zobrist, B., Soonsin, V., Luo, B.P., Peter, T. et al., Phys. Chem. Chem. Phys., 13,3514-3526, 2011

Adapting HYDRUS-1D to Simulate Overland Flow and Reactive Transport During Sheet Flow Deviations

NASA Astrophysics Data System (ADS)

Liang, J.; Bradford, S. A.; Simunek, J.; Hartmann, A.

2017-12-01

The HYDRUS-1D code is a popular numerical model for solving the Richards equation for variably-saturated water flow and solute transport in porous media. This code was adapted to solve rather than the Richards equation for subsurface flow the diffusion wave equation for overland flow at the soil surface. The numerical results obtained by the new model produced an excellent agreement with the analytical solution of the kinematic wave equation. Model tests demonstrated its applicability to simulate the transport and fate of many different solutes, such as non-adsorbing tracers, nutrients, pesticides, and microbes. However, the diffusion wave or kinematic wave equations describe surface runoff as sheet flow with a uniform depth and velocity across the slope. In reality, overland water flow and transport processes are rarely uniform. Local soil topography, vegetation, and spatial soil heterogeneity control directions and magnitudes of water fluxes, and strongly influence runoff characteristics. There is increasing evidence that variations in soil surface characteristics influence the distribution of overland flow and transport of pollutants. These spatially varying surface characteristics are likely to generate non-equilibrium flow and transport processes. HYDRUS-1D includes a hierarchical series of models of increasing complexity to account for both physical equilibrium and non-equilibrium, e.g., dual-porosity and dual-permeability models, up to a dual-permeability model with immobile water. The same conceptualization as used for the subsurface was implemented to simulate non-equilibrium overland flow and transport at the soil surface. The developed model improves our ability to describe non-equilibrium overland flow and transport processes and to improves our understanding of factors that cause this behavior. The HYDRUS-1D overland flow and transport model was additionally also extended to simulate soil erosion. The HYDRUS-1D Soil Erosion Model has been verified by comparing with other soil erosion models. The model performed well when the average soil particle size is relatively large. The performance of the soil erosion model has been further validated by comparing with selected experimental datasets from the literature.

Minimal wave speed for a class of non-cooperative reaction-diffusion systems of three equations

NASA Astrophysics Data System (ADS)

Zhang, Tianran

2017-05-01

In this paper, we study the traveling wave solutions and minimal wave speed for a class of non-cooperative reaction-diffusion systems consisting of three equations. Based on the eigenvalues, a pair of upper-lower solutions connecting only the invasion-free equilibrium are constructed and the Schauder's fixed-point theorem is applied to show the existence of traveling semi-fronts for an auxiliary system. Then the existence of traveling semi-fronts of original system is obtained by limit arguments. The traveling semi-fronts are proved to connect another equilibrium if natural birth and death rates are not considered and to be persistent if these rates are incorporated. Then non-existence of bounded traveling semi-fronts is obtained by two-sided Laplace transform. Then the above results are applied to some disease-transmission models and a predator-prey model.

DOE Office of Scientific and Technical Information (OSTI.GOV)

Barbante, Paolo; Frezzotti, Aldo; Gibelli, Livio

The unsteady evaporation of a thin planar liquid film is studied by molecular dynamics simulations of Lennard-Jones fluid. The obtained results are compared with the predictions of a diffuse interface model in which capillary Korteweg contributions are added to hydrodynamic equations, in order to obtain a unified description of the liquid bulk, liquid-vapor interface and vapor region. Particular care has been taken in constructing a diffuse interface model matching the thermodynamic and transport properties of the Lennard-Jones fluid. The comparison of diffuse interface model and molecular dynamics results shows that, although good agreement is obtained in equilibrium conditions, remarkable deviationsmore » of diffuse interface model predictions from the reference molecular dynamics results are observed in the simulation of liquid film evaporation. It is also observed that molecular dynamics results are in good agreement with preliminary results obtained from a composite model which describes the liquid film by a standard hydrodynamic model and the vapor by the Boltzmann equation. The two mathematical model models are connected by kinetic boundary conditions assuming unit evaporation coefficient.« less

Dynamic scaling for the growth of non-equilibrium fluctuations during thermophoretic diffusion in microgravity

DOE PAGES

Cerbino, Roberto; Sun, Yifei; Donev, Aleksandar; ...

2015-09-30

Diffusion processes are widespread in biological and chemical systems, where they play a fundamental role in the exchange of substances at the cellular level and in determining the rate of chemical reactions. Recently, the classical picture that portrays diffusion as random uncorrelated motion of molecules has been revised, when it was shown that giant non-equilibrium fluctuations develop during diffusion processes. Under microgravity conditions and at steady-state, non-equilibrium fluctuations exhibit scale invariance and their size is only limited by the boundaries of the system. Here in this work, we investigate the onset of non-equilibrium concentration fluctuations induced by thermophoretic diffusion inmore » microgravity, a regime not accessible to analytical calculations but of great relevance for the understanding of several natural and technological processes. A combination of state of the art simulations and experiments allows us to attain a fully quantitative description of the development of fluctuations during transient diffusion in microgravity. Both experiments and simulations show that during the onset the fluctuations exhibit scale invariance at large wave vectors. In a broader range of wave vectors simulations predict a spinodal-like growth of fluctuations, where the amplitude and length-scale of the dominant mode are determined by the thickness of the diffuse layer.« less

Dynamic scaling for the growth of non-equilibrium fluctuations during thermophoretic diffusion in microgravity

PubMed Central

Cerbino, Roberto; Sun, Yifei; Donev, Aleksandar; Vailati, Alberto

2015-01-01

Diffusion processes are widespread in biological and chemical systems, where they play a fundamental role in the exchange of substances at the cellular level and in determining the rate of chemical reactions. Recently, the classical picture that portrays diffusion as random uncorrelated motion of molecules has been revised, when it was shown that giant non-equilibrium fluctuations develop during diffusion processes. Under microgravity conditions and at steady-state, non-equilibrium fluctuations exhibit scale invariance and their size is only limited by the boundaries of the system. In this work, we investigate the onset of non-equilibrium concentration fluctuations induced by thermophoretic diffusion in microgravity, a regime not accessible to analytical calculations but of great relevance for the understanding of several natural and technological processes. A combination of state of the art simulations and experiments allows us to attain a fully quantitative description of the development of fluctuations during transient diffusion in microgravity. Both experiments and simulations show that during the onset the fluctuations exhibit scale invariance at large wave vectors. In a broader range of wave vectors simulations predict a spinodal-like growth of fluctuations, where the amplitude and length-scale of the dominant mode are determined by the thickness of the diffuse layer. PMID:26419420

Dynamic scaling for the growth of non-equilibrium fluctuations during thermophoretic diffusion in microgravity.

PubMed

Cerbino, Roberto; Sun, Yifei; Donev, Aleksandar; Vailati, Alberto

2015-09-30

Diffusion processes are widespread in biological and chemical systems, where they play a fundamental role in the exchange of substances at the cellular level and in determining the rate of chemical reactions. Recently, the classical picture that portrays diffusion as random uncorrelated motion of molecules has been revised, when it was shown that giant non-equilibrium fluctuations develop during diffusion processes. Under microgravity conditions and at steady-state, non-equilibrium fluctuations exhibit scale invariance and their size is only limited by the boundaries of the system. In this work, we investigate the onset of non-equilibrium concentration fluctuations induced by thermophoretic diffusion in microgravity, a regime not accessible to analytical calculations but of great relevance for the understanding of several natural and technological processes. A combination of state of the art simulations and experiments allows us to attain a fully quantitative description of the development of fluctuations during transient diffusion in microgravity. Both experiments and simulations show that during the onset the fluctuations exhibit scale invariance at large wave vectors. In a broader range of wave vectors simulations predict a spinodal-like growth of fluctuations, where the amplitude and length-scale of the dominant mode are determined by the thickness of the diffuse layer.

Isotope effect of mercury diffusion in air

PubMed Central

Koster van Groos, Paul G.; Esser, Bradley K.; Williams, Ross W.; Hunt, James R.

2014-01-01

Identifying and reducing impacts from mercury sources in the environment remains a considerable challenge and requires process based models to quantify mercury stocks and flows. The stable isotope composition of mercury in environmental samples can help address this challenge by serving as a tracer of specific sources and processes. Mercury isotope variations are small and result only from isotope fractionation during transport, equilibrium, and transformation processes. Because these processes occur in both industrial and environmental settings, knowledge of their associated isotope effects is required to interpret mercury isotope data. To improve the mechanistic modeling of mercury isotope effects during gas phase diffusion, an experimental program tested the applicability of kinetic gas theory. Gas-phase elemental mercury diffusion through small bore needles from finite sources demonstrated mass dependent diffusivities leading to isotope fractionation described by a Rayleigh distillation model. The measured relative atomic diffusivities among mercury isotopes in air are large and in agreement with kinetic gas theory. Mercury diffusion in air offers a reasonable explanation of recent field results reported in the literature. PMID:24364380

Isotope effect of mercury diffusion in air.

PubMed

Koster van Groos, Paul G; Esser, Bradley K; Williams, Ross W; Hunt, James R

2014-01-01

Identifying and reducing impacts from mercury sources in the environment remains a considerable challenge and requires process based models to quantify mercury stocks and flows. The stable isotope composition of mercury in environmental samples can help address this challenge by serving as a tracer of specific sources and processes. Mercury isotope variations are small and result only from isotope fractionation during transport, equilibrium, and transformation processes. Because these processes occur in both industrial and environmental settings, knowledge of their associated isotope effects is required to interpret mercury isotope data. To improve the mechanistic modeling of mercury isotope effects during gas phase diffusion, an experimental program tested the applicability of kinetic gas theory. Gas-phase elemental mercury diffusion through small bore needles from finite sources demonstrated mass dependent diffusivities leading to isotope fractionation described by a Rayleigh distillation model. The measured relative atomic diffusivities among mercury isotopes in air are large and in agreement with kinetic gas theory. Mercury diffusion in air offers a reasonable explanation of recent field results reported in the literature.

Diffusion Coefficients from Molecular Dynamics Simulations in Binary and Ternary Mixtures

NASA Astrophysics Data System (ADS)

Liu, Xin; Schnell, Sondre K.; Simon, Jean-Marc; Krüger, Peter; Bedeaux, Dick; Kjelstrup, Signe; Bardow, André; Vlugt, Thijs J. H.

2013-07-01

Multicomponent diffusion in liquids is ubiquitous in (bio)chemical processes. It has gained considerable and increasing interest as it is often the rate limiting step in a process. In this paper, we review methods for calculating diffusion coefficients from molecular simulation and predictive engineering models. The main achievements of our research during the past years can be summarized as follows: (1) we introduced a consistent method for computing Fick diffusion coefficients using equilibrium molecular dynamics simulations; (2) we developed a multicomponent Darken equation for the description of the concentration dependence of Maxwell-Stefan diffusivities. In the case of infinite dilution, the multicomponent Darken equation provides an expression for [InlineEquation not available: see fulltext.] which can be used to parametrize the generalized Vignes equation; and (3) a predictive model for self-diffusivities was proposed for the parametrization of the multicomponent Darken equation. This equation accurately describes the concentration dependence of self-diffusivities in weakly associating systems. With these methods, a sound framework for the prediction of mutual diffusion in liquids is achieved.

Uranium biosorption by Padina sp. algae biomass: kinetics and thermodynamics.

PubMed

Khani, Mohammad Hassan

2011-11-01

Kinetic, thermodynamic, and equilibrium isotherms of the biosorption of uranium ions onto Padina sp., a brown algae biomass, in a batch system have been studied. The kinetic data were found to follow the pseudo-second-order model. Intraparticle diffusion is not the sole rate-controlling factor. The equilibrium experimental results were analyzed in terms of Langmuir isotherm depending with temperature. Equilibrium data fitted very well to the Langmuir model. The maximum uptakes estimated by using the Langmuir model were 434.8, 416.7, 400.0, and 370.4 mg/g at 10°C, 20°C, 30°C, and 40°C, respectively. Gibbs free energy was spontaneous for all interactions, and the adsorption process exhibited exothermic enthalpy values. Padina sp. algae were shown to be a favorable biosorbent for uranium removal from aqueous solutions.

Molecular simulations of diffusion in electrolytes

NASA Astrophysics Data System (ADS)

Wheeler, Dean Richard

This work demonstrates new methodologies for simulating multicomponent diffusion in concentrated solutions using molecular dynamics (MD). Experimental diffusion data for concentrated multicomponent solutions are often lacking, as are accurate methods of predicting diffusion for nonideal solutions. MD can be a viable means of understanding and predicting multicomponent diffusion. While there have been several prior reports of MD simulations of mutual diffusion, no satisfactory expressions for simulating Stefan-Maxwell diffusivities for an arbitrary number of species exist. The approaches developed here allow for the computation of a full diffusion matrix for any number of species in both nonequilibrium and equilibrium MD ensembles. Our nonequilibrium approach is based on the application of constant external fields to drive species diffusion. Our equilibrium approach uses a newly developed Green-Kubo formula for Stefan-Maxwell diffusivities. In addition, as part of this work, we demonstrate a widely applicable means of increasing the computational efficiency of the Ewald sum, a technique for handling long-range Coulombic interactions in simulations. The theoretical development is applicable to any solution which can be simulated using MD; nevertheless, our primary interest is in electrochemical applications. To this end, the methods are tested by simulations of aqueous salt solutions and lithium-battery electrolytes. KCl and NaCl aqueous solutions were simulated over the concentration range 1 to 4 molal. Intermolecular-potential models were parameterized for these transport-based simulations. This work is the first to simulate all three independent diffusion coefficients for aqueous NaCl and KCl solutions. The results show that the nonequilibrium and equilibrium methods are consistent with each other, and in moderate agreement with experiment. We simulate lithium-battery electrolytes containing LiPF6 in propylene carbonate and mixed ethylene carbonate-dimethyl carbonate solvents. As with the aqueous-solution work, potential parameters were generated for these molecules. These nonaqueous electrolytes demonstrate rich transport behavior, which the simulations are able to reproduce qualitatively. In a mixed-solvent simulation we regress all six independent transport coefficients. The simulations show that strong ion pairing is responsible for the increase in viscosity and maximum in conductivity as ion concentrations are increased.

Influence of arc current and pressure on non-chemical equilibrium air arc behavior

NASA Astrophysics Data System (ADS)

Yi, WU; Yufei, CUI; Jiawei, DUAN; Hao, SUN; Chunlin, WANG; Chunping, NIU

2018-01-01

The influence of arc current and pressure on the non-chemical equilibrium (non-CE) air arc behavior of a nozzle structure was investigated based on the self-consistent non-chemical equilibrium model. The arc behavior during both the arc burning and arc decay phases were discussed at different currents and different pressures. We also devised the concept of a non-equilibrium parameter for a better understanding of non-CE effects. During the arc burning phase, the increasing current leads to a decrease of the non-equilibrium parameter of the particles in the arc core, while the increasing pressure leads to an increase of the non-equilibrium parameter of the particles in the arc core. During the arc decay phase, the non-CE effect will decrease by increasing the arc burning current and the nozzle pressure. Three factors together—convection, diffusion and chemical reactions—influence non-CE behavior.

Analytical and computational studies on the vacuum performance of a chevron ejector

NASA Astrophysics Data System (ADS)

Kong, F. S.; Jin, Y. Z.; Kim, H. D.

2016-11-01

The effects of chevrons on the performance of a supersonic vacuum ejector-diffuser system are investigated numerically and evaluated theoretically in this work. A three-dimensional geometrical domain is numerically solved using a fully implicit finite volume scheme based on the unsteady Reynolds stress model. A one-dimensional mathematical model provides a useful tool to reveal the steady flow physics inside the vacuum ejector-diffuser system. The effects of the chevron nozzle on the generation of recirculation regions and Reynolds stress behaviors are studied and compared with those of a conventional convergent nozzle. The present performance parameters obtained from the simulated results and the mathematical results are validated with existing experimental data and show good agreement. Primary results show that the duration of the transient period and the secondary chamber pressure at a dynamic equilibrium state depend strongly on the primary jet conditions, such as inlet pressure and primary nozzle shape. Complicated oscillatory flow, generated by the unsteady movement of recirculation, finally settles into a dynamic equilibrium state. As a vortex generator, the chevron demonstrated its strong entrainment capacity to accelerate the starting transient flows to a certain extent and reduce the dynamic equilibrium pressure of the secondary chamber significantly.

Molecular finite-size effects in stochastic models of equilibrium chemical systems.

PubMed

Cianci, Claudia; Smith, Stephen; Grima, Ramon

2016-02-28

The reaction-diffusion master equation (RDME) is a standard modelling approach for understanding stochastic and spatial chemical kinetics. An inherent assumption is that molecules are point-like. Here, we introduce the excluded volume reaction-diffusion master equation (vRDME) which takes into account volume exclusion effects on stochastic kinetics due to a finite molecular radius. We obtain an exact closed form solution of the RDME and of the vRDME for a general chemical system in equilibrium conditions. The difference between the two solutions increases with the ratio of molecular diameter to the compartment length scale. We show that an increase in the fraction of excluded space can (i) lead to deviations from the classical inverse square root law for the noise-strength, (ii) flip the skewness of the probability distribution from right to left-skewed, (iii) shift the equilibrium of bimolecular reactions so that more product molecules are formed, and (iv) strongly modulate the Fano factors and coefficients of variation. These volume exclusion effects are found to be particularly pronounced for chemical species not involved in chemical conservation laws. Finally, we show that statistics obtained using the vRDME are in good agreement with those obtained from Brownian dynamics with excluded volume interactions.

The two-stage dynamics in the Fermi-Pasta-Ulam problem: From regular to diffusive behavior

NASA Astrophysics Data System (ADS)

Ponno, A.; Christodoulidi, H.; Skokos, Ch.; Flach, S.

2011-12-01

A numerical and analytical study of the relaxation to equilibrium of both the Fermi-Pasta-Ulam (FPU) α-model and the integrable Toda model, when the fundamental mode is initially excited, is reported. We show that the dynamics of both systems is almost identical on the short term, when the energies of the initially unexcited modes grow in geometric progression with time, through a secular avalanche process. At the end of this first stage of the dynamics, the time-averaged modal energy spectrum of the Toda system stabilizes to its final profile, well described, at low energy, by the spectrum of a q-breather. The Toda equilibrium state is clearly shown to describe well the long-living quasi-state of the FPU system. On the long term, the modal energy spectrum of the FPU system slowly detaches from the Toda one by a diffusive-like rising of the tail modes, and eventually reaches the equilibrium flat shape. We find a simple law describing the growth of tail modes, which enables us to estimate the time-scale to equipartition of the FPU system, even when, at small energies, it becomes unobservable.

Transport diffusion in deformed carbon nanotubes

NASA Astrophysics Data System (ADS)

Feng, Jiamei; Chen, Peirong; Zheng, Dongqin; Zhong, Weirong

2018-03-01

Using non-equilibrium molecular dynamics and Monte Carlo methods, we have studied the transport diffusion of gas in deformed carbon nanotubes. Perfect carbon nanotube and various deformed carbon nanotubes are modeled as transport channels. It is found that the transport diffusion coefficient of gas does not change in twisted carbon nanotubes, but changes in XY-distortion, Z-distortion and local defect carbon nanotubes comparing with that of the perfect carbon nanotube. Furthermore, the change of transport diffusion coefficient is found to be associated with the deformation factor. The relationship between transport diffusion coefficient and temperature is also discussed in this paper. Our results may contribute to understanding the mechanism of molecular transport in nano-channel.

Diffusion of interacting particles in discrete geometries: Equilibrium and dynamical properties

NASA Astrophysics Data System (ADS)

Becker, T.; Nelissen, K.; Cleuren, B.; Partoens, B.; Van den Broeck, C.

2014-11-01

We expand on a recent study of a lattice model of interacting particles [Phys. Rev. Lett. 111, 110601 (2013), 10.1103/PhysRevLett.111.110601]. The adsorption isotherm and equilibrium fluctuations in particle number are discussed as a function of the interaction. Their behavior is similar to that of interacting particles in porous materials. Different expressions for the particle jump rates are derived from transition-state theory. Which expression should be used depends on the strength of the interparticle interactions. Analytical expressions for the self- and transport diffusion are derived when correlations, caused by memory effects in the environment, are neglected. The diffusive behavior is studied numerically with kinetic Monte Carlo (kMC) simulations, which reproduces the diffusion including correlations. The effect of correlations is studied by comparing the analytical expressions with the kMC simulations. It is found that the Maxwell-Stefan diffusion can exceed the self-diffusion. To our knowledge, this is the first time this is observed. The diffusive behavior in one-dimensional and higher-dimensional systems is qualitatively the same, with the effect of correlations decreasing for increasing dimension. The length dependence of both the self- and transport diffusion is studied for one-dimensional systems. For long lengths the self-diffusion shows a 1 /L dependence. Finally, we discuss when agreement with experiments and simulations can be expected. The assumption that particles in different cavities do not interact is expected to hold quantitatively at low and medium particle concentrations if the particles are not strongly interacting.

Insights into the equilibrium, kinetic and thermodynamics of nickel removal by environmental friendly Lansium domesticum peel biosorbent.

PubMed

Lam, Yun Fung; Lee, Lai Yee; Chua, Song Jun; Lim, Siew Shee; Gan, Suyin

2016-05-01

Lansium domesticum peel (LDP), a waste material generated from the fruit consumption, was evaluated as a biosorbent for nickel removal from aqueous media. The effects of dosage, contact time, initial pH, initial concentration and temperature on the biosorption process were investigated in batch experiments. Equilibrium data were fitted by the Langmuir, Freundlich, Temkin and Dubinin-Radushkevich models using nonlinear regression method with the best-fit model evaluated based on coefficient of determination (R(2)) and Chi-square (χ(2)). The best-fit isotherm was found to be the Langmuir model exhibiting R(2) very close to unity (0.997-0.999), smallest χ(2) (0.0138-0.0562) and largest biosorption capacity (10.1mg/g) at 30°C. Kinetic studies showed that the initial nickel removal was rapid with the equilibrium state established within 30min. Pseudo-second-order model was the best-fit kinetic model indicating the chemisorption nature of the biosorption process. Further data analysis by the intraparticle diffusion model revealed the involvement of several rate-controlling steps such as boundary layer and intraparticle diffusion. Thermodynamically, the process was exothermic, spontaneous and feasible. Regeneration studies indicated that LDP biosorbent could be regenerated using hydrochloric acid solution with up to 85% efficiency. The present investigation proved that LDP having no economic value can be used as an alternative eco-friendly biosorbent for remediation of nickel contaminated water. Copyright © 2016 Elsevier Inc. All rights reserved.

A Computational Approach to Increase Time Scales in Brownian Dynamics–Based Reaction-Diffusion Modeling

PubMed Central

Frazier, Zachary

2012-01-01

Abstract Particle-based Brownian dynamics simulations offer the opportunity to not only simulate diffusion of particles but also the reactions between them. They therefore provide an opportunity to integrate varied biological data into spatially explicit models of biological processes, such as signal transduction or mitosis. However, particle based reaction-diffusion methods often are hampered by the relatively small time step needed for accurate description of the reaction-diffusion framework. Such small time steps often prevent simulation times that are relevant for biological processes. It is therefore of great importance to develop reaction-diffusion methods that tolerate larger time steps while maintaining relatively high accuracy. Here, we provide an algorithm, which detects potential particle collisions prior to a BD-based particle displacement and at the same time rigorously obeys the detailed balance rule of equilibrium reactions. We can show that for reaction-diffusion processes of particles mimicking proteins, the method can increase the typical BD time step by an order of magnitude while maintaining similar accuracy in the reaction diffusion modelling. PMID:22697237

Synthesis of a novel magnetic Fe3O4/γ-Al2O3 hybrid composite using electrode-alternation technique for the removal of an azo dye

NASA Astrophysics Data System (ADS)

Jung, Kyung-Won; Choi, Brian Hyun; Ahn, Kyu-Hong; Lee, Sang-Hyup

2017-11-01

A novel magnetic adsorbent of Fe3O4/γ-Al2O3 hybrid composite (denoted as M-Fe/Al-H) was developed electrochemically via a sequential application of iron and aluminum electrodes in a one-pot fashion, which called here as electrode-alternation technique, followed by pyrolysis. Physical and chemical properties of the prepared adsorbents were characterized and their feasibility towards the removal of di-anionic azo dye Acid Black 1 (AB1) was assessed. Textural and structural characterization revealed that the prepared M-Fe/Al-H possesses superior properties than those of M-Fe (sole usage of iron electrode), which may improve the adsorption capacity. Kinetics revealed that the adsorption equilibrium was reached within 12 h with approximately 90% of the equilibrium adsorption capacity within the first 3 h. Comprehensive analysis using the pseudo-second order and intraparticle diffusion models indicated that the dominant mechanism of the reaction is film diffusion with intraparticle diffusion being the rate determining step. The adsorption equilibrium isotherm data were best represented by the Sips isotherm model, which found to be approximately 1501, 1786, and 1959 mg/g at 283, 293, and 303 K, respectively. The exceptional performance as well as its ease of separation allows M-Fe/Al-H to be a promising candidate as an effective for azo dye removal from various aqueous medium.

Analysis on a diffusive SIS epidemic model with logistic source

NASA Astrophysics Data System (ADS)

Li, Bo; Li, Huicong; Tong, Yachun

2017-08-01

In this paper, we are concerned with an SIS epidemic reaction-diffusion model with logistic source in spatially heterogeneous environment. We first discuss some basic properties of the parabolic system, including the uniform upper bound of solutions and global stability of the endemic equilibrium when spatial environment is homogeneous. Our primary focus is to determine the asymptotic profile of endemic equilibria (when exist) if the diffusion (migration) rate of the susceptible or infected population is small or large. Combined with the results of Li et al. (J Differ Equ 262:885-913, 2017) where the case of linear source is studied, our analysis suggests that varying total population enhances persistence of infectious disease.

High-order regularization in lattice-Boltzmann equations

NASA Astrophysics Data System (ADS)

Mattila, Keijo K.; Philippi, Paulo C.; Hegele, Luiz A.

2017-04-01

A lattice-Boltzmann equation (LBE) is the discrete counterpart of a continuous kinetic model. It can be derived using a Hermite polynomial expansion for the velocity distribution function. Since LBEs are characterized by discrete, finite representations of the microscopic velocity space, the expansion must be truncated and the appropriate order of truncation depends on the hydrodynamic problem under investigation. Here we consider a particular truncation where the non-equilibrium distribution is expanded on a par with the equilibrium distribution, except that the diffusive parts of high-order non-equilibrium moments are filtered, i.e., only the corresponding advective parts are retained after a given rank. The decomposition of moments into diffusive and advective parts is based directly on analytical relations between Hermite polynomial tensors. The resulting, refined regularization procedure leads to recurrence relations where high-order non-equilibrium moments are expressed in terms of low-order ones. The procedure is appealing in the sense that stability can be enhanced without local variation of transport parameters, like viscosity, or without tuning the simulation parameters based on embedded optimization steps. The improved stability properties are here demonstrated using the perturbed double periodic shear layer flow and the Sod shock tube problem as benchmark cases.

Modeling of outgassing and matrix decomposition in carbon-phenolic composites

NASA Technical Reports Server (NTRS)

Mcmanus, Hugh L.

1993-01-01

A new release rate equation to model the phase change of water to steam in composite materials was derived from the theory of molecular diffusion and equilibrium moisture concentration. The new model is dependent on internal pressure, the microstructure of the voids and channels in the composite materials, and the diffusion properties of the matrix material. Hence, it is more fundamental and accurate than the empirical Arrhenius rate equation currently in use. The model was mathematically formalized and integrated into the thermostructural analysis code CHAR. Parametric studies on variation of several parameters have been done. Comparisons to Arrhenius and straight-line models show that the new model produces physically realistic results under all conditions.

Diffusion approximations to the chemical master equation only have a consistent stochastic thermodynamics at chemical equilibrium

NASA Astrophysics Data System (ADS)

Horowitz, Jordan M.

2015-07-01

The stochastic thermodynamics of a dilute, well-stirred mixture of chemically reacting species is built on the stochastic trajectories of reaction events obtained from the chemical master equation. However, when the molecular populations are large, the discrete chemical master equation can be approximated with a continuous diffusion process, like the chemical Langevin equation or low noise approximation. In this paper, we investigate to what extent these diffusion approximations inherit the stochastic thermodynamics of the chemical master equation. We find that a stochastic-thermodynamic description is only valid at a detailed-balanced, equilibrium steady state. Away from equilibrium, where there is no consistent stochastic thermodynamics, we show that one can still use the diffusive solutions to approximate the underlying thermodynamics of the chemical master equation.

Diffusion approximations to the chemical master equation only have a consistent stochastic thermodynamics at chemical equilibrium.

PubMed

Horowitz, Jordan M

2015-07-28

The stochastic thermodynamics of a dilute, well-stirred mixture of chemically reacting species is built on the stochastic trajectories of reaction events obtained from the chemical master equation. However, when the molecular populations are large, the discrete chemical master equation can be approximated with a continuous diffusion process, like the chemical Langevin equation or low noise approximation. In this paper, we investigate to what extent these diffusion approximations inherit the stochastic thermodynamics of the chemical master equation. We find that a stochastic-thermodynamic description is only valid at a detailed-balanced, equilibrium steady state. Away from equilibrium, where there is no consistent stochastic thermodynamics, we show that one can still use the diffusive solutions to approximate the underlying thermodynamics of the chemical master equation.

Viscosity and viscoelasticity of two-phase systems having diffuse interfaces

NASA Technical Reports Server (NTRS)

Hopper, R. W.

1976-01-01

The equilibrium stability criterion for diffuse interfaces in a two-component solution with a miscibility gap requires that the interdiffusion flux vanish. If the system is continuously deformed, convective fluxes disrupt the equilibrium in the interface regions and induce a counter diffusive flux, which is dissipative and contributes to the apparent viscosity of the mixture. Chemical free energy is recoverably stored, causing viscoelastic phenomena. Both effects are significant.

Solute partitioning under continuous cooling conditions as a cooling rate indicator. [in lunar rocks

NASA Technical Reports Server (NTRS)

Onorato, P. I. K.; Hopper, R. W.; Yinnon, H.; Uhlmann, D. R.; Taylor, L. A.; Garrison, J. R.; Hunter, R.

1981-01-01

A model of solute partitioning in a finite body under conditions of continuous cooling is developed for the determination of cooling rates from concentration profile data, and applied to the partitioning of zirconium between ilmenite and ulvospinel in the Apollo 15 Elbow Crater rocks. Partitioning in a layered composite solid is described numerically in terms of concentration profiles and diffusion coefficients which are functions of time and temperature, respectively; a program based on the model can be used to calculate concentration profiles for various assumed cooling rates given the diffusion coefficients in the two phases and the equilibrium partitioning ratio over a range of temperatures. In the case of the Elbow Rock gabbros, the cooling rates are calculated from measured concentration ratios 10 microns from the interphase boundaries under the assumptions of uniform and equilibrium initial conditions at various starting temperatures. It is shown that the specimens could not have had uniform concentrations profiles at the previously suggested initial temperature of 1350 K. It is concluded that even under conditions where the initial temperature, grain sizes and solute diffusion coefficients are not well characterized, the model can be used to estimate the cooling rate of a grain assemblage to within an order of magnitude.

Diffusion model validation and interpretation of stable isotopes in river and lake ice

USGS Publications Warehouse

Ferrick, M.G.; Calkins, D.J.; Perron, N.M.; Cragin, J.H.; Kendall, C.

2002-01-01

The stable isotope stratigraphy of river- and lake-ice archives winter hydroclimatic conditions, and can potentially be used to identify changing water sources or to provide important insights into ice formation processes and growth rates. However, accurate interpretations rely on known isotopic fractionation during ice growth. A one-dimensional diffusion model of the liquid boundary layer adjacent to an advancing solid interface, originally developed to simulate solute rejection by growing crystals, has been used without verification to describe non-equilibrium fractionation during congelation ice growth. Results are not in agreement, suggesting the presence of important uncertainties. In this paper we seek validation of the diffusion model for this application using large-scale laboratory experiments with controlled freezing rates and frequent sampling. We obtained consistent, almost constant, isotopic boundary layer thicknesses over a representative range of ice growth rates on both quiescent and well-mixed water. With the 18O boundary layer thickness from the laboratory, the model successfully quantified reduced river-ice growth rates relative to those of a nearby lake. These results were more representative and easier to obtain than those of a conventional thermal ice-growth model. This diffusion model validation and boundary layer thickness determination provide a powerful tool for interpreting the stable isotope stratigraphy of floating ice. The laboratory experiment also replicated successive fractionation events in response to a freeze-thaw-refreeze cycle, providing a mechanism for apparent ice fractionation that exceeds equilibrium. Analysis of the composition of snow ice and frazil ice in river and lake cores indicated surprising similarities between these ice forms. Published in 2002 by John Wiley & Sons, Ltd.

Characterization and Computational Modeling of Minor Phases in Alloy LSHR

NASA Technical Reports Server (NTRS)

Jou, Herng-Jeng; Olson, Gregory; Gabb, Timothy; Garg, Anita; Miller, Derek

2012-01-01

The minor phases of powder metallurgy disk superalloy LSHR were studied. Samples were consistently heat treated at three different temperatures for long times to approach equilibrium. Additional heat treatments were also performed for shorter times, to assess minor phase kinetics in non-equilibrium conditions. Minor phases including MC carbides, M23C6 carbides, M3B2 borides, and sigma were identified. Their average sizes and total area fractions were determined. CALPHAD thermodynamics databases and PrecipiCalc(TradeMark), a computational precipitation modeling tool, were employed with Ni-base thermodynamics and diffusion databases to model and simulate the phase microstructural evolution observed in the experiments with an objective to identify the model limitations and the directions of model enhancement.

Thermal and non-thermal X-rays from the Galactic supernova remnant G348.5+0.1

NASA Astrophysics Data System (ADS)

Yamauchi, Shigeo; Minami, Sari; Ota, Naomi; Koyama, Katsuji

2014-02-01

We report on Suzaku results of the two distinct regions in the Galactic supernova remnant G348.5+0.1: extended thermal X-rays ("soft diffuse") at the north-east region and non-thermal X-rays (CXOU J171419.8-383023) at the north-west region. The X-ray spectrum of the soft diffuse X-rays can be fitted with neither an ionization equilibrium nor a non-equilibrium (ionizing) plasma model, leaving saw- tooth residuals in the 1.5-3 keV energy band. The residual structures can be produced when free electrons are recombined to the K-shells of highly ionized Mg and Si ions. In fact, the X-ray spectrum is nicely fitted with a recombination-dominant plasma model. We propose a scenario whereby the plasma in a nearly fully ionized state at high temperature quickly changed to a recombining phase due to selective cooling of electrons to a lower temperature of ˜ 0.5 keV. The spectrum of CXOU J171419.8-383023 is well explained by a simple power-law model with a photon index of 1.9, nearly equal to the typical value for pulsar wind nebulae. Since the distance is estimated to be the same as that of the soft diffuse radiation, we infer that both the soft diffuse X-rays and CXOU J171419.8-383023 are associated with the same object, SNR G348.5+0.1.

Nebula Models of Non-Equilibrium Mineralogy: Wark-Lovering Rims

NASA Technical Reports Server (NTRS)

Cuzzi, J. N.; Petaev, M.; Krot, A. N.

2005-01-01

Introduction: The meteorite record contains several examples of minerals that would not persist if allowed to come to equilibrium with a cooling gas of solar composition. This includes all minerals in CAIs and AOAs. Their survival is generally ascribed to physical removal of the object from the gas (isolation into a large parent object, or ejection by a stellar wind), but could also result from outward radial diffusion into cooler regions, which we discuss here. Accretion of CAIs into planetesimals has also been relied on to preserve them against loss into the sun. However, this suggestion faces several objections. Simple outward diffusion in turbulence has recently been modeled in some detail, and can preserve CAIs against loss into the sun [2]. Naturally, outward radial diffusion in turbulence is slower than immediate ejection by a stellar wind, which occurs on an orbital timescale. Here we ask whether these different transport mechanisms can be distinguished by nonequilibrium mineralogy, which provides a sort of clock. Our application here is to one aspect of CAI mineralogy - the Wark-Lovering rims (WLR); even more specifically, to alteration of one layer in the WLR sequence from melilite (Mel) to anorthite (An).

Analysis of non-equilibrium phenomena in inductively coupled plasma generators

DOE Office of Scientific and Technical Information (OSTI.GOV)

Zhang, W.; Panesi, M., E-mail: mpanesi@illinois.edu; Lani, A.

This work addresses the modeling of non-equilibrium phenomena in inductively coupled plasma discharges. In the proposed computational model, the electromagnetic induction equation is solved together with the set of Navier-Stokes equations in order to compute the electromagnetic and flow fields, accounting for their mutual interaction. Semi-classical statistical thermodynamics is used to determine the plasma thermodynamic properties, while transport properties are obtained from kinetic principles, with the method of Chapman and Enskog. Particle ambipolar diffusive fluxes are found by solving the Stefan-Maxwell equations with a simple iterative method. Two physico-mathematical formulations are used to model the chemical reaction processes: (1) Amore » Local Thermodynamics Equilibrium (LTE) formulation and (2) a thermo-chemical non-equilibrium (TCNEQ) formulation. In the TCNEQ model, thermal non-equilibrium between the translational energy mode of the gas and the vibrational energy mode of individual molecules is accounted for. The electronic states of the chemical species are assumed in equilibrium with the vibrational temperature, whereas the rotational energy mode is assumed to be equilibrated with translation. Three different physical models are used to account for the coupling of chemistry and energy transfer processes. Numerical simulations obtained with the LTE and TCNEQ formulations are used to characterize the extent of non-equilibrium of the flow inside the Plasmatron facility at the von Karman Institute. Each model was tested using different kinetic mechanisms to assess the sensitivity of the results to variations in the reaction parameters. A comparison of temperatures and composition profiles at the outlet of the torch demonstrates that the flow is in non-equilibrium for operating conditions characterized by pressures below 30 000 Pa, frequency 0.37 MHz, input power 80 kW, and mass flow 8 g/s.« less

Analysis of non-equilibrium phenomena in inductively coupled plasma generators

NASA Astrophysics Data System (ADS)

Zhang, W.; Lani, A.; Panesi, M.

2016-07-01

This work addresses the modeling of non-equilibrium phenomena in inductively coupled plasma discharges. In the proposed computational model, the electromagnetic induction equation is solved together with the set of Navier-Stokes equations in order to compute the electromagnetic and flow fields, accounting for their mutual interaction. Semi-classical statistical thermodynamics is used to determine the plasma thermodynamic properties, while transport properties are obtained from kinetic principles, with the method of Chapman and Enskog. Particle ambipolar diffusive fluxes are found by solving the Stefan-Maxwell equations with a simple iterative method. Two physico-mathematical formulations are used to model the chemical reaction processes: (1) A Local Thermodynamics Equilibrium (LTE) formulation and (2) a thermo-chemical non-equilibrium (TCNEQ) formulation. In the TCNEQ model, thermal non-equilibrium between the translational energy mode of the gas and the vibrational energy mode of individual molecules is accounted for. The electronic states of the chemical species are assumed in equilibrium with the vibrational temperature, whereas the rotational energy mode is assumed to be equilibrated with translation. Three different physical models are used to account for the coupling of chemistry and energy transfer processes. Numerical simulations obtained with the LTE and TCNEQ formulations are used to characterize the extent of non-equilibrium of the flow inside the Plasmatron facility at the von Karman Institute. Each model was tested using different kinetic mechanisms to assess the sensitivity of the results to variations in the reaction parameters. A comparison of temperatures and composition profiles at the outlet of the torch demonstrates that the flow is in non-equilibrium for operating conditions characterized by pressures below 30 000 Pa, frequency 0.37 MHz, input power 80 kW, and mass flow 8 g/s.

Diffusion of water-soluble sorptive drugs in HEMA/MAA hydrogels.

PubMed

Liu, D E; Dursch, T J; Taylor, N O; Chan, S Y; Bregante, D T; Radke, C J

2016-10-10

We measure and, for the first time, theoretically predict four prototypical aqueous-drug diffusion coefficients in five soft-contact-lens material hydrogels where solute-specific adsorption is pronounced. Two-photon fluorescence confocal microscopy and UV/Vis-absorption spectrophotometry assess transient solute concentration profiles and concentration histories, respectively. Diffusion coefficients are obtained for acetazolamide, riboflavin, sodium fluorescein, and theophylline in 2-hydroxyethyl methacrylate/methacrylic acid (HEMA/MAA) copolymer hydrogels as functions of composition, equilibrium water content (30-90%), and aqueous pH (2 and 7.4). At pH2, MAA chains are nonionic, whereas at pH7.4, MAA chains are anionic (pKa≈5.2). All studied prototypical drugs specifically interact with HEMA and nonionic MAA (at pH2) moieties. Conversely, none of the prototypical drugs adsorb specifically to anionic MAA (at pH7.4) chains. As expected, diffusivities of adsorbing solutes are significantly diminished by specific interactions with hydrogel strands. Despite similar solute size, relative diffusion coefficients in the hydrogels span several orders of magnitude because of varying degrees of solute interactions with hydrogel-polymer chains. To provide a theoretical framework for the new diffusion data, we apply an effective-medium model extended for solute-specific interactions with hydrogel copolymer strands. Sorptive-diffusion kinetics is successfully described by local equilibrium and Henry's law. All necessary parameters are determined independently. Predicted diffusivities are in good agreement with experiment. Copyright © 2016 Elsevier B.V. All rights reserved.

A double medium model for diffusion in fluid-bearing rock

NASA Astrophysics Data System (ADS)

Wang, H. F.

1993-09-01

The concept of a double porosity medium to model fluid flow in fractured rock has been applied to model diffusion in rock containing a small amount of a continuous fluid phase that surrounds small volume elements of the solid matrix. The model quantifies the relative role of diffusion in the fluid and solid phases of the rock. The fluid is the fast diffusion path, but the solid contains the volumetrically significant amount of the diffusing species. The double medium model consists of two coupled differential equations. One equation is the diffusion equation for the fluid concentration; it contains a source term for change in the average concentration of the diffusing species in the solid matrix. The second equation represents the assumption that the change in average concentration in a solid element is proportional to the difference between the average concentration in the solid and the concentration in the fluid times the solid-fluid partition coefficient. The double medium model is shown to apply to laboratory data on iron diffusion in fluid-bearing dunite and to measured oxygen isotope ratios at marble-metagranite contacts. In both examples, concentration profiles are calculated for diffusion taking place at constant temperature, where a boundary value changes suddenly and is subsequently held constant. Knowledge of solid diffusivities can set a lower bound to the length of time over which diffusion occurs, but only the product of effective fluid diffusivity and time is constrained for times longer than the characteristic solid diffusion time. The double medium results approach a local, grain-scale equilibrium model for times that are large relative to the time constant for solid diffusion.

Assessing the inherent uncertainty of one-dimensional diffusions

NASA Astrophysics Data System (ADS)

Eliazar, Iddo; Cohen, Morrel H.

2013-01-01

In this paper we assess the inherent uncertainty of one-dimensional diffusion processes via a stochasticity classification which provides an à la Mandelbrot categorization into five states of uncertainty: infra-mild, mild, borderline, wild, and ultra-wild. Two settings are considered. (i) Stopped diffusions: the diffusion initiates from a high level and is stopped once it first reaches a low level; in this setting we analyze the inherent uncertainty of the diffusion's maximal exceedance above its initial high level. (ii) Stationary diffusions: the diffusion is in dynamical statistical equilibrium; in this setting we analyze the inherent uncertainty of the diffusion's equilibrium level. In both settings general closed-form analytic results are established, and their application is exemplified by stock prices in the stopped-diffusions setting, and by interest rates in the stationary-diffusions setting. These results provide a highly implementable decision-making tool for the classification of uncertainty in the context of one-dimensional diffusions.

Adsorption of direct dyes from aqueous solutions by carbon nanotubes: determination of equilibrium, kinetics and thermodynamics parameters.

PubMed

Kuo, Chao-Yin; Wu, Chung-Hsin; Wu, Jane-Yii

2008-11-15

This study examined the feasibility of removing direct dyes C.I. Direct Yellow 86 (DY86) and C.I. Direct Red 224 (DR224) from aqueous solutions using carbon nanotubes (CNTs). The effects of dye concentration, CNT dosage, ionic strength and temperature on adsorption of direct dyes by CNTs were also evaluated. Pseudo second-order, intraparticle diffusion and Bangham models were adopted to evaluate experimental data and thereby elucidate the kinetic adsorption process. Additionally, this study used the Langmuir, Freundlich, Dubinin and Radushkevich (D-R) and Temkin isotherms to describe equilibrium adsorption. The adsorption percentage of direct dyes increased as CNTs dosage, NaCl addition and temperature increased. Conversely, the adsorption percentage of direct dyes decreased as dye concentration increased. The pseudo second-order model best represented adsorption kinetics. Based on the regressions of intraparticle diffusion and Bangham models, experimental data suggest that the adsorption of direct dyes onto CNTs involved intraparticle diffusion, but that was not the only rate-controlling step. The equilibrium adsorption of DR86 is best fitted in the Freundlich isotherm and that of DR224 was best fitted in the D-R isotherm. The capacity of CNTs to adsorb DY86 and DR224 was 56.2 and 61.3 mg/g, respectively. For DY86, enthalpy (DeltaH(0)) and entropy (DeltaS(0)) were 13.69 kJ/mol and 139.51 J/mol K, respectively, and those for DR224 were 24.29 kJ/mol and 172.06 J/mol K, respectively. The values of DeltaH(0), DeltaG(0) and E all indicate that the adsorption of direct dyes onto CNTs was a physisorption process.

Dissolution without disappearing: multicomponent gas exchange for CO2 bubbles in a microfluidic channel.

PubMed

Shim, Suin; Wan, Jiandi; Hilgenfeldt, Sascha; Panchal, Prathamesh D; Stone, Howard A

2014-07-21

We studied the dissolution dynamics of CO2 gas bubbles in a microfluidic channel, both experimentally and theoretically. In the experiments, spherical CO2 bubbles in a flow of a solution of sodium dodecyl sulfate (SDS) first shrink rapidly before attaining an equilibrium size. In the rapid dissolution regime, the time to obtain a new equilibrium is 30 ms regardless of SDS concentration, and the equilibrium radius achieved varies with the SDS concentration. To explain the lack of complete dissolution, we interpret the results by considering the effects of other gases (O2, N2) that are already dissolved in the aqueous phase, and we develop a multicomponent dissolution model that includes the effect of surface tension and the liquid pressure drop along the channel. Solutions of the model for a stationary gas bubble show good agreement with the experimental results, which lead to our conclusion that the equilibrium regime is obtained by gas exchange between the bubbles and liquid phase. Also, our observations from experiments and model calculations suggest that SDS molecules on the gas-liquid interface form a diffusion barrier, which controls the dissolution behaviour and the eventual equilibrium radius of the bubble.

Liquid phase stabilization versus bubble formation at a nanoscale curved interface

NASA Astrophysics Data System (ADS)

Schiffbauer, Jarrod; Luo, Tengfei

2018-03-01

We investigate the nature of vapor bubble formation near a nanoscale-curved convex liquid-solid interface using two models: an equilibrium Gibbs model for homogenous nucleation, and a nonequilibrium dynamic van der Waals-diffuse-interface model for phase change in an initially cool liquid. Vapor bubble formation is shown to occur for sufficiently large radius of curvature and is suppressed for smaller radii. Solid-fluid interactions are accounted for and it is shown that liquid-vapor interfacial energy, and hence Laplace pressure, has limited influence over bubble formation. The dominant factor is the energetic cost of creating the solid-vapor interface from the existing solid-liquid interface, as demonstrated via both equilibrium and nonequilibrium arguments.

Lifetime of Major Histocompatibility Complex Class-I Membrane Clusters Is Controlled by the Actin Cytoskeleton

PubMed Central

Lavi, Yael; Gov, Nir; Edidin, Michael; Gheber, Levi A.

2012-01-01

Lateral heterogeneity of cell membranes has been demonstrated in numerous studies showing anomalous diffusion of membrane proteins; it has been explained by models and experiments suggesting dynamic barriers to free diffusion, that temporarily confine membrane proteins into microscopic patches. This picture, however, comes short of explaining a steady-state patchy distribution of proteins, in face of the transient opening of the barriers. In our previous work we directly imaged persistent clusters of MHC-I, a type I transmembrane protein, and proposed a model of a dynamic equilibrium between proteins newly delivered to the cell surface by vesicle traffic, temporary confinement by dynamic barriers to lateral diffusion, and dispersion of the clusters by diffusion over the dynamic barriers. Our model predicted that the clusters are dynamic, appearing when an exocytic vesicle fuses with the plasma membrane and dispersing with a typical lifetime that depends on lateral diffusion and the dynamics of barriers. In a subsequent work, we showed this to be the case. Here we test another prediction of the model, and show that changing the stability of actin barriers to lateral diffusion changes cluster lifetimes. We also develop a model for the distribution of cluster lifetimes, consistent with the function of barriers to lateral diffusion in maintaining MHC-I clusters. PMID:22500754

Modeling the rate-controlled sorption of hexavalent chromium

USGS Publications Warehouse

Grove, D.B.; Stollenwerk, K.G.

1985-01-01

Sorption of chromium VI on the iron-oxide- and hydroxide-coated surface of alluvial material was numerically simulated with rate-controlled reactions. Reaction kinetics and diffusional processes, in the form of film, pore, and particle diffusion, were simulated and compared with experimental results. The use of empirically calculated rate coefficients for diffusion through the reacting surface was found to simulate experimental data; pore or particle diffusion is believed to be a possible rate-controlling mechanism. The use of rate equations to predict conservative transport and rate- and local-equilibrium-controlled reactions was shown to be feasible.

Diffusion approximations to the chemical master equation only have a consistent stochastic thermodynamics at chemical equilibrium

DOE Office of Scientific and Technical Information (OSTI.GOV)

Horowitz, Jordan M., E-mail: jordan.horowitz@umb.edu

The stochastic thermodynamics of a dilute, well-stirred mixture of chemically reacting species is built on the stochastic trajectories of reaction events obtained from the chemical master equation. However, when the molecular populations are large, the discrete chemical master equation can be approximated with a continuous diffusion process, like the chemical Langevin equation or low noise approximation. In this paper, we investigate to what extent these diffusion approximations inherit the stochastic thermodynamics of the chemical master equation. We find that a stochastic-thermodynamic description is only valid at a detailed-balanced, equilibrium steady state. Away from equilibrium, where there is no consistent stochasticmore » thermodynamics, we show that one can still use the diffusive solutions to approximate the underlying thermodynamics of the chemical master equation.« less

Breakdown and Limit of Continuum Diffusion Velocity for Binary Gas Mixtures from Direct Simulation

NASA Astrophysics Data System (ADS)

Martin, Robert Scott; Najmabadi, Farrokh

2011-05-01

This work investigates the breakdown of the continuum relations for diffusion velocity in inert binary gas mixtures. Values of the relative diffusion velocities for components of a gas mixture may be calculated using of Chapman-Enskog theory and occur not only due to concentration gradients, but also pressure and temperature gradients in the flow as described by Hirschfelder. Because Chapman-Enskog theory employs a linear perturbation around equilibrium, it is expected to break down when the velocity distribution deviates significantly from equilibrium. This breakdown of the overall flow has long been an area of interest in rarefied gas dynamics. By comparing the continuum values to results from Bird's DS2V Monte Carlo code, we propose a new limit on the continuum approach specific to binary gases. To remove the confounding influence of an inconsistent molecular model, we also present the application of the variable hard sphere (VSS) model used in DS2V to the continuum diffusion velocity calculation. Fitting sample asymptotic curves to the breakdown, a limit, Vmax, that is a fraction of an analytically derived limit resulting from the kinetic temperature of the mixture is proposed. With an expected deviation of only 2% between the physical values and continuum calculations within ±Vmax/4, we suggest this as a conservative estimate on the range of applicability for the continuum theory.

Glucose diffusion in pancreatic islets of Langerhans.

PubMed Central

Bertram, R; Pernarowski, M

1998-01-01

We investigate the time required for glucose to diffuse through an isolated pancreatic islet of Langerhans and reach an equilibrium. This question is relevant in the context of in vitro electrophysiological studies of the response of an islet to step changes in the bath glucose concentration. Islet cells are electrically coupled by gap junctions, so nonuniformities in islet glucose concentration may be reflected in the activity of cells on the islet periphery, where electrical recordings are made. Using a mathematical model of hindered glucose diffusion, we investigate the effects of the islet porosity and the permeability of a surrounding layer of acinar cells. A major factor in the determination of the equilibrium time is the transport of glucose into islet beta-cells, which removes glucose from the interstitial spaces where diffusion occurs. This transport is incorporated by using a model of the GLUT-2 glucose transporter. We find that several minutes are required for the islet to equilibrate to a 10 mM change in bath glucose, a typical protocol in islet experiments. It is therefore likely that in electrophysiological islet experiments the glucose distribution is nonuniform for several minutes after a step change in bath glucose. The delay in glucose penetration to the inner portions of the islet may be a major contributing factor to the 1-2-min delay in islet electrical activity typically observed after bath application of a stimulatory concentration of glucose. PMID:9545035

Relationships between self-diffusivity, packing fraction, and excess entropy in simple bulk and confined fluids.

PubMed

Mittal, Jeetain; Errington, Jeffrey R; Truskett, Thomas M

2007-08-30

Static measures such as density and entropy, which are intimately connected to structure, have featured prominently in modern thinking about the dynamics of the liquid state. Here, we explore the connections between self-diffusivity, density, and excess entropy for two of the most widely used model "simple" liquids, the equilibrium Lennard-Jones and square-well fluids, in both bulk and confined environments. We find that the self-diffusivity data of the Lennard-Jones fluid can be approximately collapsed onto a single curve (i) versus effective packing fraction and (ii) in appropriately reduced form versus excess entropy, as suggested by two well-known scaling laws. Similar data collapse does not occur for the square-well fluid, a fact that can be understood on the basis of the nontrivial effects that temperature has on its static structure. Nonetheless, we show that the implications of confinement for the self-diffusivity of both of these model fluids, over a broad range of equilibrium conditions, can be predicted on the basis of knowledge of the bulk fluid behavior and either the effective packing fraction or the excess entropy of the confined fluid. Excess entropy is perhaps the most preferable route due to its superior predictive ability and because it is a standard, unambiguous thermodynamic quantity that can be readily predicted via classical density functional theories of inhomogeneous fluids.

DOE Office of Scientific and Technical Information (OSTI.GOV)

Choi, Jeong

The research program reported here is focused on critical issues that represent conspicuous gaps in current understanding of rapid solidification, limiting our ability to predict and control microstructural evolution (i.e. morphological dynamics and microsegregation) at high undercooling, where conditions depart significantly from local equilibrium. More specifically, through careful application of phase-field modeling, using appropriate thin-interface and anti-trapping corrections and addressing important details such as transient effects and a velocity-dependent (i.e. adaptive) numerics, the current analysis provides a reasonable simulation-based picture of non-equilibrium solute partitioning and the corresponding oscillatory dynamics associated with single-phase rapid solidification and show that this method ismore » a suitable means for a self-consistent simulation of transient behavior and operating point selection under rapid growth conditions. Moving beyond the limitations of conventional theoretical/analytical treatments of non-equilibrium solute partitioning, these results serve to substantiate recent experimental findings and analytical treatments for single-phase rapid solidification. The departure from the equilibrium solid concentration at the solid-liquid interface was often observed during rapid solidification, and the energetic associated non-equilibrium solute partitioning has been treated in detail, providing possible ranges of interface concentrations for a given growth condition. Use of these treatments for analytical description of specific single-phase dendritic and cellular operating point selection, however, requires a model for solute partitioning under a given set of growth conditions. Therefore, analytical solute trapping models which describe the chemical partitioning as a function of steady state interface velocities have been developed and widely utilized in most of the theoretical investigations of rapid solidification. However, these solute trapping models are not rigorously verified due to the difficulty in experimentally measuring under rapid growth conditions. Moreover, since these solute trapping models include kinetic parameters which are difficult to directly measure from experiments, application of the solute trapping models or the associated analytic rapid solidification model is limited. These theoretical models for steady state rapid solidification which incorporate the solute trapping models do not describe the interdependency of solute diffusion, interface kinetics, and alloy thermodynamics. The phase-field approach allows calculating, spontaneously, the non-equilibrium growth effects of alloys and the associated time-dependent growth dynamics, without making the assumptions that solute partitioning is an explicit function of velocity, as is the current convention. In the research described here, by utilizing the phase-field model in the thin-interface limit, incorporating the anti-trapping current term, more quantitatively valid interface kinetics and solute diffusion across the interface are calculated. In order to sufficiently resolve the physical length scales (i.e. interface thickness and diffusion boundary length), grid spacings are continually adjusted in calculations. The full trajectories of transient planar growth dynamics under rapid directional solidification conditions with different pulling velocities are described. As a validation of a model, the predicted steady state conditions are consistent with the analytic approach for rapid growth. It was confirmed that rapid interface dynamics exhibits the abrupt acceleration of the planar front when the effect of the non-equilibrium solute partitioning at the interface becomes signi ficant. This is consistent with the previous linear stability analysis for the non-equilibrium interface dynamics. With an appropriate growth condition, the continuous oscillation dynamics was able to be simulated using continually adjusting grid spacings. This oscillatory dynamics including instantaneous jump of interface velocities are consistent with a previous phenomenological model by and a numerical investigation, which may cause the formation of banded structures. Additionally, the selection of the steady state growth dynamics in the highly undercooled melt is demonstrated. The transition of the growth morphology, interface velocity selection, and solute trapping phenomenon with increasing melt supersaturations was described by the phase-field simulation. The tip selection for the dendritic growth was consistent with Ivantsov's function, and the non-equilibrium chemical partitioning behavior shows good qualitative agreement with the Aziz's solute trapping model even though the model parameter(V D) remains as an arbitrary constant. This work is able to show the possibility of comprehensive description of rapid alloy growth over the entire time-dependent non-equilibrium phenomenon.« less

Low cost biosorbent "banana peel" for the removal of phenolic compounds from olive mill wastewater: kinetic and equilibrium studies.

PubMed

Achak, M; Hafidi, A; Ouazzani, N; Sayadi, S; Mandi, L

2009-07-15

The aim of this work is to determine the potential of application of banana peel as a biosorbent for removing phenolic compounds from olive mill wastewaters. The effect of adsorbent dosage, pH and contact time were investigated. The results showed that the increase in the banana peel dosage from 10 to 30 g/L significantly increased the phenolic compounds adsorption rates from 60 to 88%. Increase in the pH to above neutrality resulted in the increase in the phenolic compounds adsorption capacity. The adsorption process was fast, and it reached equilibrium in 3-h contact time. The Freundlich and Langmuir adsorption models were used for mathematical description of the adsorption equilibrium and it was found that experimental data fitted very well to both Freundlich and Langmuir models. Batch adsorption models, based on the assumption of the pseudo-first-order, pseudo-second-order and intraparticle diffusion mechanism, showed that kinetic data follow closely the pseudo-second-order than the pseudo-first-order and intraparticle diffusion. Desorption studies showed that low pH value was efficient for desorption of phenolic compounds. These results indicate clearly the efficiency of banana peel as a low-cost solution for olive mill wastewaters treatment and give some preliminary elements for the comprehension of the interactions between banana peel as a bioadsorbent and the very polluting compounds from the olive oil industry.

Phase Transitions and Scaling in Systems Far from Equilibrium

NASA Astrophysics Data System (ADS)

Täuber, Uwe C.

2017-03-01

Scaling ideas and renormalization group approaches proved crucial for a deep understanding and classification of critical phenomena in thermal equilibrium. Over the past decades, these powerful conceptual and mathematical tools were extended to continuous phase transitions separating distinct nonequilibrium stationary states in driven classical and quantum systems. In concordance with detailed numerical simulations and laboratory experiments, several prominent dynamical universality classes have emerged that govern large-scale, long-time scaling properties both near and far from thermal equilibrium. These pertain to genuine specific critical points as well as entire parameter space regions for steady states that display generic scale invariance. The exploration of nonstationary relaxation properties and associated physical aging scaling constitutes a complementary potent means to characterize cooperative dynamics in complex out-of-equilibrium systems. This review describes dynamic scaling features through paradigmatic examples that include near-equilibrium critical dynamics, driven lattice gases and growing interfaces, correlation-dominated reaction-diffusion systems, and basic epidemic models.

Stem Hydraulic Conductivity depends on the Pressure at Which It Is Measured and How This Dependence Can Be Used to Assess the Tempo of Bubble Pressurization in Recently Cavitated Vessels1[OPEN

PubMed Central

Liu, Jinyu; Tyree, Melvin T.

2015-01-01

Cavitation of water in xylem vessels followed by embolism formation has been authenticated for more than 40 years. Embolism formation involves the gradual buildup of bubble pressure (air) to atmospheric pressure as demanded by Henry’s law of equilibrium between gaseous and liquid phases. However, the tempo of pressure increase has not been quantified. In this report, we show that the rate of pressurization of embolized vessels is controlled by both fast and slow kinetics, where both tempos are controlled by diffusion but over different spatial scales. The fast tempo involves a localized diffusion from endogenous sources: over a distance of about 0.05 mm from water-filled wood to the nearest embolized vessels; this process, in theory, should take <2 min. The slow tempo involves diffusion of air from exogenous sources (outside the stem). The latter diffusion process is slower because of the increased distance of diffusion of up to 4 mm. Radial diffusion models and experimental measurements both confirm that the average time constant is >17 h, with complete equilibrium requiring 1 to 2 d. The implications of these timescales for the standard methods of measuring percentage loss of hydraulic conductivity are discussed in theory and deserve more research in future. PMID:26468516

Stem Hydraulic Conductivity depends on the Pressure at Which It Is Measured and How This Dependence Can Be Used to Assess the Tempo of Bubble Pressurization in Recently Cavitated Vessels.

PubMed

Wang, Yujie; Liu, Jinyu; Tyree, Melvin T

2015-12-01

Cavitation of water in xylem vessels followed by embolism formation has been authenticated for more than 40 years. Embolism formation involves the gradual buildup of bubble pressure (air) to atmospheric pressure as demanded by Henry's law of equilibrium between gaseous and liquid phases. However, the tempo of pressure increase has not been quantified. In this report, we show that the rate of pressurization of embolized vessels is controlled by both fast and slow kinetics, where both tempos are controlled by diffusion but over different spatial scales. The fast tempo involves a localized diffusion from endogenous sources: over a distance of about 0.05 mm from water-filled wood to the nearest embolized vessels; this process, in theory, should take <2 min. The slow tempo involves diffusion of air from exogenous sources (outside the stem). The latter diffusion process is slower because of the increased distance of diffusion of up to 4 mm. Radial diffusion models and experimental measurements both confirm that the average time constant is >17 h, with complete equilibrium requiring 1 to 2 d. The implications of these timescales for the standard methods of measuring percentage loss of hydraulic conductivity are discussed in theory and deserve more research in future. © 2015 American Society of Plant Biologists. All Rights Reserved.

Oxygen exchange at gas/oxide interfaces: how the apparent activation energy of the surface exchange coefficient depends on the kinetic regime.

PubMed

Fielitz, Peter; Borchardt, Günter

2016-08-10

In the dedicated literature the oxygen surface exchange coefficient KO and the equilibrium oxygen exchange rate [Fraktur R] are considered to be directly proportional to each other regardless of the experimental circumstances. Recent experimental observations, however, contradict the consequences of this assumption. Most surprising is the finding that the apparent activation energy of KO depends dramatically on the kinetic regime in which it has been determined, i.e. surface exchange controlled vs. mixed or diffusion controlled. This work demonstrates how the diffusion boundary condition at the gas/solid interface inevitably entails a correlation between the oxygen surface exchange coefficient KO and the oxygen self-diffusion coefficient DO in the bulk ("on top" of the correlation between KO and [Fraktur R] for the pure surface exchange regime). The model can thus quantitatively explain the range of apparent activation energies measured in the different regimes: in the surface exchange regime the apparent activation energy only contains the contribution of the equilibrium exchange rate, whereas in the mixed or in the diffusion controlled regime the contribution of the oxygen self-diffusivity has also to be taken into account, which may yield significantly higher apparent activation energies and simultaneously quantifies the correlation KO ∝ DO(1/2) observed for a large number of oxides in the mixed or diffusion controlled regime, respectively.

Dynamical behaviours and control measures of rumour-spreading model with consideration of network topology

NASA Astrophysics Data System (ADS)

Zhu, Linhe; Zhao, Hongyong

2017-07-01

A series of online rumours have seriously influenced the normal production and living of people. This paper aims to study the combined impact of psychological factor, propagation delay, network topology and control strategy on rumour diffusion over the online social networks. Based on an online social network, which is seen as a scale-free network, we model the spread of rumours by using a delayed SIS (Susceptible and Infected) epidemic-like model with consideration of psychological factor and network topology. First, through theoretical analysis, we illustrate the boundedness of the density of rumour-susceptible individuals and rumour-infected individuals. Second, we obtain the basic reproduction number R0 and prove the stability of the non-rumour equilibrium point and the rumour-spreading equilibrium point. Third, control strategies, such as uniform immunisation control, proportional immunisation control, targeted immunisation control and optimum control, are put forward to restrain rumour diffusion. Meanwhile, we have compared the differences of these control strategies. Finally, some representative numerical simulations are performed to verify the theoretical analysis results.

Induced-Charge Enhancement of the Diffusion Potential in Membranes with Polarizable Nanopores

NASA Astrophysics Data System (ADS)

Ryzhkov, I. I.; Lebedev, D. V.; Solodovnichenko, V. S.; Shiverskiy, A. V.; Simunin, M. M.

2017-12-01

When a charged membrane separates two salt solutions of different concentrations, a potential difference appears due to interfacial Donnan equilibrium and the diffusion junction. Here, we report a new mechanism for the generation of a membrane potential in polarizable conductive membranes via an induced surface charge. It results from an electric field generated by the diffusion of ions with different mobilities. For uncharged membranes, this effect strongly enhances the diffusion potential and makes it highly sensitive to the ion mobilities ratio, electrolyte concentration, and pore size. Theoretical predictions on the basis of the space-charge model extended to polarizable nanopores fully agree with experimental measurements in KCl and NaCl aqueous solutions.

Detection of Extraplanar Diffuse Ionized Gas in M83

NASA Astrophysics Data System (ADS)

Boettcher, Erin; Gallagher, J. S., III; Zweibel, Ellen G.

2017-08-01

We present the first kinematic study of extraplanar diffuse ionized gas (eDIG) in the nearby, face-on disk galaxy M83 using optical emission-line spectroscopy from the Robert Stobie Spectrograph on the Southern African Large Telescope. We use a Markov Chain Monte Carlo method to decompose the [N II]λ λ 6548, 6583, Hα, and [S II]λ λ 6717, 6731 emission lines into H II region and diffuse ionized gas emission. Extraplanar, diffuse gas is distinguished by its emission-line ratios ([N II]λ6583/Hα ≳ 1.0) and its rotational velocity lag with respect to the disk ({{Δ }}v=-24 km s-1 in projection). With interesting implications for isotropy, the velocity dispersion of the diffuse gas, σ =96 km s-1, is a factor of a few higher in M83 than in the Milky Way and nearby, edge-on disk galaxies. The turbulent pressure gradient is sufficient to support the eDIG layer in dynamical equilibrium at an electron scale height of {h}z=1 kpc. However, this dynamical equilibrium model must be finely tuned to reproduce the rotational velocity lag. There is evidence of local bulk flows near star-forming regions in the disk, suggesting that the dynamical state of the gas may be intermediate between a dynamical equilibrium and a galactic fountain flow. As one of the first efforts to study eDIG kinematics in a face-on galaxy, this study demonstrates the feasibility of characterizing the radial distribution, bulk velocities, and vertical velocity dispersions in low-inclination systems. Based on observations made with the Southern African Large Telescope (SALT) under program 2015-2-SCI-004 (PI: E. Boettcher).

Transport of neutral solute across articular cartilage: the role of zonal diffusivities.

PubMed

Arbabi, V; Pouran, B; Weinans, H; Zadpoor, A A

2015-07-01

Transport of solutes through diffusion is an important metabolic mechanism for the avascular cartilage tissue. Three types of interconnected physical phenomena, namely mechanical, electrical, and chemical, are all involved in the physics of transport in cartilage. In this study, we use a carefully designed experimental-computational setup to separate the effects of mechanical and chemical factors from those of electrical charges. Axial diffusion of a neutral solute Iodixanol into cartilage was monitored using calibrated microcomputed tomography micro-CT images for up to 48 hr. A biphasic-solute computational model was fitted to the experimental data to determine the diffusion coefficients of cartilage. Cartilage was modeled either using one single diffusion coefficient (single-zone model) or using three diffusion coefficients corresponding to superficial, middle, and deep cartilage zones (multizone model). It was observed that the single-zone model cannot capture the entire concentration-time curve and under-predicts the near-equilibrium concentration values, whereas the multizone model could very well match the experimental data. The diffusion coefficient of the superficial zone was found to be at least one order of magnitude larger than that of the middle zone. Since neutral solutes were used, glycosaminoglycan (GAG) content cannot be the primary reason behind such large differences between the diffusion coefficients of the different cartilage zones. It is therefore concluded that other features of the different cartilage zones such as water content and the organization (orientation) of collagen fibers may be enough to cause large differences in diffusion coefficients through the cartilage thickness.

Efecto de la difusión y la velocidad en la ionización del átomo de Carbono

NASA Astrophysics Data System (ADS)

Rovira, M. G.; Fontenla, J. M.

The equations of statistical equilibrium for all ionization states of the atom are solved. The effects of diffusion and center of mass velocity are included. In order to estimate the modifications of the ionization curves, they were applied to the Carbon atom. To solve these equations, solar prominences' models obtained in a previous paper were adopted. They were extended to reach a temperature of 1.5 × 106 K and the complete model of the prominence was calculated. Ionization curves for different values of velocity, diffusion and medium models were obtained. The different models represent structures with different densities. Considerable modifications due to these effects are found.

Unimolecular diffusion-mediated reactions with a nonrandom time-modulated absorbing barrier

NASA Technical Reports Server (NTRS)

Bashford, D.; Weaver, D. L.

1986-01-01

A diffusion-reaction model with time-dependent reactivity is formulated and applied to unimolecular reactions. The model is solved exactly numerically and approximately analytically for the unreacted fraction as a function of time. It is shown that the approximate analytical solution is valid even when the system is far from equilibrium, and when the reactivity probability is more complicated than a square-wave function of time. A discussion is also given of an approach to problems of this type using a stochastically fluctuating reactivity, and the first-passage time for a particular example is derived.

Molecular-dynamics simulation of mutual diffusion in nonideal liquid mixtures

NASA Astrophysics Data System (ADS)

Rowley, R. L.; Stoker, J. M.; Giles, N. F.

1991-05-01

The mutual-diffusion coefficients, D 12, of n-hexane, n-heptane, and n-octane in chloroform were modeled using equilibrium molecular-dynamics (MD) simulations of simple Lennard-Jones (LJ) fluids. Pure-component LJ parameters were obtained by comparison of simulations to experimental self-diffusion coefficients. While values of “effective” LJ parameters are not expected to simulate accurately diverse thermophysical properties over a wide range of conditions, it was recently shown that effective parameters obtained from pure self-diffusion coefficients can accurately model mutual diffusion in ideal, liquid mixtures. In this work, similar simulations are used to model diffusion in nonideal mixtures. The same combining rules used in the previous study for the cross-interaction parameters were found to be adequate to represent the composition dependence of D 12. The effect of alkane chain length on D 12 is also correctly predicted by the simulations. A commonly used assumption in empirical correlations of D 12, that its kinetic portion is a simple, compositional average of the intradiffusion coefficients, is inconsistent with the simulation results. In fact, the value of the kinetic portion of D 12 was often outside the range of values bracketed by the two intradiffusion coefficients for the nonideal system modeled here.

Comparison of fluid neutral models for one-dimensional plasma edge modeling with a finite volume solution of the Boltzmann equation

DOE Office of Scientific and Technical Information (OSTI.GOV)

Horsten, N., E-mail: niels.horsten@kuleuven.be; Baelmans, M.; Dekeyser, W.

2016-01-15

We derive fluid neutral approximations for a simplified 1D edge plasma model, suitable to study the neutral behavior close to the target of a nuclear fusion divertor, and compare its solutions to the solution of the corresponding kinetic Boltzmann equation. The plasma is considered as a fixed background extracted from a detached 2D simulation. We show that the Maxwellian equilibrium distribution is already obtained very close to the target, justifying the use of a fluid approximation. We compare three fluid neutral models: (i) a diffusion model; (ii) a pressure-diffusion model (i.e., a combination of a continuity and momentum equation) assumingmore » equal neutral and ion temperatures; and (iii) the pressure-diffusion model coupled to a neutral energy equation taking into account temperature differences between neutrals and ions. Partial reflection of neutrals reaching the boundaries is included in both the kinetic and fluid models. We propose two methods to obtain an incident neutral flux boundary condition for the fluid models: one based on a diffusion approximation and the other assuming a truncated Chapman-Enskog distribution. The pressure-diffusion model predicts the plasma sources very well. The diffusion boundary condition gives slightly better results overall. Although including an energy equation still improves the results, the assumption of equal ion and neutral temperature already gives a very good approximation.« less

PAINeT: An object-oriented software package for simulations of flow-field, transport coefficients and flux terms in non-equilibrium gas mixture flows

NASA Astrophysics Data System (ADS)

Istomin, V. A.

2018-05-01

The software package Planet Atmosphere Investigator of Non-equilibrium Thermodynamics (PAINeT) has been devel-oped for studying the non-equilibrium effects associated with electronic excitation, chemical reactions and ionization. These studies are necessary for modeling process in shock tubes, in high enthalpy flows, in nozzles or jet engines, in combustion and explosion processes, in modern plasma-chemical and laser technologies. The advantages and possibilities of the package implementation are stated. Within the framework of the package implementation, based on kinetic theory approximations (one-temperature and state-to-state approaches), calculations are carried out, and the limits of applicability of a simplified description of shock-heated air flows and any other mixtures chosen by the user are given. Using kinetic theory algorithms, a numerical calculation of the heat fluxes and relaxation terms can be performed, which is necessary for further comparison of engineering simulation with experi-mental data. The influence of state-to-state distributions over electronic energy levels on the coefficients of thermal conductivity, diffusion, heat fluxes and diffusion velocities of the components of various gas mixtures behind shock waves is studied. Using the software package the accuracy of different approximations of the kinetic theory of gases is estimated. As an example state-resolved atomic ionized mixture of N/N+/O/O+/e- is considered. It is shown that state-resolved diffusion coefficients of neutral and ionized species vary from level to level. Comparing results of engineering applications with those given by PAINeT, recommendations for adequate models selection are proposed.

Measurement of diffusion coefficients important in modeling the absorption rate of carbon dioxide into aqueous N-methyldiethanolamine

DOE Office of Scientific and Technical Information (OSTI.GOV)

Rowley, R.L.; Adams, M.E.; Marshall, T.L.

1997-03-01

Natural gas processors use amine treating processes to remove the acid gases H{sub 2}S and CO{sub 2} from gas streams. Absorption rates of gaseous CO{sub 2} into aqueous N-methyldiethanolamine (MDEA) solutions were measured in a quiescent, inverted-tube diffusiometer by monitoring the rate of pressure drop. The absorption rate was found to be insensitive to the diffusion coefficient of CO{sub 2} in solution but very sensitive to the diffusion rate of bicarbonate and protonated MDEA ions. Evidence also suggested that chemical reaction equilibrium is rapid relative to diffusion. A numerical model was developed on the basis of these observations. The modelmore » was used to regress diffusion coefficients of bicarbonate and protonated amine, which must be equivalent by electroneutrality arguments, from measured absorption rates. Complete modeling of the absorption process also required data for the diffusion coefficient of MDEA in water. These were measured using a Taylor dispersion apparatus. CO{sub 2} absorption rates and diffusion coefficients of bicarbonate and protonated MDEA were obtained at 298.2 K and 318.2 K in solutions containing 20, 35, and 50 mass % MDEA in water.« less

Removing polycyclic aromatic hydrocarbons from water using granular activated carbon: kinetic and equilibrium adsorption studies.

PubMed

Eeshwarasinghe, Dinushika; Loganathan, Paripurnanda; Kalaruban, Mahatheva; Sounthararajah, Danious Pratheep; Kandasamy, Jaya; Vigneswaran, Saravanamuthu

2018-05-01

Polycyclic aromatic hydrocarbons (PAHs) constitute a group of highly persistent, toxic and widespread environmental micropollutants that are increasingly found in water. A study was conducted in removing five PAHs, specifically naphthalene, acenaphthylene, acenaphthene, fluorene and phenanthrene, from water by adsorption onto granular activated carbon (GAC). The pseudo-first-order (PFO) model satisfactorily described the kinetics of adsorption of the PAHs. The Weber and Morris diffusion model's fit to the data showed that there were faster and slower rates of intra-particle diffusion probably into the mesopores and micropores of the GAC, respectively. These rates were negatively related to the molar volumes of the PAHs. Batch equilibrium adsorption data fitted well to the Langmuir, Freundlich and Dubinin-Radushkevich models, of which the Freundlich model exhibited the best fit. The adsorption affinities were related to the hydrophobicity of the PAHs as determined by the log K ow values. Free energies of adsorption calculated from the Dubinin-Radushkevich model and the satisfactory kinetic data fitting to the PFO model suggested physical adsorption of the PAHs. Adsorption of naphthalene, acenaphthylene and acenaphthene in fixed-bed columns containing a mixture of GAC (0.5 g) + sand (24.5 g) was satisfactorily simulated by the Thomas model.

The coupled effects of chemistry and diffusion on the stratospheric ozone reduction

NASA Technical Reports Server (NTRS)

Gupta, R. N.; Grose, W. L.

1980-01-01

The effect of diffusive-mixing on O3-depletion is estimated using the five-step chemistry model. The coupled treatment uses an equilibrium turbulence field and retains the key features of the kinetics while keeping the chemistry simple. Results indicate that those calculations of Hilst and Donaldson (1973) employing the conservation of NO2/NO will yield erroneous results, and it is found that any significant level of turbulence will reduce the severity of the NOx catalytic cycle for O3 destruction.

Finite-deformation phase-field chemomechanics for multiphase, multicomponent solids

NASA Astrophysics Data System (ADS)

Svendsen, Bob; Shanthraj, Pratheek; Raabe, Dierk

2018-03-01

The purpose of this work is the development of a framework for the formulation of geometrically non-linear inelastic chemomechanical models for a mixture of multiple chemical components diffusing among multiple transforming solid phases. The focus here is on general model formulation. No specific model or application is pursued in this work. To this end, basic balance and constitutive relations from non-equilibrium thermodynamics and continuum mixture theory are combined with a phase-field-based description of multicomponent solid phases and their interfaces. Solid phase modeling is based in particular on a chemomechanical free energy and stress relaxation via the evolution of phase-specific concentration fields, order-parameter fields (e.g., related to chemical ordering, structural ordering, or defects), and local internal variables. At the mixture level, differences or contrasts in phase composition and phase local deformation in phase interface regions are treated as mixture internal variables. In this context, various phase interface models are considered. In the equilibrium limit, phase contrasts in composition and local deformation in the phase interface region are determined via bulk energy minimization. On the chemical side, the equilibrium limit of the current model formulation reduces to a multicomponent, multiphase, generalization of existing two-phase binary alloy interface equilibrium conditions (e.g., KKS). On the mechanical side, the equilibrium limit of one interface model considered represents a multiphase generalization of Reuss-Sachs conditions from mechanical homogenization theory. Analogously, other interface models considered represent generalizations of interface equilibrium conditions consistent with laminate and sharp-interface theory. In the last part of the work, selected existing models are formulated within the current framework as special cases and discussed in detail.

Effect of particle- and specimen-level transport on product state in compacted-powder combustion synthesis and thermal debinding of polymers from molded powders

NASA Astrophysics Data System (ADS)

Oliveira, Amir Antonio Martins

The existence of large gradients within particles and fast temporal variations in the temperature and species concentration prevents the use of asymptotic approximations for the closure of the volume-averaged, specimen-level formulations. In this case a solution of the particle-level transport problem is needed to complement the specimen-level volume-averaged equations. Here, the use of combined specimen-level and particle-level models for transport in reactive porous media is demonstrated with two examples. For the gasless compacted-powder combustion synthesis, a three-scale model is developed. The specimen-level model is based on the volume-averaged equations for species and temperature. Local thermal equilibrium is assumed and the macroscopic mass diffusion and convection fluxes are neglected. The particle-level model accounts for the interparticle diffusion (i.e., the liquid migration from liquid-rich to liquid-lean regions) and the intraparticle diffusion (i.e., the species mass diffusion within the product layer formed at the surface of the high melting temperature component). It is found that the interparticle diffusion controls the extent of conversion to the final product, the maximum temperature, and to a smaller degree the propagation velocity. The intraparticle diffusion controls the propagation velocity and to a smaller degree the maximum temperature. The initial stages of thermal degradation of EVA from molded specimens is modeled using volume-averaged equations for the species and empirical models for the kinetics of the thermal degradation, the vapor-liquid equilibrium, and the diffusion coefficient of acetic acid in the molten polymer. It is assumed that a bubble forms when the partial pressure of acetic acid exceeds the external ambient pressure. It is found that the removal of acetic acid is characterized by two regimes, a pre-charge dominated regime and a generation dominated regime. For the development of an optimum debinding schedule, the heating rate is modulated to avoid bubbling, while the concentration and temperature follow the bubble-point line for the mixture. The results show a strong dependence on the presence of a pre-charge. It is shown that isolation of the pre-charge effect by using temporary lower heating rates results in an optimum schedule for which the process time is reduced by over 70% when compared to a constant heating rate schedule.

Modeling Secondary Organic Aerosols over Europe: Impact of Activity Coefficients and Viscosity

NASA Astrophysics Data System (ADS)

Kim, Y.; Sartelet, K.; Couvidat, F.

2014-12-01

Semi-volatile organic species (SVOC) can condense on suspended particulate materials (PM) in the atmosphere. The modeling of condensation/evaporation of SVOC often assumes that gas-phase and particle-phase concentrations are at equilibrium. However, recent studies show that secondary organic aerosols (SOA) may not be accurately represented by an equilibrium approach between the gas and particle phases, because organic aerosols in the particle phase may be very viscous. The condensation in the viscous liquid phase is limited by the diffusion from the surface of PM to its core. Using a surrogate approach to represent SVOC, depending on the user's choice, the secondary organic aerosol processor (SOAP) may assume equilibrium or model dynamically the condensation/evaporation between the gas and particle phases to take into account the viscosity of organic aerosols. The model is implemented in the three-dimensional chemistry-transport model of POLYPHEMUS. In SOAP, activity coefficients for organic mixtures can be computed using UNIFAC for short-range interactions between molecules and AIOMFAC to also take into account the effect of inorganic species on activity coefficients. Simulations over Europe are performed and POLYPHEMUS/SOAP is compared to POLYPHEMUS/H2O, which was previously used to model SOA using the equilibrium approach with activity coefficients from UNIFAC. Impacts of the dynamic approach on modeling SOA over Europe are evaluated. The concentrations of SOA using the dynamic approach are compared with those using the equilibrium approach. The increase of computational cost is also evaluated.

Dissociative diffusion mechanism in vacancy-rich materials according to mass action kinetics

DOE Office of Scientific and Technical Information (OSTI.GOV)

Biderman, N. J.; Sundaramoorthy, R.; Haldar, Pradeep

We conducted two sets of diffusion-reaction numerical simulations using a finite difference method (FDM) in order to investigate fast impurity diffusion via interstitial sites in vacancy-rich materials such as Cu(In,Ga)Se 2 (CIGS) and Cu 2ZnSn(S, Se) 4 (CZTSSe or CZTS) via the dissociative diffusion mechanism where the interstitial diffuser ultimately reacts with a vacancy to produce a substitutional. The first set of simulations extends the standard interstitial-limited dissociative diffusion theory to vacancy-rich material conditions where vacancies are annihilated in large amounts, introducing non-equilibrium vacancy concentration profiles. The second simulation set explores the vacancy-limited dissociative diffusion where impurity incorporation increases themore » equilibrium vacancy concentration. In addition to diffusion profiles of varying concentrations and shapes that were obtained in all simulations, some of the profiles can be fitted with the constant- and limited-source solutions of Fick’s second law despite the non-equilibrium condition induced by the interstitial-vacancy reaction. The first set of simulations reveals that the dissociative diffusion coefficient in vacancy-rich materials is inversely proportional to the initial vacancy concentration. In the second set of numerical simulations, impurity-induced changes in the vacancy concentration lead to distinctive diffusion profile shapes. The simulation results are also compared with published data of impurity diffusion in CIGS. And according to the characteristic properties of diffusion profiles from the two set of simulations, experimental detection of the dissociative diffusion mechanism in vacancy-rich materials may be possible.« less

Dissociative diffusion mechanism in vacancy-rich materials according to mass action kinetics

DOE PAGES

Biderman, N. J.; Sundaramoorthy, R.; Haldar, Pradeep; ...

2016-05-13

We conducted two sets of diffusion-reaction numerical simulations using a finite difference method (FDM) in order to investigate fast impurity diffusion via interstitial sites in vacancy-rich materials such as Cu(In,Ga)Se 2 (CIGS) and Cu 2ZnSn(S, Se) 4 (CZTSSe or CZTS) via the dissociative diffusion mechanism where the interstitial diffuser ultimately reacts with a vacancy to produce a substitutional. The first set of simulations extends the standard interstitial-limited dissociative diffusion theory to vacancy-rich material conditions where vacancies are annihilated in large amounts, introducing non-equilibrium vacancy concentration profiles. The second simulation set explores the vacancy-limited dissociative diffusion where impurity incorporation increases themore » equilibrium vacancy concentration. In addition to diffusion profiles of varying concentrations and shapes that were obtained in all simulations, some of the profiles can be fitted with the constant- and limited-source solutions of Fick’s second law despite the non-equilibrium condition induced by the interstitial-vacancy reaction. The first set of simulations reveals that the dissociative diffusion coefficient in vacancy-rich materials is inversely proportional to the initial vacancy concentration. In the second set of numerical simulations, impurity-induced changes in the vacancy concentration lead to distinctive diffusion profile shapes. The simulation results are also compared with published data of impurity diffusion in CIGS. And according to the characteristic properties of diffusion profiles from the two set of simulations, experimental detection of the dissociative diffusion mechanism in vacancy-rich materials may be possible.« less

Kinetics and equilibrium modelling of lead uptake by algae Gelidium and algal waste from agar extraction industry.

PubMed

Vilar, Vítor J P; Botelho, Cidália M S; Boaventura, Rui A R

2007-05-08

Pb(II) biosorption onto algae Gelidium, algal waste from agar extraction industry and a composite material was studied. Discrete and continuous site distribution models were used to describe the biosorption equilibrium at different pH (5.3, 4 and 3), considering competition among Pb(II) ions and protons. The affinity distribution function of Pb(II) on the active sites was calculated by the Sips distribution. The Langmuir equilibrium constant was compared with the apparent affinity calculated by the discrete model, showing higher affinity for lead ions at higher pH values. Kinetic experiments were conducted at initial Pb(II) concentrations of 29-104 mgl(-1) and data fitted to pseudo-first Lagergren and second-order models. The adsorptive behaviour of biosorbent particles was modelled using a batch mass transfer kinetic model, which successfully predicts Pb(II) concentration profiles at different initial lead concentration and pH, and provides significant insights on the biosorbents performance. Average values of homogeneous diffusivity, D(h), are 3.6 x 10(-8); 6.1 x 10(-8) and 2.4 x 10(-8)cm(2)s(-1), respectively, for Gelidium, algal waste and composite material. The concentration of lead inside biosorbent particles follows a parabolic profile that becomes linear near equilibrium.

Geochemical modeling of leaching of Ca, Mg, Al, and Pb from cementitious waste forms

DOE Office of Scientific and Technical Information (OSTI.GOV)

Martens, E., E-mail: evelien.martens@csiro.a; Jacques, D.; Van Gerven, T.

2010-08-15

Results from extraction tests on cement-waste samples were simulated with a thermodynamic equilibrium model using a consistent database, to which lead data were added. Subsequent diffusion tests were modeled by means of a 3D diffusive transport model combined with the geochemical model derived from the extraction tests. Modeling results of the leached major element concentrations for both uncarbonated and (partially) carbonated samples agreed well with the extraction test using the set of pure minerals and solid solutions present in the database. The observed decrease in Ca leaching with increasing carbonation level was qualitatively predicted. Simulations also revealed that Pb leachingmore » is not controlled by dissolution/precipitation only. The addition of the calcite-cerrusite solid solution and adsorption reactions on amorphous Fe- and Al-oxides improved the predictions and are considered to control the Pb leaching during the extractions tests. The dynamic diffusive leaching tests were appropriately modeled for Na, K, Ca and Pb.« less

Caliber Corrected Markov Modeling (C2M2): Correcting Equilibrium Markov Models.

PubMed

Dixit, Purushottam D; Dill, Ken A

2018-02-13

Rate processes are often modeled using Markov State Models (MSMs). Suppose you know a prior MSM and then learn that your prediction of some particular observable rate is wrong. What is the best way to correct the whole MSM? For example, molecular dynamics simulations of protein folding may sample many microstates, possibly giving correct pathways through them while also giving the wrong overall folding rate when compared to experiment. Here, we describe Caliber Corrected Markov Modeling (C 2 M 2 ), an approach based on the principle of maximum entropy for updating a Markov model by imposing state- and trajectory-based constraints. We show that such corrections are equivalent to asserting position-dependent diffusion coefficients in continuous-time continuous-space Markov processes modeled by a Smoluchowski equation. We derive the functional form of the diffusion coefficient explicitly in terms of the trajectory-based constraints. We illustrate with examples of 2D particle diffusion and an overdamped harmonic oscillator.

Plasma Equilibrium in a Magnetic Field with Stochastic Regions

DOE Office of Scientific and Technical Information (OSTI.GOV)

J.A. Krommes and Allan H. Reiman

The nature of plasma equilibrium in a magnetic field with stochastic regions is examined. It is shown that the magnetic differential equation that determines the equilibrium Pfirsch-Schluter currents can be cast in a form similar to various nonlinear equations for a turbulent plasma, allowing application of the mathematical methods of statistical turbulence theory. An analytically tractable model, previously studied in the context of resonance-broadening theory, is applied with particular attention paid to the periodicity constraints required in toroidal configurations. It is shown that even a very weak radial diffusion of the magnetic field lines can have a significant effect onmore » the equilibrium in the neighborhood of the rational surfaces, strongly modifying the near-resonant Pfirsch-Schluter currents. Implications for the numerical calculation of 3D equilibria are discussed« less

Use of a chemical equilibrium model to describe surface properties and uptake of cadmium, strontium, and lead by Chlorella (UTEX 252)

DOE Office of Scientific and Technical Information (OSTI.GOV)

Hassett, J.M.

1988-01-01

Metal-aquatic biota interactions are important in both natural and engineered systems. In this study, the uptake of cadmium, strontium and lead by the unicellular green alga Chlorella (UTEX 252) was investigated. Variables included metal concentration, pH, and ionic strength. Data gathered included dry weights (mg/l), cell counts (cells/ml), electrophoretic mobilities (EPMs, {mu}m/sec/V/cm) of metal-free and metal-exposed cells, and metal uptake - difference in concentration in filtrate of cell-metal and cell-free metal solutions. Derived data included cell volumes and surface area, uptake on a {mu}M/m{sup 2} basis, {zeta}-potentials, diffuse layer potentials and charge densities. Typical uptake values were 1.1, 5.2, andmore » 6 {mu}M/m{sup 2} for Cd, Pb, and Sr, respectively, from solutions of pH 6, ionic strength 0.02M, and metal concentration 10{sup {minus}4} M. Cell EPMs were insensitive to metal; under certain conditions, however, (pM > 4, pH > 8), cadmium exposed cells exhibited a reversal in surface charge from negative to positive. The chemical equilibrium model MINEQL1 + STANFORD was used to model algal surface properties and metal uptake. Input data included site pK, density, and {Delta}pK, estimated from EPM-pH data. The model described surface properties of Chlorella (UTEX 252) as judged by a close fit of {zeta}-potentials and model-derived diffuse layer potentials. Metal uptake was modelled by adjusting site density and/or metal-surface site equilibrium constants. Attempts to model surface properties and metal uptake simultaneously were not successful.« less

Behaviors and kinetics of toluene adsorption-desorption on activated carbons with varying pore structure.

PubMed

Yang, Xi; Yi, Honghong; Tang, Xiaolong; Zhao, Shunzheng; Yang, Zhongyu; Ma, Yueqiang; Feng, Tiecheng; Cui, Xiaoxu

2018-05-01

This work was undertaken to investigate the behaviors and kinetics of toluene adsorption and desorption on activated carbons with varying pore structure. Five kinds of activated carbon from different raw materials were selected. Adsorption isotherms and breakthrough curves for toluene were measured. Langmuir and Freundlich equations were fitted to the equilibrium data, and the Freundlich equation was more suitable for simulating toluene adsorption. The process consisted of monolayer, multilayer and partial active site adsorption types. The effect of the pore structure of the activated carbons on toluene adsorption capacity was investigated. The quasi-first-order model was more suitable for describing the process than the quasi-second-order model. The adsorption data was also modeled by the internal particle diffusion model and it was found that the adsorption process could be divided into three stages. In the external surface adsorption process, the rate depended on the specific surface area. During the particle diffusion stage, pore structure and volume were the main factors affecting adsorption rate. In the final equilibrium stage, the rate was determined by the ratio of meso- and macro-pores to total pore volume. The rate over the whole adsorption process was dominated by the toluene concentration. The desorption behavior of toluene on activated carbons was investigated, and the process was divided into heat and mass transfer parts corresponding to emission and diffusion mechanisms, respectively. Physical adsorption played the main role during the adsorption process. Copyright © 2017. Published by Elsevier B.V.

An experimental and modeling study of grain-scale uranium desorption from field-contaminated sediments and the potential influence of microporosity on mass-transfer

NASA Astrophysics Data System (ADS)

Stoliker, D.; Liu, C.; Kent, D. B.; Zachara, J. M.

2012-12-01

The aquifer below the 300-Area of the Hanford site (Richland, WA, USA) is plagued by a persistent plume of dissolved uranium (U(VI)) in excess of the Environmental Protection Agency drinking water maximum contamination level even after the removal of highly contaminated sediments. The aquifer sediments in the seasonally saturated lower vadose zone act as both a source and sink for uranium during stage changes in the nearby Columbia River. Diffusion limitation of uranium mass-transfer within these sediments has been cited as a potential cause of the plume's persistence. Equilibrium U(VI) sorption is a strong function of variable chemical conditions, especially carbonate, hydrogen, and uranyl ion activities. Field-contaminated sediments from the site require up to 1,000 hours to reach equilibrium in static batch reactors. Increases in U(VI) concentrations over longer time-scales result from changes in chemical conditions, which drive reactions with sediments that favor U(VI) desorption. Grain-scale U(VI) sorption/desorption rates are slow, likely owing to diffusion of U(VI) and other solutes through intra-granular pore domains. In order to improve understanding of the impact of intra-granular diffusion and chemical reactions controlling grain-scale U(VI) release, experiments were conducted on individual particle size fractions of a <8 mm composite of field-contaminated, lower vadose zone sediments. For each size fraction, equilibrium U(VI) sorption/desorption in static batch reactors was well-described by surface complexation models over a range of chemical conditions applicable to the field site. Desorption rates from individual size fractions in flow-through batch reactors, examined under a single set of constant chemical conditions with multiple stop-flow events, were similar for all size fractions <2 mm. Kinetic U(VI) desorption in flow-through batch reactors was modeled using a multi-rate surface complexation approach, where sorption/desorption rates were assumed to be proportional to the displacement from equilibrium and multiple diffusion domains were described with a two-parameter lognormal distribution of mass-transfer rate coefficients. Parameters describing mass transfer were the same for all size fractions <2 mm but differed for the largest (2-8 mm) size fraction. The evolution of pH, along with dissolved cation and carbonate concentrations, was modeled using equilibrium cation exchange, rate-limited calcite dissolution, aerobic respiration, and silica dissolution. Desorption and chemical reaction models calibrated with individual size fractions predicted U(VI) and chemical composition as a function of time for the bulk sediment sample. Volumes of pores less than 2.4 nm, quantified using nitrogen adsorption-desorption isotherms, were the same for all size fractions < 2 mm, nearly double that of the 2-8 mm size fraction. Similarity in the observed pore volumes and multi-rate mass-transfer parameters across all size fractions <2 mm suggest the importance of pores in this size class in controlling slow grain-scale U(VI) desorption rates. Models like these provide a means for testing the influence of grain-scale mass-transfer on the persistence of U(VI) plume at the site.

Diffusion-model analysis of pPb and PbPb collisions at LHC energies

NASA Astrophysics Data System (ADS)

Schulz, P.; Wolschin, G.

2018-06-01

We present an analysis of centrality-dependent pseudorapidity distributions of produced charged hadrons in pPb and PbPb collisions at the Large Hadron Collider (LHC) energy of s NN = 5.02 TeV, and of minimum-bias pPb collisions at 8.16 TeV within the non-equilibrium-statistical relativistic diffusion model (RDM). In a three-source approach, the role of the fragmentation sources is emphasized. Together with the Jacobian transformation from rapidity to pseudorapidity and the limiting fragmentation conjecture, these are essential for modeling the centrality dependence. For central PbPb collisions, a prediction at the projected FCC energy of s NN = 39 TeV is made.

Glassy behaviour in simple kinetically constrained models: topological networks, lattice analogues and annihilation-diffusion

NASA Astrophysics Data System (ADS)

Sherrington, David; Davison, Lexie; Buhot, Arnaud; Garrahan, Juan P.

2002-02-01

We report a study of a series of simple model systems with only non-interacting Hamiltonians, and hence simple equilibrium thermodynamics, but with constrained dynamics of a type initially suggested by foams and idealized covalent glasses. We demonstrate that macroscopic dynamical features characteristic of real and more complex model glasses, such as two-time decays in energy and auto-correlation functions, arise from the dynamics and we explain them qualitatively and quantitatively in terms of annihilation-diffusion concepts and theory. The comparison is with strong glasses. We also consider fluctuation-dissipation relations and demonstrate subtleties of interpretation. We find no FDT breakdown when the correct normalization is chosen.

A Study of Interdiffusion in the Fe-C/Ti System Under Equilibrium and Nonequilibrium Conditions

NASA Astrophysics Data System (ADS)

Prasanthi, T. N.; Sudha, C.; Saroja, S.

2017-04-01

In the present study, diffusion behavior under equilibrium and nonequilibrium conditions in a Fe-C/Ti system is studied in the temperature range of 773 K to 1073 K (500 °C to 800 °C). A defect-free weld joint between mild steel (MS) (Fe-0.14 pct C) and Ti Grade 2 obtained by friction welding is diffusion annealed for various durations to study the interdiffusion behavior under equilibrium conditions, while an explosive clad joint is used to study interdiffusion under nonequilibrium conditions. From the elemental concentration profiles obtained across the MS-Ti interface using electron-probe microanalysis and imaging of the interface, the formation of distinct diffusion zones as a function of temperature and time is established. Concentration and temperature dependence of the interdiffusion coefficients ( D( c)) and activation energies are determined. Under equilibrium conditions, the change in molar volume with concentration shows a close match with the ideal Vegard's law, whereas a negative deviation is observed for nonequilibrium conditions. This deviation can be attributed to the formation of secondary phases, which, in turn, alters the D( c) values of diffusing species. Calculations showed that the D 0 and activation energy for interdiffusion under equilibrium is on the order of 10-11 m2/s and 147 kJ/mol, whereas it is far lower in the nonequilibrium case (10-10 m2/s and 117 kJ/mol) in the compositional range of 40 to 50 wt pct Fe, which also manifests as accelerated growth kinetics of the different diffusion zones.

On the time needed to reach an equilibrium structure of the radiation belts

DOE Office of Scientific and Technical Information (OSTI.GOV)

Ripoll, J. -F.; Loran, V.; Cunningham, Gregory Scott

In this paper, we complement the notion of equilibrium states of the radiation belts with a discussion on the dynamics and time needed to reach equilibrium. We solve for the equilibrium states obtained using 1D radial diffusion with recently developed hiss and chorus lifetimes at constant values of Kp = 1, 3 and 6. We find that the equilibrium states at moderately low Kp, when plotted vs L-shell (L) and energy (E), display the same interesting S-shape for the inner edge of the outer belt as recently observed by the Van Allen Probes. The S-shape is also produced as themore » radiation belts dynamically evolve toward the equilibrium state when initialized to simulate the buildup after a massive dropout or to simulate loss due to outward diffusion from a saturated state. Physically, this shape, intimately linked with the slot structure, is due to the dependence of electron loss rate (originating from wave-particle interactions) on both energy and L-shell. Equilibrium electron flux profiles are governed by the Biot number (τ Diffusion/τ loss), with large Biot number corresponding to low fluxes and low Biot number to large fluxes. The time it takes for the flux at a specific (L, E) to reach the value associated with the equilibrium state, starting from these different initial states, is governed by the initial state of the belts, the property of the dynamics (diffusion coefficients), and the size of the domain of computation. Its structure shows a rather complex scissor form in the (L, E) plane. The equilibrium value (phase space density or flux) is practically reachable only for selected regions in (L, E) and geomagnetic activity. Convergence to equilibrium requires hundreds of days in the inner belt for E > 300 keV and moderate Kp (≤3). It takes less time to reach equilibrium during disturbed geomagnetic conditions (Kp ≥ 3), when the system evolves faster. Restricting our interest to the slot region, below L = 4, we find that only small regions in (L, E) space can reach the equilibrium value: E ~ [200, 300] keV for L = [3.7, 4] at Kp = 1, E ~ [0.6, 1] MeV for L = [3, 4] at Kp = 3, and E ~ 300 keV for L = [3.5, 4] at Kp = 6 assuming no new incoming electrons.« less

On the time needed to reach an equilibrium structure of the radiation belts

DOE PAGES

Ripoll, J. -F.; Loran, V.; Cunningham, Gregory Scott; ...

2016-08-01

In this paper, we complement the notion of equilibrium states of the radiation belts with a discussion on the dynamics and time needed to reach equilibrium. We solve for the equilibrium states obtained using 1D radial diffusion with recently developed hiss and chorus lifetimes at constant values of Kp = 1, 3 and 6. We find that the equilibrium states at moderately low Kp, when plotted vs L-shell (L) and energy (E), display the same interesting S-shape for the inner edge of the outer belt as recently observed by the Van Allen Probes. The S-shape is also produced as themore » radiation belts dynamically evolve toward the equilibrium state when initialized to simulate the buildup after a massive dropout or to simulate loss due to outward diffusion from a saturated state. Physically, this shape, intimately linked with the slot structure, is due to the dependence of electron loss rate (originating from wave-particle interactions) on both energy and L-shell. Equilibrium electron flux profiles are governed by the Biot number (τ Diffusion/τ loss), with large Biot number corresponding to low fluxes and low Biot number to large fluxes. The time it takes for the flux at a specific (L, E) to reach the value associated with the equilibrium state, starting from these different initial states, is governed by the initial state of the belts, the property of the dynamics (diffusion coefficients), and the size of the domain of computation. Its structure shows a rather complex scissor form in the (L, E) plane. The equilibrium value (phase space density or flux) is practically reachable only for selected regions in (L, E) and geomagnetic activity. Convergence to equilibrium requires hundreds of days in the inner belt for E > 300 keV and moderate Kp (≤3). It takes less time to reach equilibrium during disturbed geomagnetic conditions (Kp ≥ 3), when the system evolves faster. Restricting our interest to the slot region, below L = 4, we find that only small regions in (L, E) space can reach the equilibrium value: E ~ [200, 300] keV for L = [3.7, 4] at Kp = 1, E ~ [0.6, 1] MeV for L = [3, 4] at Kp = 3, and E ~ 300 keV for L = [3.5, 4] at Kp = 6 assuming no new incoming electrons.« less

Reactive Gas transport in soil: Kinetics versus Local Equilibrium Approach

NASA Astrophysics Data System (ADS)

Geistlinger, Helmut; Jia, Ruijan

2010-05-01

Gas transport through the unsaturated soil zone was studied using an analytical solution of the gas transport model that is mathematically equivalent to the Two-Region model. The gas transport model includes diffusive and convective gas fluxes, interphase mass transfer between the gas and water phase, and biodegradation. The influence of non-equilibrium phenomena, spatially variable initial conditions, and transient boundary conditions are studied. The objective of this paper is to compare the kinetic approach for interphase mass transfer with the standard local equilibrium approach and to find conditions and time-scales under which the local equilibrium approach is justified. The time-scale of investigation was limited to the day-scale, because this is the relevant scale for understanding gas emission from the soil zone with transient water saturation. For the first time a generalized mass transfer coefficient is proposed that justifies the often used steady-state Thin-Film mass transfer coefficient for small and medium water-saturated aggregates of about 10 mm. The main conclusion from this study is that non-equilibrium mass transfer depends strongly on the temporal and small-scale spatial distribution of water within the unsaturated soil zone. For regions with low water saturation and small water-saturated aggregates (radius about 1 mm) the local equilibrium approach can be used as a first approximation for diffusive gas transport. For higher water saturation and medium radii of water-saturated aggregates (radius about 10 mm) and for convective gas transport, the non-equilibrium effect becomes more and more important if the hydraulic residence time and the Damköhler number decrease. Relative errors can range up to 100% and more. While for medium radii the local equilibrium approach describes the main features both of the spatial concentration profile and the time-dependence of the emission rate, it fails completely for larger aggregates (radius about 100 mm). From the comparative study of relevant scenarios with and without biodegradation it can be concluded that, under realistic field conditions, biodegradation within the immobile water phase is often mass-transfer limited and the local equilibrium approach assuming instantaneous mass transfer becomes rather questionable. References Geistlinger, H., Ruiyan Jia, D. Eisermann, and C.-F. Stange (2008): Spatial and temporal variability of dissolved nitrous oxide in near-surface groundwater and bubble-mediated mass transfer to the unsaturated zone, J. Plant Nutrition and Soil Science, in press. Geistlinger, H. (2009) Vapor transport in soil: concepts and mathematical description. In: Eds.: S. Saponari, E. Sezenna, and L. Bonoma, Vapor emission to outdoor air and enclosed spaces for human health risk assessment: Site characterization, monitoring, and modeling. Nova Science Publisher. Milano. Accepted for publication.

The efficiency of driving chemical reactions by a physical non-equilibrium is kinetically controlled.

PubMed

Göppel, Tobias; Palyulin, Vladimir V; Gerland, Ulrich

2016-07-27

An out-of-equilibrium physical environment can drive chemical reactions into thermodynamically unfavorable regimes. Under prebiotic conditions such a coupling between physical and chemical non-equilibria may have enabled the spontaneous emergence of primitive evolutionary processes. Here, we study the coupling efficiency within a theoretical model that is inspired by recent laboratory experiments, but focuses on generic effects arising whenever reactant and product molecules have different transport coefficients in a flow-through system. In our model, the physical non-equilibrium is represented by a drift-diffusion process, which is a valid coarse-grained description for the interplay between thermophoresis and convection, as well as for many other molecular transport processes. As a simple chemical reaction, we consider a reversible dimerization process, which is coupled to the transport process by different drift velocities for monomers and dimers. Within this minimal model, the coupling efficiency between the non-equilibrium transport process and the chemical reaction can be analyzed in all parameter regimes. The analysis shows that the efficiency depends strongly on the Damköhler number, a parameter that measures the relative timescales associated with the transport and reaction kinetics. Our model and results will be useful for a better understanding of the conditions for which non-equilibrium environments can provide a significant driving force for chemical reactions in a prebiotic setting.

Diffusion of innovations dynamics, biological growth and catenary function

NASA Astrophysics Data System (ADS)

Guseo, Renato

2016-12-01

The catenary function has a well-known role in determining the shape of chains and cables supported at their ends under the force of gravity. This enables design using a specific static equilibrium over space. Its reflected version, the catenary arch, allows the construction of bridges and arches exploiting the dual equilibrium property under uniform compression. In this paper, we emphasize a further connection with well-known aggregate biological growth models over time and the related diffusion of innovation key paradigms (e.g., logistic and Bass distributions over time) that determine self-sustaining evolutionary growth dynamics in naturalistic and socio-economic contexts. Moreover, we prove that the 'local entropy function', related to a logistic distribution, is a catenary and vice versa. This special invariance may be explained, at a deeper level, through the Verlinde's conjecture on the origin of gravity as an effect of the entropic force.

Non-Equilibrium Water-Glassy Polymer Dynamics

NASA Astrophysics Data System (ADS)

Davis, Eric; Minelli, Matteo; Baschetti, Marco; Sarti, Giulio; Elabd, Yossef

2012-02-01

For many applications (e.g., medical implants, packaging), an accurate assessment and fundamental understanding of the dynamics of water-glassy polymer interactions is of great interest. In this study, sorption and diffusion of pure water in several glassy polymers films, such as poly(styrene) (PS), poly(methyl methacrylate) (PMMA), poly(lactide) (PLA), were measured over a wide range of vapor activities and temperatures using several experimental techniques, including quartz spring microbalance (QSM), quartz crystal microbalance (QCM), and time-resolved Fourier transform infrared-attenuated total reflectance (FTIR-ATR) spectroscopy. Non-Fickian behavior (diffusion-relaxation phenomena) was observed by all three techniques, while FTIR-ATR spectroscopy also provides information about the distribution of the states of water and water transport mechanisms on a molecular-level. Specifically, the states of water are significantly different in PS compared to PMMA and PLA. Additionally, a purely predictive non-equilibrium lattice fluid (NELF) model was applied to predict the sorption isotherms of water in these glassy polymers.

Kinetics and equilibrium models for the sorption of tributyltin to nZnO, activated carbon and nZnO/activated carbon composite in artificial seawater.

PubMed

Ayanda, Olushola S; Fatoki, Olalekan S; Adekola, Folahan A; Ximba, Bhekumusa J

2013-07-15

The removal of tributyltin (TBT) from artificial seawater using nZnO, activated carbon and nZnO/activated carbon composite was systematically studied. The equilibrium and kinetics of adsorption were investigated in a batch adsorption system. Equilibrium adsorption data were analyzed using Langmuir, Freundlich, Temkin and Dubinin-Radushkevich (D-R) isotherm models. Pseudo first- and second-order, Elovich, fractional power and intraparticle diffusion models were applied to test the kinetic data. Thermodynamic parameters such as ΔG°, ΔS° and ΔH° were also calculated to understand the mechanisms of adsorption. Optimal conditions for the adsorption of TBT from artificial seawater were then applied to TBT removal from natural seawater. A higher removal efficiency of TBT (>99%) was obtained for the nZnO/activated carbon composite material and for activated carbon but not for nZnO. Copyright © 2013 Elsevier Ltd. All rights reserved.

Sodium Chloride Diffusion in Low-Acid Foods during Thermal Processing and Storage.

PubMed

Bornhorst, Ellen R; Tang, Juming; Sablani, Shyam S

2016-05-01

This study aimed at modeling sodium chloride (NaCl) diffusion in foods during thermal processing using analytical and numerical solutions and at investigating the changes in NaCl concentrations during storage after processing. Potato, radish, and salmon samples in 1% or 3% NaCl solutions were heated at 90, 105, or 121 °C for 5 to 240 min to simulate pasteurization and sterilization. Selected samples were stored at 4 or 22 °C for up to 28 d. Radish had the largest equilibrium NaCl concentrations and equilibrium distribution coefficients, but smallest effective diffusion coefficients, indicating that a greater amount of NaCl diffused into the radish at a slower rate. Effective diffusion coefficients determined using the analytical solution ranged from 0.2 × 10(-8) to 2.6 × 10(-8) m²/s. Numerical and analytical solutions showed good agreement with experimental data, with average coefficients of determination for samples in 1% NaCl at 121 °C of 0.98 and 0.95, respectively. During storage, food samples equilibrated to a similar NaCl concentration regardless of the thermal processing severity. The results suggest that sensory evaluation of multiphase (solid and liquid) products should occur at least 14 d after processing to allow enough time for the salt to equilibrate within the product. © 2016 Institute of Food Technologists®

Evolutionary model of an anonymous consumer durable market

NASA Astrophysics Data System (ADS)

Kaldasch, Joachim

2011-07-01

An analytic model is presented that considers the evolution of a market of durable goods. The model suggests that after introduction goods spread always according to a Bass diffusion. However, this phase will be followed by a diffusion process for durable consumer goods governed by a variation-selection-reproduction mechanism and the growth dynamics can be described by a replicator equation. The theory suggests that products play the role of species in biological evolutionary models. It implies that the evolution of man-made products can be arranged into an evolutionary tree. The model suggests that each product can be characterized by its product fitness. The fitness space contains elements of both sites of the market, supply and demand. The unit sales of products with a higher product fitness compared to the mean fitness increase. Durables with a constant fitness advantage replace other goods according to a logistic law. The model predicts in particular that the mean price exhibits an exponential decrease over a long time period for durable goods. The evolutionary diffusion process is directly related to this price decline and is governed by Gompertz equation. Therefore it is denoted as Gompertz diffusion. Describing the aggregate sales as the sum of first, multiple and replacement purchase the product life cycle can be derived. Replacement purchase causes periodic variations of the sales determined by the finite lifetime of the good (Juglar cycles). The model suggests that both, Bass- and Gompertz diffusion may contribute to the product life cycle of a consumer durable. The theory contains the standard equilibrium view of a market as a special case. It depends on the time scale, whether an equilibrium or evolutionary description is more appropriate. The evolutionary framework is used to derive also the size, growth rate and price distribution of manufacturing business units. It predicts that the size distribution of the business units (products) is lognormal, while the growth rates exhibit a Laplace distribution. Large price deviations from the mean price are also governed by a Laplace distribution (fat tails). These results are in agreement with empirical findings. The explicit comparison of the time evolution of consumer durables with empirical investigations confirms the close relationship between price decline and Gompertz diffusion, while the product life cycle can be described qualitatively for a long time period.

Spatiotemporal pattern in somitogenesis: a non-Turing scenario with wave propagation.

PubMed

Nagahara, Hiroki; Ma, Yue; Takenaka, Yoshiko; Kageyama, Ryoichiro; Yoshikawa, Kenichi

2009-08-01

Living organisms maintain their lives under far-from-equilibrium conditions by creating a rich variety of spatiotemporal structures in a self-organized manner, such as temporal rhythms, switching phenomena, and development of the body. In this paper, we focus on the dynamical process of morphogens in somitogenesis in mice where propagation of the gene expression level plays an essential role in creating the spatially periodic patterns of the vertebral columns. We present a simple discrete reaction-diffusion model which includes neighboring interaction through an activator, but not diffusion of an inhibitor. We can produce stationary periodic patterns by introducing the effect of spatial discreteness to the field. Based on the present model, we discuss the underlying physical principles that are independent of the details of biomolecular reactions. We also discuss the framework of spatial discreteness based on the reaction-diffusion model in relation to a cellular array, by comparison with an actual experimental observation.

Kinetics of CO2 diffusion in human carbonic anhydrase: a study using molecular dynamics simulations and the Markov-state model.

PubMed

Chen, Gong; Kong, Xian; Lu, Diannan; Wu, Jianzhong; Liu, Zheng

2017-05-10

Molecular dynamics (MD) simulations, in combination with the Markov-state model (MSM), were applied to probe CO 2 diffusion from an aqueous solution into the active site of human carbonic anhydrase II (hCA-II), an enzyme useful for enhanced CO 2 capture and utilization. The diffusion process in the hydrophobic pocket of hCA-II was illustrated in terms of a two-dimensional free-energy landscape. We found that CO 2 diffusion in hCA-II is a rate-limiting step in the CO 2 diffusion-binding-reaction process. The equilibrium distribution of CO 2 shows its preferential accumulation within a hydrophobic domain in the protein core region. An analysis of the committors and reactive fluxes indicates that the main pathway for CO 2 diffusion into the active site of hCA-II is through a binding pocket where residue Gln 136 contributes to the maximal flux. The simulation results offer a new perspective on the CO 2 hydration kinetics and useful insights toward the development of novel biochemical processes for more efficient CO 2 sequestration and utilization.

Molecular model for the diffusion of associating telechelic polymer networks

NASA Astrophysics Data System (ADS)

Ramirez, Jorge; Dursch, Thomas; Olsen, Bradley

Understanding the mechanisms of motion and stress relaxation of associating polymers at the molecular level is critical for advanced technological applications such as enhanced oil-recovery, self-healing materials or drug delivery. In associating polymers, the strength and rates of association/dissociation of the reversible physical crosslinks govern the dynamics of the network and therefore all the macroscopic properties, like self-diffusion and rheology. Recently, by means of forced Rayleigh scattering experiments, we have proved that associating polymers of different architectures show super-diffusive behavior when the free motion of single molecular species is slowed down by association/dissociation kinetics. Here we discuss a new molecular picture for unentangled associating telechelic polymers that considers concentration, molecular weight, number of arms of the molecules and equilibrium and rate constants of association/dissociation. The model predicts super-diffusive behavior under the right combination of values of the parameters. We discuss some of the predictions of the model using scaling arguments, show detailed results from Brownian dynamics simulations of the FRS experiments, and attempt to compare the predictions of the model to experimental data.

Coarse-graining and hybrid methods for efficient simulation of stochastic multi-scale models of tumour growth.

PubMed

de la Cruz, Roberto; Guerrero, Pilar; Calvo, Juan; Alarcón, Tomás

2017-12-01

The development of hybrid methodologies is of current interest in both multi-scale modelling and stochastic reaction-diffusion systems regarding their applications to biology. We formulate a hybrid method for stochastic multi-scale models of cells populations that extends the remit of existing hybrid methods for reaction-diffusion systems. Such method is developed for a stochastic multi-scale model of tumour growth, i.e. population-dynamical models which account for the effects of intrinsic noise affecting both the number of cells and the intracellular dynamics. In order to formulate this method, we develop a coarse-grained approximation for both the full stochastic model and its mean-field limit. Such approximation involves averaging out the age-structure (which accounts for the multi-scale nature of the model) by assuming that the age distribution of the population settles onto equilibrium very fast. We then couple the coarse-grained mean-field model to the full stochastic multi-scale model. By doing so, within the mean-field region, we are neglecting noise in both cell numbers (population) and their birth rates (structure). This implies that, in addition to the issues that arise in stochastic-reaction diffusion systems, we need to account for the age-structure of the population when attempting to couple both descriptions. We exploit our coarse-graining model so that, within the mean-field region, the age-distribution is in equilibrium and we know its explicit form. This allows us to couple both domains consistently, as upon transference of cells from the mean-field to the stochastic region, we sample the equilibrium age distribution. Furthermore, our method allows us to investigate the effects of intracellular noise, i.e. fluctuations of the birth rate, on collective properties such as travelling wave velocity. We show that the combination of population and birth-rate noise gives rise to large fluctuations of the birth rate in the region at the leading edge of front, which cannot be accounted for by the coarse-grained model. Such fluctuations have non-trivial effects on the wave velocity. Beyond the development of a new hybrid method, we thus conclude that birth-rate fluctuations are central to a quantitatively accurate description of invasive phenomena such as tumour growth.

Coarse-graining and hybrid methods for efficient simulation of stochastic multi-scale models of tumour growth

NASA Astrophysics Data System (ADS)

de la Cruz, Roberto; Guerrero, Pilar; Calvo, Juan; Alarcón, Tomás

2017-12-01

The development of hybrid methodologies is of current interest in both multi-scale modelling and stochastic reaction-diffusion systems regarding their applications to biology. We formulate a hybrid method for stochastic multi-scale models of cells populations that extends the remit of existing hybrid methods for reaction-diffusion systems. Such method is developed for a stochastic multi-scale model of tumour growth, i.e. population-dynamical models which account for the effects of intrinsic noise affecting both the number of cells and the intracellular dynamics. In order to formulate this method, we develop a coarse-grained approximation for both the full stochastic model and its mean-field limit. Such approximation involves averaging out the age-structure (which accounts for the multi-scale nature of the model) by assuming that the age distribution of the population settles onto equilibrium very fast. We then couple the coarse-grained mean-field model to the full stochastic multi-scale model. By doing so, within the mean-field region, we are neglecting noise in both cell numbers (population) and their birth rates (structure). This implies that, in addition to the issues that arise in stochastic-reaction diffusion systems, we need to account for the age-structure of the population when attempting to couple both descriptions. We exploit our coarse-graining model so that, within the mean-field region, the age-distribution is in equilibrium and we know its explicit form. This allows us to couple both domains consistently, as upon transference of cells from the mean-field to the stochastic region, we sample the equilibrium age distribution. Furthermore, our method allows us to investigate the effects of intracellular noise, i.e. fluctuations of the birth rate, on collective properties such as travelling wave velocity. We show that the combination of population and birth-rate noise gives rise to large fluctuations of the birth rate in the region at the leading edge of front, which cannot be accounted for by the coarse-grained model. Such fluctuations have non-trivial effects on the wave velocity. Beyond the development of a new hybrid method, we thus conclude that birth-rate fluctuations are central to a quantitatively accurate description of invasive phenomena such as tumour growth.

Swelling and gas release in oxide fuels during fast temperature transients

NASA Astrophysics Data System (ADS)

Dollins, C. C.; Jursich, M.

1982-05-01

A previously reported intergranular swelling and gas release model for oxide fuels has been modified to predict fission gas behavior during fast temperature transients. Under steady state or slowly varying conditions it has been assumed in the previous model that the pressure caused by the fission gas within the gas bubbles is in equilibrium with the surface tension of the bubbles. During a fast transient, however, net vacancy migration to the bubbles may be insufficient to maintain this equilibrium. In order to ascertain the net vacancy flow, it is necessary to model the point defect behavior in the fuel. Knowing the net flow of vacancies to the bubble and the bubble size, the bubble diffusivity can be determined and the long range migration of the gas out of the fuel can be calculated. The model has also been modified to allow release of all the gas on the grain boundaries during a fast temperature transient. The gas release predicted by the revised model shows good agreement to fast transient gas release data from an EBR-II TREAT H-3 (Transient Reactor Test Facility) test. Agreement has also been obtained between predictions using the model and gas release data obtained by Argonne National Laboratory from out-of-reactor transient heating experiments on irradiated UO 2. It was found necessary to increase the gas bubble diffusivity used in the model by a factor of thirty during the transient to provide agreement between calculations and measurements. Other workers have also found that such an increase is necessary for agreement and attribute the increased diffusivity to yielding at the bubble surface due to the increased pressure.

Numerical modeling of sorption kinetics of organic compounds to soil and sediment particles

NASA Astrophysics Data System (ADS)

Wu, Shian-chee; Gschwend, Phillip M.

1988-08-01

A numerical model is developed to simulate hydrophobic organic compound sorption kinetics, based on a retarded intraaggregate diffusion conceptualization of this solid-water exchange process. This model was used to ascertain the sensitivity of the sorption process for various sorbates to nonsteady solution concentrations and to polydisperse soil or sediment aggregate particle size distributions. Common approaches to modeling sorption kinetics amount to simplifications of our model and appear justified only when (1) the concentration fluctuations occur on a time scale which matches the sorption timescale of interest and (2) the particle size distribution is relatively narrow. Finally, a means is provided to estimate the extent of approach of a sorbing system to equilibrium as a function of aggregate size, chemical diffusivity and hydrophobicity, and system solids concentration.

Renormalization group analysis of anisotropic diffusion in turbulent shear flows

NASA Technical Reports Server (NTRS)

Rubinstein, Robert; Barton, J. Michael

1991-01-01

The renormalization group is applied to compute anisotropic corrections to the scalar eddy diffusivity representation of turbulent diffusion of a passive scalar. The corrections are linear in the mean velocity gradients. All model constants are computed theoretically. A form of the theory valid at arbitrary Reynolds number is derived. The theory applies only when convection of the velocity-scalar correlation can be neglected. A ratio of diffusivity components, found experimentally to have a nearly constant value in a variety of shear flows, is computed theoretically for flows in a certain state of equilibrium. The theoretical value is well within the fairly narrow range of experimentally observed values. Theoretical predictions of this diffusivity ratio are also compared with data from experiments and direct numerical simulations of homogeneous shear flows with constant velocity and scalar gradients.

Oxygen self-diffusion mechanisms in monoclinic Zr O2 revealed and quantified by density functional theory, random walk analysis, and kinetic Monte Carlo calculations

NASA Astrophysics Data System (ADS)

Yang, Jing; Youssef, Mostafa; Yildiz, Bilge

2018-01-01

In this work, we quantify oxygen self-diffusion in monoclinic-phase zirconium oxide as a function of temperature and oxygen partial pressure. A migration barrier of each type of oxygen defect was obtained by first-principles calculations. Random walk theory was used to quantify the diffusivities of oxygen interstitials by using the calculated migration barriers. Kinetic Monte Carlo simulations were used to calculate diffusivities of oxygen vacancies by distinguishing the threefold- and fourfold-coordinated lattice oxygen. By combining the equilibrium defect concentrations obtained in our previous work together with the herein calculated diffusivity of each defect species, we present the resulting oxygen self-diffusion coefficients and the corresponding atomistically resolved transport mechanisms. The predicted effective migration barriers and diffusion prefactors are in reasonable agreement with the experimentally reported values. This work provides insights into oxygen diffusion engineering in Zr O2 -related devices and parametrization for continuum transport modeling.

Adsorption of methylene blue onto activated carbon produced from tea (Camellia sinensis L.) seed shells: kinetics, equilibrium, and thermodynamics studies.

PubMed

Gao, Jun-Jie; Qin, Ye-Bo; Zhou, Tao; Cao, Dong-Dong; Xu, Ping; Hochstetter, Danielle; Wang, Yue-Fei

2013-07-01

Tea (Camellia sinensis L.) seed shells, the main byproduct of the manufacture of tea seed oil, were used as precursors for the preparation of tea activated carbon (TAC) in the present study. A high yield (44.1%) of TAC was obtained from tea seed shells via a one-step chemical method using ZnCl2 as an agent. The Brunauer-Emmett-Teller (BET) surface area and the total pore volumes of the obtained TAC were found to be 1530.67 mg(2)/g and 0.7826 cm(3)/g, respectively. The equilibrium adsorption results were complied with Langmuir isotherm model and its maximum monolayer adsorption capacity was 324.7 mg/g for methylene blue. Adsorption kinetics studies indicated that the pseudo-second-order model yielded the best fit for the kinetic data. An intraparticle diffusion model suggested that the intraparticle diffusion was not the only rate-controlling step. Thermodynamics studies revealed the spontaneous and exothermic nature of the sorption process. These results indicate that tea seed shells could be utilized as a renewable resource to develop activated carbon which is a potential adsorbent for methylene blue.

Adsorption of methylene blue onto activated carbon produced from tea (Camellia sinensis L.) seed shells: kinetics, equilibrium, and thermodynamics studies*

PubMed Central

Gao, Jun-jie; Qin, Ye-bo; Zhou, Tao; Cao, Dong-dong; Xu, Ping; Hochstetter, Danielle; Wang, Yue-fei

2013-01-01

Tea (Camellia sinensis L.) seed shells, the main byproduct of the manufacture of tea seed oil, were used as precursors for the preparation of tea activated carbon (TAC) in the present study. A high yield (44.1%) of TAC was obtained from tea seed shells via a one-step chemical method using ZnCl2 as an agent. The Brunauer-Emmett-Teller (BET) surface area and the total pore volumes of the obtained TAC were found to be 1 530.67 mg2/g and 0.782 6 cm3/g, respectively. The equilibrium adsorption results were complied with Langmuir isotherm model and its maximum monolayer adsorption capacity was 324.7 mg/g for methylene blue. Adsorption kinetics studies indicated that the pseudo-second-order model yielded the best fit for the kinetic data. An intraparticle diffusion model suggested that the intraparticle diffusion was not the only rate-controlling step. Thermodynamics studies revealed the spontaneous and exothermic nature of the sorption process. These results indicate that tea seed shells could be utilized as a renewable resource to develop activated carbon which is a potential adsorbent for methylene blue. PMID:23825151

A Nonequilibrium Rate Formula for Collective Motions of Complex Molecular Systems

NASA Astrophysics Data System (ADS)

Yanao, Tomohiro; Koon, Wang Sang; Marsden, Jerrold E.

2010-09-01

We propose a compact reaction rate formula that accounts for a non-equilibrium distribution of residence times of complex molecules, based on a detailed study of the coarse-grained phase space of a reaction coordinate. We take the structural transition dynamics of a six-atom Morse cluster between two isomers as a prototype of multi-dimensional molecular reactions. Residence time distribution of one of the isomers shows an exponential decay, while that of the other isomer deviates largely from the exponential form and has multiple peaks. Our rate formula explains such equilibrium and non-equilibrium distributions of residence times in terms of the rates of diffusions of energy and the phase of the oscillations of the reaction coordinate. Rapid diffusions of energy and the phase generally give rise to the exponential decay of residence time distribution, while slow diffusions give rise to a non-exponential decay with multiple peaks. We finally make a conjecture about a general relationship between the rates of the diffusions and the symmetry of molecular mass distributions.

The Secondary Organic Aerosol Processor (SOAP v1.0) model: a unified model with different ranges of complexity based on the molecular surrogate approach

NASA Astrophysics Data System (ADS)

Couvidat, F.; Sartelet, K.

2014-01-01

The Secondary Organic Aerosol Processor (SOAP v1.0) model is presented. This model is designed to be modular with different user options depending on the computing time and the complexity required by the user. This model is based on the molecular surrogate approach, in which each surrogate compound is associated with a molecular structure to estimate some properties and parameters (hygroscopicity, absorption on the aqueous phase of particles, activity coefficients, phase separation). Each surrogate can be hydrophilic (condenses only on the aqueous phase of particles), hydrophobic (condenses only on the organic phase of particles) or both (condenses on both the aqueous and the organic phases of particles). Activity coefficients are computed with the UNIFAC thermodynamic model for short-range interactions and with the AIOMFAC parameterization for medium and long-range interactions between electrolytes and organic compounds. Phase separation is determined by Gibbs energy minimization. The user can choose between an equilibrium and a dynamic representation of the organic aerosol. In the equilibrium representation, compounds in the particle phase are assumed to be at equilibrium with the gas phase. However, recent studies show that the organic aerosol (OA) is not at equilibrium with the gas phase because the organic phase could be semi-solid (very viscous liquid phase). The condensation or evaporation of organic compounds could then be limited by the diffusion in the organic phase due to the high viscosity. A dynamic representation of secondary organic aerosols (SOA) is used with OA divided into layers, the first layer at the center of the particle (slowly reaches equilibrium) and the final layer near the interface with the gas phase (quickly reaches equilibrium).

Kinetic, equilibrium and thermodynamic studies on sorption of uranium and thorium from aqueous solutions by a selective impregnated resin containing carminic acid.

PubMed

Rahmani-Sani, Abolfazl; Hosseini-Bandegharaei, Ahmad; Hosseini, Seyyed-Hossein; Kharghani, Keivan; Zarei, Hossein; Rastegar, Ayoob

2015-04-09

In this work, the removal of uranium and thorium ions from aqueous solutions was studied by solid-liquid extraction using an advantageous extractant-impregnated resin (EIR) prepared by loading carminic acid (CA) onto Amberlite XAD-16 resin beads. Batch sorption experiments using CA/XAD-16 beads for the removal of U(VI) and Th(IV) ions were carried out as a function of several parameters, like equilibration time, metal ion concentration, etc. The equilibrium data obtained from the sorption experiments were adjusted to the Langmuir isotherm model and the calculated maximum sorption capacities in terms of monolayer sorption were in agreement with those obtained from the experiments. The experimental data on the sorption behavior of both metal ions onto the EIR beads fitted well in both Bangham and intra-particle diffusion kinetic models, indicating that the intra-particle diffusion is the rate-controlling step. The thermodynamic studies at different temperatures revealed the feasibility and the spontaneous nature of the sorption process for both uranium and thorium ions. Copyright © 2014 Elsevier B.V. All rights reserved.

Removal of sulfur compounds from petroleum refinery wastewater through adsorption on modified activated carbon.

PubMed

Ben Hariz, Ichrak; Al Ayni, Foued; Monser, Lotfi

2014-01-01

The adsorption of sulfur compounds from petroleum refinery wastewater on a chemically modified activated carbon (MAC) was investigated. The modification technique (nitric acid, hydrogen peroxide and thermal modification) enhanced the removal capacity of carbon and therefore decreases cost-effective removal of sulfide from refinery wastewater. Adsorption equilibrium and kinetics data were determined for sulfur removal from real refinery wastewater. The data were evaluated according to several adsorption isotherm and kinetics models. The Freundlich isotherm fitted well with the equilibrium data of sulfur on different adsorbents, whereas the kinetics data were best fitted by the pseudo-second-order model. Insights of sulfide removal mechanisms indicated that the sorption was controlled through the intraparticle diffusion mechanism with a significant contribution of film diffusion. The MAC adsorbent was found to have an effective removal capacity of approximately 2.5 times that of non-modified carbon. Using different MAC, sulfides were eliminated with a removal capacity of 52 mg g(-1). Therefore, MAC can be utilized as an effective and less expensive adsorbent for the reduction of sulfur in refinery wastewater.

Modeling of turbulent chemical reaction

NASA Technical Reports Server (NTRS)

Chen, J.-Y.

1995-01-01

Viewgraphs are presented on modeling turbulent reacting flows, regimes of turbulent combustion, regimes of premixed and regimes of non-premixed turbulent combustion, chemical closure models, flamelet model, conditional moment closure (CMC), NO(x) emissions from turbulent H2 jet flames, probability density function (PDF), departures from chemical equilibrium, mixing models for PDF methods, comparison of predicted and measured H2O mass fractions in turbulent nonpremixed jet flames, experimental evidence of preferential diffusion in turbulent jet flames, and computation of turbulent reacting flows.

Effects of soft interactions and bound mobility on diffusion in crowded environments: a model of sticky and slippery obstacles

NASA Astrophysics Data System (ADS)

Stefferson, Michael W.; Norris, Samantha L.; Vernerey, Franck J.; Betterton, Meredith D.; E Hough, Loren

2017-08-01

Crowded environments modify the diffusion of macromolecules, generally slowing their movement and inducing transient anomalous subdiffusion. The presence of obstacles also modifies the kinetics and equilibrium behavior of tracers. While previous theoretical studies of particle diffusion have typically assumed either impenetrable obstacles or binding interactions that immobilize the particle, in many cellular contexts bound particles remain mobile. Examples include membrane proteins or lipids with some entry and diffusion within lipid domains and proteins that can enter into membraneless organelles or compartments such as the nucleolus. Using a lattice model, we studied the diffusive movement of tracer particles which bind to soft obstacles, allowing tracers and obstacles to occupy the same lattice site. For sticky obstacles, bound tracer particles are immobile, while for slippery obstacles, bound tracers can hop without penalty to adjacent obstacles. In both models, binding significantly alters tracer motion. The type and degree of motion while bound is a key determinant of the tracer mobility: slippery obstacles can allow nearly unhindered diffusion, even at high obstacle filling fraction. To mimic compartmentalization in a cell, we examined how obstacle size and a range of bound diffusion coefficients affect tracer dynamics. The behavior of the model is similar in two and three spatial dimensions. Our work has implications for protein movement and interactions within cells.

Predicting Salt Permeability Coefficients in Highly Swollen, Highly Charged Ion Exchange Membranes.

PubMed

Kamcev, Jovan; Paul, Donald R; Manning, Gerald S; Freeman, Benny D

2017-02-01

This study presents a framework for predicting salt permeability coefficients in ion exchange membranes in contact with an aqueous salt solution. The model, based on the solution-diffusion mechanism, was tested using experimental salt permeability data for a series of commercial ion exchange membranes. Equilibrium salt partition coefficients were calculated using a thermodynamic framework (i.e., Donnan theory), incorporating Manning's counterion condensation theory to calculate ion activity coefficients in the membrane phase and the Pitzer model to calculate ion activity coefficients in the solution phase. The model predicted NaCl partition coefficients in a cation exchange membrane and two anion exchange membranes, as well as MgCl 2 partition coefficients in a cation exchange membrane, remarkably well at higher external salt concentrations (>0.1 M) and reasonably well at lower external salt concentrations (<0.1 M) with no adjustable parameters. Membrane ion diffusion coefficients were calculated using a combination of the Mackie and Meares model, which assumes ion diffusion in water-swollen polymers is affected by a tortuosity factor, and a model developed by Manning to account for electrostatic effects. Agreement between experimental and predicted salt diffusion coefficients was good with no adjustable parameters. Calculated salt partition and diffusion coefficients were combined within the framework of the solution-diffusion model to predict salt permeability coefficients. Agreement between model and experimental data was remarkably good. Additionally, a simplified version of the model was used to elucidate connections between membrane structure (e.g., fixed charge group concentration) and salt transport properties.

Aggregation and Disaggregation of Senile Plaques in Alzheimer Disease

NASA Astrophysics Data System (ADS)

Cruz, L.; Urbanc, B.; Buldyrev, S. V.; Christie, R.; Gomez-Isla, T.; Havlin, S.; McNamara, M.; Stanley, H. E.; Hyman, B. T.

1997-07-01

We quantitatively analyzed, using laser scanning confocal microscopy, the three-dimensional structure of individual senile plaques in Alzheimer disease. We carried out the quantitative analysis using statistical methods to gain insights about the processes that govern Aβ peptide deposition. Our results show that plaques are complex porous structures with characteristic pore sizes. We interpret plaque morphology in the context of a new dynamical model based on competing aggregation and disaggregation processes in kinetic steady-state equilibrium with an additional diffusion process allowing Aβ deposits to diffuse over the surface of plaques.

Recovery of oil from oil-in-water emulsion using biopolymers by adsorptive method.

PubMed

Elanchezhiyan, S Sd; Sivasurian, N; Meenakshi, Sankaran

2014-09-01

In the present study, it is aimed to identify, a low cost sorbent for the recovery of oil from oil-in-water emulsion using biopolymers such as chitin and chitosan. Chitin has the greater adsorption capacity than chitosan due to its hydrophobic nature. The characterizations of chitin and chitosan were done using FTIR, SEM, EDAX, XRD, TGA and DSC techniques. Under batch equilibrium mode, a systematic study was performed to optimize the various equilibrium parameters viz., contact time, pH, dosage, initial concentration of oil, and temperature. The adsorption process reached equilibrium at 40 min of contact time and the percentage removal of oil was found to be higher (90%) in the acidic medium. The Freundlich and Langmuir models were applied to describe the equilibrium isotherms and the isotherm constants were calculated. Thermodynamic parameters such as ΔG°, ΔH° and ΔS° were calculated to find out the nature of the sorption mechanism. The kinetic studies were investigated with reaction-based and diffusion-based models. The suitable mechanism for the removal of oil has been established. Copyright © 2014 Elsevier B.V. All rights reserved.

Thermodynamic modelling of phase equilibrium in system Ti-B-Si-C, synthesis and phases composition of borides and carbides layers on titanic alloyVT-1 at electron beam treatment in vacuum

NASA Astrophysics Data System (ADS)

Smirnyagina, N. N.; Khaltanova, V. M.; Lapina, A. E.; Dasheev, D. E.

2017-01-01

Composite layers on the basis of carbides and borides the titan and silicon on titanic alloy VT-1 are generated at diffused saturation in vacuum. Formation in a composite of MAX phase Ti3SiC2 is shown. Thermodynamic research of phase equilibrium in systems Ti-Si-C and Ti-B-C in the conditions of high vacuum is executed. The thermodynamics, formation mechanisms of superfirm layers borides and carbides of the titan and silicon are investigated.

Modeling Ignition of HMX with the Gibbs Formulation

NASA Astrophysics Data System (ADS)

Lee, Kibaek; Stewart, D. Scott

2017-06-01

We present a HMX model with the Gibbs formulation in which stress tensor and temperature are assumed to be in local equilibrium, but phase/chemical changes are not assumed to be in equilibrium. We assume multi-components for HMX including beta- and delta-phase, liquid, and gas phase of HMX and its gas products. Isotropic small strain solid model, modified Fried Howard liquid EOS, and ideal gas EOS are used for its relevant component. Phase/chemical changes are characterized as reactions and are in individual reaction rate. Maxwell-Stefan model is used for diffusion. Excited gas products in the local domain lead unreacted HMX solid to the ignition event. Density of the mixture, stress, strain, displacement, mass fractions, and temperature are considered in 1D domain with time histories. Office of Naval Research and Air Force Office of Scientific Research.

Cs{sup +} ion exchange kinetics in complex electrolyte solutions using hydrous crystalline silicotitanates

DOE Office of Scientific and Technical Information (OSTI.GOV)

Gu, D.; Nguyen, L.; Philip, C.V.

1997-12-01

TAM-5 is a hydrous crystalline sodium silicotitanate inorganic ion exchanger with a high selectivity for Cs{sup +}. The kinetics of Cs{sup +}-Na{sup +} ion exchange using TAM-5 in multicomponent electrolyte solutions were determined using batch experiments. For the powder, which is composed of crystals, a single-phase, homogeneous model fit the data best. For the granules, which were prepared from the powder, a two-phase, heterogeneous model resulted in an excellent fit of the data. Macropore and crystal diffusivities were determined by fitting the model to experimental data collected on the powder and the granules. Intracrystalline diffusivities were concentration dependent and weremore » on the order of 10{sup {minus}19} m{sup 2}/s. Macropore diffusivities were on the order of 10{sup {minus}10} m{sup 2}/s. Resistance to diffusion in the macropores was not significant for granules with diameters less than 15 {micro}m. A two-phase, homogeneous model, where liquid within the pores is in equilibrium with the solid, was also evaluated for the granules. Surprisingly, for the granules, an excellent fit of the data was obtained; however, the effective macropore diffusivity was 1.1 {times} 10{sup {minus}11} m{sup 2}/s, an order of magnitude smaller than the macropore diffusivity found using the two-phase, heterogeneous model.« less

Direct measurement of the Einstein relation in a macroscopic, non-equilibrium system of chaotic surface waves

NASA Astrophysics Data System (ADS)

Welch, Kyle; Liebman-Pelaez, Alexander; Corwin, Eric

Equilibrium statistical mechanics is traditionally limited to thermal systems. Can it be applied to athermal, non-equilibrium systems that nonetheless satisfy the basic criteria of steady-state chaos and isotropy? We answer this question using a macroscopic system of chaotic surface waves which is, by all measures, non-equilibrium. The waves are generated in a dish of water that is vertically oscillated above a critical amplitude. We have constructed a rheometer that actively measures the drag imparted by the waves on a buoyant particle, a quantity entirely divorced in origin from the drag imparted by the fluid in which the particle floats. We also perform a separate, passive measurement, extracting a diffusion constant and effective temperature. Having directly measured all three properties (temperature, diffusion constant, and drag coefficient) we go on to show that our macroscopic, non-equilibrium case is wholly consistent with the Einstein relation, a classic result for equilibrium thermal systems.

Sorption-desorption equilibrium and diffusion of tetracycline in poultry litter and municipal biosolids soil amendments.

PubMed

D'Angelo, E

2017-12-01

Tetracycline (TET) is commonly used to treat bacterial diseases in humans and chickens (Gallus gallus domesticus), is largely excreted, and is found at elevated concentrations in treated sewage sludge (biosolids) and poultry litter (excrement plus bedding materials). Routine application of these nutrient-and carbon-enriched materials to soils improves fertility and other characteristics, but the presence of antibiotics (and other pharmaceuticals) in amendments raises questions about potential adverse effects on biota and development of antibiotic resistance in the environment. Hazard risks are largely dictated by sorption-desorption and diffusion behavior in amendments, so these processes were evaluated from sorption-desorption equilibrium isotherm and diffusion cell experiments with four types amendments (biosolids, poultry manure, wood chip litter, and rice hull litter) at three temperatures (8 °C, 20 °C and 32 °C). Linear sorption-desorption equilibrium distribution constants (Kd) in native amendments ranged between 124-2418 L kg -1 . TET sorption was significantly increased after treatment with alum, and there was a strong exponential relationship between Kd and the concentration of bound Al 3+ in amendments (R 2  = 0.94), which indicated that amendments contained functional groups capable of chelating Al 3+ and forming metal bridges with TET. Effective diffusion coefficients of TET in amendments ranged between 0.1 and 5.2 × 10 -6  cm 2  s -1 , which were positively related to temperature and inversely related to Kd by a multiple regression model (R 2  = 0.86). Treatment of organic amendments with alum greatly increased Kd, would decrease D s , and so would greatly reduce hazard risks of applying these organic amendments with this antibiotic to soils. Copyright © 2017 Elsevier Ltd. All rights reserved.

Spatial interactions in a modified Daisyworld model: Heat diffusivity and greenhouse effects

NASA Astrophysics Data System (ADS)

Alberti, T.; Primavera, L.; Vecchio, A.; Lepreti, F.; Carbone, V.

2015-11-01

In this work we investigate a modified version of the Daisyworld model, originally introduced by Lovelock and Watson to describe in a simple way the interactions between an Earth-like planet, its biosphere, and the incoming solar radiation. Here a spatial dependency on latitude is included, and both a variable heat diffusivity along latitudes and a simple greenhouse effect description are introduced in the model. We show that the spatial interactions between the variables of the system can locally stabilize the coexistence of the two vegetation types. The feedback on albedo is able to generate equilibrium solutions which can efficiently self-regulate the planet climate, even for values of the solar luminosity relatively far from the current Earth conditions.

Coarse-grained hydrodynamics from correlation functions

NASA Astrophysics Data System (ADS)

Palmer, Bruce

2018-02-01

This paper will describe a formalism for using correlation functions between different grid cells as the basis for determining coarse-grained hydrodynamic equations for modeling the behavior of mesoscopic fluid systems. Configurations from a molecular dynamics simulation or other atomistic simulation are projected onto basis functions representing grid cells in a continuum hydrodynamic simulation. Equilibrium correlation functions between different grid cells are evaluated from the molecular simulation and used to determine the evolution operator for the coarse-grained hydrodynamic system. The formalism is demonstrated on a discrete particle simulation of diffusion with a spatially dependent diffusion coefficient. Correlation functions are calculated from the particle simulation and the spatially varying diffusion coefficient is recovered using a fitting procedure.

A Heuristic Approach to Examining Volatile Equilibrium at Titan's Surface

NASA Technical Reports Server (NTRS)

Samuelson, Robert E.

1999-01-01

R. D. Lorenz, J. I. Lunine, and C. P. McKay have shown in a manuscript accepted for publication that, for a given ethane abundance and surface temperature, the nitrogen and methane abundances in Titan's atmosphere can be calculated, yielding a surface pressure that can be compared with the observed value. This is potentially a very valuable tool for examining the evolution of Titan's climatology. Its validity does depend on two important assumptions, however: 1) that the atmosphere of Titan is in global radiative equilibrium, and 2) that volatiles present are in vapor equilibrium with the surface. The former assumption has been shown to be likely, but the latter has not. Water vapor in the Earth's atmosphere, in fact, is generally not very close to equilibrium in a global sense. In the present work a heuristic approach is used to examine the likelihood that methane vapor is in equilibrium with Titan's surface. Plausible climate scenerios are examined that are consistent with methane vapor abundances derived from Voyager IRIS data. Simple precipitation and surface diffusion models are incorporated into the analysis. It is tentatively inferred that methane may be in surface equilibrium near the poles, but that equilibrium at low latitudes is more difficult to establish.

The number statistics and optimal history of non-equilibrium steady states of mortal diffusing particles

NASA Astrophysics Data System (ADS)

Meerson, Baruch

2015-05-01

Suppose that a point-like steady source at x = 0 injects particles into a half-infinite line. The particles diffuse and die. At long times a non-equilibrium steady state sets in, and we assume that it involves many particles. If the particles are non-interacting, their total number N in the steady state is Poisson-distributed with mean \\bar{N} predicted from a deterministic reaction-diffusion equation. Here we determine the most likely density history of this driven system conditional on observing a given N. We also consider two prototypical examples of interacting diffusing particles: (i) a family of mortal diffusive lattice gases with constant diffusivity (as illustrated by the simple symmetric exclusion process with mortal particles), and (ii) random walkers that can annihilate in pairs. In both examples we calculate the variances of the (non-Poissonian) stationary distributions of N.

Transport coefficients and heat fluxes in non-equilibrium high-temperature flows with electronic excitation

NASA Astrophysics Data System (ADS)

Istomin, V. A.; Kustova, E. V.

2017-02-01

The influence of electronic excitation on transport processes in non-equilibrium high-temperature ionized mixture flows is studied. Two five-component mixtures, N 2 / N2 + / N / N + / e - and O 2 / O2 + / O / O + / e - , are considered taking into account the electronic degrees of freedom for atomic species as well as the rotational-vibrational-electronic degrees of freedom for molecular species, both neutral and ionized. Using the modified Chapman-Enskog method, the transport coefficients (thermal conductivity, shear viscosity and bulk viscosity, diffusion and thermal diffusion) are calculated in the temperature range 500-50 000 K. Thermal conductivity and bulk viscosity coefficients are strongly affected by electronic states, especially for neutral atomic species. Shear viscosity, diffusion, and thermal diffusion coefficients are not sensible to electronic excitation if the size of excited states is assumed to be constant. The limits of applicability for the Stokes relation are discussed; at high temperatures, this relation is violated not only for molecular species but also for electronically excited atomic gases. Two test cases of strongly non-equilibrium flows behind plane shock waves corresponding to the spacecraft re-entry (Hermes and Fire II) are simulated numerically. Fluid-dynamic variables and heat fluxes are evaluated in gases with electronic excitation. In inviscid flows without chemical-radiative coupling, the flow-field is weakly affected by electronic states; however, in viscous flows, their influence can be more important, in particular, on the convective heat flux. The contribution of different dissipative processes to the heat transfer is evaluated as well as the effect of reaction rate coefficients. The competition of diffusion and heat conduction processes reduces the overall effect of electronic excitation on the convective heating, especially for the Fire II test case. It is shown that reliable models of chemical reaction rates are of great importance for accurate predictions of the fluid dynamic variables and heat fluxes.

A novel game theoretic approach for modeling competitive information diffusion in social networks with heterogeneous nodes

NASA Astrophysics Data System (ADS)

Agha Mohammad Ali Kermani, Mehrdad; Fatemi Ardestani, Seyed Farshad; Aliahmadi, Alireza; Barzinpour, Farnaz

2017-01-01

Influence maximization deals with identification of the most influential nodes in a social network given an influence model. In this paper, a game theoretic framework is developed that models a competitive influence maximization problem. A novel competitive influence model is additionally proposed that incorporates user heterogeneity, message content, and network structure. The proposed game-theoretic model is solved using Nash Equilibrium in a real-world dataset. It is shown that none of the well-known strategies are stable and at least one player has the incentive to deviate from the proposed strategy. Moreover, violation of Nash equilibrium strategy by each player leads to their reduced payoff. Contrary to previous works, our results demonstrate that graph topology, as well as the nodes' sociability and initial tendency measures have an effect on the determination of the influential node in the network.

Prediction of the moments in advection-diffusion lattice Boltzmann method. II. Attenuation of the boundary layers via double-Λ bounce-back flux scheme.

PubMed

Ginzburg, Irina

2017-01-01

Impact of the unphysical tangential advective-diffusion constraint of the bounce-back (BB) reflection on the impermeable solid surface is examined for the first four moments of concentration. Despite the number of recent improvements for the Neumann condition in the lattice Boltzmann method-advection-diffusion equation, the BB rule remains the only known local mass-conserving no-flux condition suitable for staircase porous geometry. We examine the closure relation of the BB rule in straight channel and cylindrical capillary analytically, and show that it excites the Knudsen-type boundary layers in the nonequilibrium solution for full-weight equilibrium stencil. Although the d2Q5 and d3Q7 coordinate schemes are sufficient for the modeling of isotropic diffusion, the full-weight stencils are appealing for their advanced stability, isotropy, anisotropy and anti-numerical-diffusion ability. The boundary layers are not covered by the Chapman-Enskog expansion around the expected equilibrium, but they accommodate the Chapman-Enskog expansion in the bulk with the closure relation of the bounce-back rule. We show that the induced boundary layers introduce first-order errors in two primary transport properties, namely, mean velocity (first moment) and molecular diffusion coefficient (second moment). As a side effect, the Taylor-dispersion coefficient (second moment), skewness (third moment), and kurtosis (fourth moment) deviate from their physical values and predictions of the fourth-order Chapman-Enskog analysis, even though the kurtosis error in pure diffusion does not depend on grid resolution. In two- and three-dimensional grid-aligned channels and open-tubular conduits, the errors of velocity and diffusion are proportional to the diagonal weight values of the corresponding equilibrium terms. The d2Q5 and d3Q7 schemes do not suffer from this deficiency in grid-aligned geometries but they cannot avoid it if the boundaries are not parallel to the coordinate lines. In order to vanish or attenuate the disparity of the modeled transport coefficients with the equilibrium weights without any modification of the BB rule, we propose to use the two-relaxation-times collision operator with free-tunable product of two eigenfunctions Λ. Two different values Λ_{v} and Λ_{b} are assigned for bulk and boundary nodes, respectively. The rationale behind this is that Λ_{v} is adjustable for stability, accuracy, or other purposes, while the corresponding Λ_{b}(Λ_{v}) controls the primary accommodation effects. Two distinguished but similar functional relations Λ_{b}(Λ_{v}) are constructed analytically: they preserve advection velocity in parabolic profile, exactly in the two-dimensional channel and very accurately in a three-dimensional cylindrical capillary. For any velocity-weight stencil, the (local) double-Λ BB scheme produces quasi-identical solutions with the (nonlocal) specular-forward reflection for first four moments in a channel. In a capillary, this strategy allows for the accurate modeling of the Taylor-dispersion and non-Gaussian effects. As illustrative example, it is shown that in the flow around a circular obstacle, the double-Λ scheme may also vanish the dependency of mean velocity on the velocity weight; the required value for Λ_{b}(Λ_{v}) can be identified in a few bisection iterations in given geometry. A positive solution for Λ_{b}(Λ_{v}) may not exist in pure diffusion, but a sufficiently small value of Λ_{b} significantly reduces the disparity in diffusion coefficient with the mass weight in ducts and in the presence of rectangular obstacles. Although Λ_{b} also controls the effective position of straight or curved boundaries, the double-Λ scheme deals with the lower-order effects. Its idea and construction may help understanding and amelioration of the anomalous, zero- and first-order behavior of the macroscopic solution in the presence of the bulk and boundary or interface discontinuities, commonly found in multiphase flow and heterogeneous transport.

Prediction of the moments in advection-diffusion lattice Boltzmann method. II. Attenuation of the boundary layers via double-Λ bounce-back flux scheme

NASA Astrophysics Data System (ADS)

Ginzburg, Irina

2017-01-01

Impact of the unphysical tangential advective-diffusion constraint of the bounce-back (BB) reflection on the impermeable solid surface is examined for the first four moments of concentration. Despite the number of recent improvements for the Neumann condition in the lattice Boltzmann method-advection-diffusion equation, the BB rule remains the only known local mass-conserving no-flux condition suitable for staircase porous geometry. We examine the closure relation of the BB rule in straight channel and cylindrical capillary analytically, and show that it excites the Knudsen-type boundary layers in the nonequilibrium solution for full-weight equilibrium stencil. Although the d2Q5 and d3Q7 coordinate schemes are sufficient for the modeling of isotropic diffusion, the full-weight stencils are appealing for their advanced stability, isotropy, anisotropy and anti-numerical-diffusion ability. The boundary layers are not covered by the Chapman-Enskog expansion around the expected equilibrium, but they accommodate the Chapman-Enskog expansion in the bulk with the closure relation of the bounce-back rule. We show that the induced boundary layers introduce first-order errors in two primary transport properties, namely, mean velocity (first moment) and molecular diffusion coefficient (second moment). As a side effect, the Taylor-dispersion coefficient (second moment), skewness (third moment), and kurtosis (fourth moment) deviate from their physical values and predictions of the fourth-order Chapman-Enskog analysis, even though the kurtosis error in pure diffusion does not depend on grid resolution. In two- and three-dimensional grid-aligned channels and open-tubular conduits, the errors of velocity and diffusion are proportional to the diagonal weight values of the corresponding equilibrium terms. The d2Q5 and d3Q7 schemes do not suffer from this deficiency in grid-aligned geometries but they cannot avoid it if the boundaries are not parallel to the coordinate lines. In order to vanish or attenuate the disparity of the modeled transport coefficients with the equilibrium weights without any modification of the BB rule, we propose to use the two-relaxation-times collision operator with free-tunable product of two eigenfunctions Λ . Two different values Λv and Λb are assigned for bulk and boundary nodes, respectively. The rationale behind this is that Λv is adjustable for stability, accuracy, or other purposes, while the corresponding Λb(Λv) controls the primary accommodation effects. Two distinguished but similar functional relations Λb(Λv) are constructed analytically: they preserve advection velocity in parabolic profile, exactly in the two-dimensional channel and very accurately in a three-dimensional cylindrical capillary. For any velocity-weight stencil, the (local) double-Λ BB scheme produces quasi-identical solutions with the (nonlocal) specular-forward reflection for first four moments in a channel. In a capillary, this strategy allows for the accurate modeling of the Taylor-dispersion and non-Gaussian effects. As illustrative example, it is shown that in the flow around a circular obstacle, the double-Λ scheme may also vanish the dependency of mean velocity on the velocity weight; the required value for Λb(Λv) can be identified in a few bisection iterations in given geometry. A positive solution for Λb(Λv) may not exist in pure diffusion, but a sufficiently small value of Λb significantly reduces the disparity in diffusion coefficient with the mass weight in ducts and in the presence of rectangular obstacles. Although Λb also controls the effective position of straight or curved boundaries, the double-Λ scheme deals with the lower-order effects. Its idea and construction may help understanding and amelioration of the anomalous, zero- and first-order behavior of the macroscopic solution in the presence of the bulk and boundary or interface discontinuities, commonly found in multiphase flow and heterogeneous transport.

Modeling CO2 Storage in Fractured Reservoirs: Fracture-Matrix Interactions of Free-Phase and Dissolved CO2

NASA Astrophysics Data System (ADS)

Oldenburg, C. M.; Zhou, Q.; Birkholzer, J. T.

2017-12-01

The injection of supercritical CO2 (scCO2) in fractured reservoirs has been conducted at several storage sites. However, no site-specific dual-continuum modeling for fractured reservoirs has been reported and modeling studies have generally underestimated the fracture-matrix interactions. We developed a conceptual model for enhanced CO2 storage to take into account global scCO2 migration in the fracture continuum, local storage of scCO2 and dissolved CO2 (dsCO2) in the matrix continuum, and driving forces for scCO2 invasion and dsCO2 diffusion from fractures. High-resolution discrete fracture-matrix models were developed for a column of idealized matrix blocks bounded by vertical and horizontal fractures and for a km-scale fractured reservoir. The column-scale simulation results show that equilibrium storage efficiency strongly depends on matrix entry capillary pressure and matrix-matrix connectivity while the time scale to reach equilibrium is sensitive to fracture spacing and matrix flow properties. The reservoir-scale modeling results shows that the preferential migration of scCO2 through fractures is coupled with bulk storage in the rock matrix that in turn retards the fracture scCO2 plume. We also developed unified-form diffusive flux equations to account for dsCO2 storage in brine-filled matrix blocks and found solubility trapping is significant in fractured reservoirs with low-permeability matrix.

Controlling reactivity of nanoporous catalyst materials by tuning reaction product-pore interior interactions: Statistical mechanical modeling

DOE Office of Scientific and Technical Information (OSTI.GOV)

Wang, Jing; Ackerman, David M.; Lin, Victor S.-Y.

2013-04-02

Statistical mechanical modeling is performed of a catalytic conversion reaction within a functionalized nanoporous material to assess the effect of varying the reaction product-pore interior interaction from attractive to repulsive. A strong enhancement in reactivity is observed not just due to the shift in reaction equilibrium towards completion but also due to enhanced transport within the pore resulting from reduced loading. The latter effect is strongest for highly restricted transport (single-file diffusion), and applies even for irreversible reactions. The analysis is performed utilizing a generalized hydrodynamic formulation of the reaction-diffusion equations which can reliably capture the complex interplay between reactionmore » and restricted transport.« less

Adsorption of saturated fatty acid in urea complexation: Kinetics and equilibrium studies

NASA Astrophysics Data System (ADS)

Setyawardhani, Dwi Ardiana; Sulistyo, Hary; Sediawan, Wahyudi Budi; Fahrurrozi, Mohammad

2018-02-01

Urea complexation is fractionation process for concentrating poly-unsaturated fatty acids (PUFAs) from vegetable oil or animal fats. For process design and optimization in commercial industries, it is necessary to provide kinetics and equilibrium data. Urea inclusion compounds (UICs) as the product is a unique complex form which one molecule (guest) is enclosed within another molecule (host). In urea complexation, the guest-host bonding exists between saturated fatty acids (SFAs) and crystalline urea. This research studied the complexation is analogous to an adsorption process. The Batch adsorption process was developed to obtain the experimental data. The ethanolic urea solution was mixed with SFA in certain compositions and adsorption times. The mixture was heated until it formed homogenous and clear solution, then it cooled very slowly until the first numerous crystal appeared. Adsorption times for the kinetic data were determined since the crystal formed. The temperature was maintained constant at room temperature. Experimental sets of data were observed with adsorption kinetics and equilibrium models. High concentration of saturated fatty acid (SFA) was used to represent adsorption kinetics and equilibrium parameters. Kinetic data were examined with pseudo first-order, pseudo second-order and intra particle diffusion models. Linier, Freundlich and Langmuir isotherm were used to study the equilibrium model of this adsorption. The experimental data showed that SFA adsorption in urea crystal followed pseudo second-order model. The compatibility of the data with Langmuir isotherm showed that urea complexation was a monolayer adsorption.

The effects of bound state motion on macromolecular diffusion

NASA Astrophysics Data System (ADS)

Hough, Loren; Stefferson, Michael; Norris, Samantha; Maguire, Laura; Vernerey, Franck; Betterton, Meredith

The diffusion of macromolecules is modified in crowded environments by both inert obstacles and interaction sites. Molecules are generally slowed in their movement inducing transient anomalous subdiffusion. Obstacles also modify the kinetics and equilibrium behavior of interaction between mobile proteins. In some biophysical contexts, bound molecules can still experience mobility, for example transcription factors sliding along DNA, membrane proteins with some entry and diffusion within lipid domains, or proteins that can enter into non-membrane bound compartments such as the nucleolus. We used lattice and continuum models to study the diffusive behavior of tracer particles which bind to obstacles and can diffuse within them. We show that binding significantly alters the motion of tracers. The type and degree of motion while bound is a key determinant of the tracer mobility. Our work has implications for protein-protein movement and interactions within living cells, including those involving intrinsically disordered proteins.

Detecting and Correcting Melt Inclusion Modification

NASA Astrophysics Data System (ADS)

Cottrell, E.; Kelley, K. A.

2008-12-01

Post entrapment diffusive modification of melt inclusions may mute or erase primary signatures. Corrections for post-entrapment crystallization (PEC) and Fe-loss are routinely applied and, because recent experimental studies suggest rapid diffusion of trace components into and out of olivine-hosted inclusions, the ability to discriminate between primary and secondary signatures is now even more critical. Two tools may assist in this endeavor. XANES measurements of Fe3+/ΣFe ratios in undegassed ol-hosted basaltic melt inclusions from global arcs are 16-36% (n=16), significantly higher than the 7-10% commonly assumed, and higher than in MORB or BABB lavas (Kelley and Cottrell, this mtg). The Fe3+/ΣFe ratios indicate melt-host equilibrium, with significantly less PEC or Fe-loss than would have been otherwise assumed. We conclude that Fe2+ diffusion has been minimal; therefore the residence time of these primitive inclusions in an evolved magma must have been short. Fe3+/ΣFe correlates positively with water concentration, but not with CO2 and S concentrations or Mg#. The oxidized nature of arc lavas and melt inclusions may therefore indicate an oxidized source rather than late-stage degassing or fractionation. Trace element concentrations evolve with time if an inclusion is out of equilibrium with its host. The numerical model of Cottrell et al., 2002, makes specific predictions about how suites of melt inclusions evolve, creating a tool to detect post-entrapment modification. Recent laboratory measurements of REE diffusion in olivine greatly diverge (at 1300°C, 1015 vs 1019m2/s). If REE diffusivity is extremely fast, melt inclusion HREE diversity shouldn't survive more than a few years in a magma chamber; but if slow, HREE variance could be preserved for >104 yrs. Model analysis of published suites of ol-hosted inclusions indicates that either REE diffusion is quite slow, or the residence time of melt inclusions at high temperature is very short. Loss of variance in suites of pl-hosted inclusions is consistent with long (>103 yrs) residence times. Suites of ol- and pl-hosted inclusions from the same magmatic system can therefore bracket residence times if diffusivities are known, or put reasonable bounds on diffusion rates.

Numerical modeling of an alloy droplet deposition with non-equilibrium solidification

NASA Astrophysics Data System (ADS)

Ramanuj, Vimal

Droplet deposition is a process of extensive relevance to the microfabrication industry. Various bonding and film deposition methods utilize single or multiple droplet impingements on a substrate with subsequent splat formation through simultaneous spreading and solidification. Splat morphology and solidification characteristics play vital roles in determining the final outcome. Experimental methods have limited reach in studying such phenomena owing to the extremely small time and length scales involved. Fundamental understanding of the governing principles of fluid flow, heat transfer and phase change provide effective means of studying such processes through computational techniques. The present study aims at numerically modeling and analyzing the phenomenon of splat formation and phase change in an alloy droplet deposition process. Phase change in alloys occurs non-isothermally and its formulation poses mathematical challenges. A highly non-linear flow field in conjunction with multiple interfaces and convection-diffusion governed phase transition are some of the highlighting features involved in the numerical formulation. Moreover, the non-equilibrium solidification behavior in eutectic systems is of prime concern. The peculiar phenomenon requires special treatments in terms of modeling solid phase species diffusion, liquid phase enrichment during solute partitioning and isothermal eutectic transformation. The flow field is solved using a two-step projection algorithm coupled with enhanced interface modeling schemes. The free surface tracking and reconstruction is achieved through two approaches: VOF-PLIC and CLSVOF to achieve optimum interface accuracy with minimal computational resources. The energy equation is written in terms of enthalpy with an additional source term to account for the phase change. The solidification phenomenon is modeled using a coupled temperature-solute scheme that reflects the microscopic effects arising due to dendritic growth taking place in rapidly solidifying domains. Solid phase diffusion theories proposed in the literature are incorporated in the solute conservation equation through a back diffusion parameter till the eutectic composition; beyond which a special treatment is proposed. A simplified homogeneous mushy region model has also been outline. Both models are employed to reproduce analytical results under limiting conditions and also experimentally verified. The primary objective of the present work is to examine the splat morphology, solidification behavior and microstructural characteristics under varying operational parameters. A simplified homogeneous mushy region model is first applied to study the role of convection in an SS304 droplet deposition with substrate remelting. The results are compared with experimental findings reported in the literature and a good agreement is observed. Furthermore, a hypoeutectic Sn-Pb alloy droplet deposition is studied using a comprehensive coupled temperature solute model that accounts for the non-equilibrium solidification occurring in eutectic type of alloys. Particular focus is laid on the limitations of a homogeneous mushy region assumption, role of species composition in governing solidification, estimation of the microstructural properties and eutectic formation.

Star Formation and Gas Dynamics in Galactic Disks: Physical Processes and Numerical Models

NASA Astrophysics Data System (ADS)

Ostriker, Eve C.

2011-04-01

Star formation depends on the available gaseous ``fuel'' as well as galactic environment, with higher specific star formation rates where gas is predominantly molecular and where stellar (and dark matter) densities are higher. The partition of gas into different thermal components must itself depend on the star formation rate, since a steady state distribution requires a balance between heating (largely from stellar UV for the atomic component) and cooling. In this presentation, I discuss a simple thermal and dynamical equilibrium model for the star formation rate in disk galaxies, where the basic inputs are the total surface density of gas and the volume density of stars and dark matter, averaged over ~kpc scales. Galactic environment is important because the vertical gravity of the stars and dark matter compress gas toward the midplane, helping to establish the pressure, and hence the cooling rate. In equilibrium, the star formation rate must evolve until the gas heating rate is high enough to balance this cooling rate and maintain the pressure imposed by the local gravitational field. In addition to discussing the formulation of this equilibrium model, I review the current status of numerical simulations of multiphase disks, focusing on measurements of quantities that characterize the mean properties of the diffuse ISM. Based on simulations, turbulence levels in the diffuse ISM appear relatively insensitive to local disk conditions and energetic driving rates, consistent with observations. It remains to be determined, both from observations and simulations, how mass exchange processes control the ratio of cold-to-warm gas in the atomic ISM.

Microimaging of transient guest profiles to monitor mass transfer in nanoporous materials

NASA Astrophysics Data System (ADS)

Kärger, Jörg; Binder, Tomas; Chmelik, Christian; Hibbe, Florian; Krautscheid, Harald; Krishna, Rajamani; Weitkamp, Jens

2014-04-01

The intense interactions of guest molecules with the pore walls of nanoporous materials is the subject of continued fundamental research. Stimulated by their thermal energy, the guest molecules in these materials are subject to a continuous, irregular motion, referred to as diffusion. Diffusion, which is omnipresent in nature, influences the efficacy of nanoporous materials in reaction and separation processes. The recently introduced techniques of microimaging by interference and infrared microscopy provide us with a wealth of information on diffusion, hitherto inaccessible from commonly used techniques. Examples include the determination of surface barriers and the sticking coefficient's analogue, namely the probability that, on colliding with the particle surface, a molecule may continue its diffusion path into the interior. Microimaging is further seen to open new vistas in multicomponent guest diffusion (including the detection of a reversal in the preferred diffusion pathways), in guest-induced phase transitions in nanoporous materials and in matching the results of diffusion studies under equilibrium and non-equilibrium conditions.

Effect of Na+ impregnated activated carbon on the adsorption of NH4(+)-N from aqueous solution.

PubMed

Shi, Mo; Wang, Zhengfang; Zheng, Zheng

2013-08-01

Two kinds of activated carbons modified by Na+ impregnation after pre-treatments involving oxidation by nitric acid or acidification by hydrochloric acid (denoted as AC/N-Na and AC/HCl-Na, respectively), were used as adsorbents to remove NH4(+)-N. The surface features of samples were investigated by BET, SEM, XRD and FT-IR. The adsorption experiments were conducted in equilibrium and kinetic conditions. Influencing factors such as initial solution pH and initial concentration were investigated. A possible mechanism was proposed. Results showed that optimal NH4(+)-N removal efficiency was achieved at a neutral pH condition for the modified ACs. The Langmuir isotherm adsorption equation provided a better fit than other models for the equilibrium study. The adsorption kinetics followed both the pseudo second-order kinetics model and intra-particle kinetic model. Chemical surface analysis indicated that Na+ ions form ionic bonds with available surface functional groups created by pre-treatment, especially oxidation by nitric acid, thus increasing the removal efficiency of the modified ACs for NH4(+)-N. Na(+)-impregnated ACs had a higher removal capability in removing NH4(+)-N than unmodified AC, possibly resulting from higher numbers of surface functional groups and better intra-particle diffusion. The good fit of Langmuir isotherm adsorption to the data indicated the presence of monolayer NH4(+)-N adsorption on the active homogenous sites within the adsorbents. The applicability of pseudo second-order and intra-particle kinetic models revealed the complex nature of the adsorption mechanism. The intra-particle diffusion model revealed that the adsorption process consisted not only of surface adsorption but also intra-particle diffusion.

Mass-conserving advection-diffusion Lattice Boltzmann model for multi-species reacting flows

NASA Astrophysics Data System (ADS)

Hosseini, S. A.; Darabiha, N.; Thévenin, D.

2018-06-01

Given the complex geometries usually found in practical applications, the Lattice Boltzmann (LB) method is becoming increasingly attractive. In addition to the simple treatment of intricate geometrical configurations, LB solvers can be implemented on very large parallel clusters with excellent scalability. However, reacting flows and especially combustion lead to additional challenges and have seldom been studied by LB methods. Indeed, overall mass conservation is a pressing issue in modeling multi-component flows. The classical advection-diffusion LB model recovers the species transport equations with the generalized Fick approximation under the assumption of an incompressible flow. However, for flows involving multiple species with different diffusion coefficients and density fluctuations - as is the case with weakly compressible solvers like Lattice Boltzmann -, this approximation is known not to conserve overall mass. In classical CFD, as the Fick approximation does not satisfy the overall mass conservation constraint a diffusion correction velocity is usually introduced. In the present work, a local expression is first derived for this correction velocity in a LB framework. In a second step, the error due to the incompressibility assumption is also accounted for through a modified equilibrium distribution function. Theoretical analyses and simulations show that the proposed scheme performs much better than the conventional advection-diffusion Lattice Boltzmann model in terms of overall mass conservation.

(Energetics of silicate melts from thermal diffusion studies)

DOE Office of Scientific and Technical Information (OSTI.GOV)

Not Available

1989-01-01

Research during the past year has been concentrated in four major areas. We are continuing work initiated during the first two years on modelling thermal diffusion on multicomponent silicate liquids. We have derived appropriate relations for ternary and quaternary systems and reanalyzed experimental thermal diffusion data for the ternary system fayalite-leucite-silica. In our manuscript entitled Thermal Diffusion in Petrology'', to be published in Adv. in Phy. Geochem., we show that these model results independently recover the compositional extent and temperature of liquid immiscibility in this system. Such retrieval provides a rigorous test of our theoretical predictions and simplified treatment ofmore » complex silicate liquids reported in Geochimica Cosmochimica Acta in 1986. The usefulness of our Soret research in providing mixing energies of silicate liquids has been recently confirmed by Ghiorso (1987, Cont. Min. Pet.). This demonstration provides a strategy for incorporating Soret data into the calibration of phase equilibrium-based solution models such as the one developed by Ghiorso. During the past year we also have resumed our studies of thermal diffusion in borosilicate glasses which also exhibit liquid immiscibility. Our objectives in studying these systems are (1) to further test of our multicomponent thermal diffusion model and (2) to provide quantitative constraints on the mixing properties of these glass-forming systems which are important for evaluating their suitability for storage of high-level nuclear waste. 16 refs.« less

Improved understanding of the acoustophoretic focusing of dense suspensions in a microchannel

NASA Astrophysics Data System (ADS)

Karthick, S.; Sen, A. K.

2017-11-01

We provide improved understanding of acoustophoretic focusing of a dense suspension (volume fraction φ >10 % ) in a microchannel subjected to an acoustic standing wave using a proposed theoretical model and experiments. The model is based on the theory of interacting continua and utilizes a momentum transport equation for the mixture, continuity equation, and transport equation for the solid phase. The model demonstrates the interplay between acoustic radiation and shear-induced diffusion (SID) forces that is critical in the focusing of dense suspensions. The shear-induced particle migration model of Leighton and Acrivos, coupled with the acoustic radiation force, is employed to simulate the continuum behavior of particles. In the literature, various closures for the diffusion coefficient Dφ* are available for rigid spheres at high concentrations and nonspherical deformable particles [e.g., red blood cells (RBCs)] at low concentrations. Here we propose a closure for Dφ* for dense suspension of RBCs and validate the proposed model with experimental data. While the available closures for Dφ* fail to predict the acoustic focusing of a dense suspension of nonspherical deformable particles like RBCs, the predictions of the proposed model match experimental data within 15%. Both the model and experiments reveal a competition between acoustic radiation and SID forces that gives rise to an equilibrium width w* of a focused stream of particles at some distance Leq* along the flow direction. Using different shear rates, acoustic energy densities, and particle concentrations, we show that the equilibrium width is governed by Péclet number Pe and Strouhal number Stas w*=1.4(PeSt) -0.5 while the length required to obtain the equilibrium-focused width depends on St as Leq*=3.8 /(St)0.6 . The proposed model and correlations would find significance in the design of microchannels for acoustic focusing of dense suspensions such as undiluted blood.

Mutual diffusion of binary liquid mixtures containing methanol, ethanol, acetone, benzene, cyclohexane, toluene, and carbon tetrachloride

DOE Office of Scientific and Technical Information (OSTI.GOV)

Guevara-Carrion, Gabriela; Janzen, Tatjana; Muñoz-Muñoz, Y. Mauricio

Mutual diffusion coefficients of all 20 binary liquid mixtures that can be formed out of methanol, ethanol, acetone, benzene, cyclohexane, toluene, and carbon tetrachloride without a miscibility gap are studied at ambient conditions of temperature and pressure in the entire composition range. The considered mixtures show a varying mixing behavior from almost ideal to strongly non-ideal. Predictive molecular dynamics simulations employing the Green-Kubo formalism are carried out. Radial distribution functions are analyzed to gain an understanding of the liquid structure influencing the diffusion processes. It is shown that cluster formation in mixtures containing one alcoholic component has a significant impactmore » on the diffusion process. The estimation of the thermodynamic factor from experimental vapor-liquid equilibrium data is investigated, considering three excess Gibbs energy models, i.e., Wilson, NRTL, and UNIQUAC. It is found that the Wilson model yields the thermodynamic factor that best suits the simulation results for the prediction of the Fick diffusion coefficient. Four semi-empirical methods for the prediction of the self-diffusion coefficients and nine predictive equations for the Fick diffusion coefficient are assessed and it is found that methods based on local composition models are more reliable. Finally, the shear viscosity and thermal conductivity are predicted and in most cases favorably compared with experimental literature values.« less

Modelling deuterium release from tungsten after high flux high temperature deuterium plasma exposure

NASA Astrophysics Data System (ADS)

Grigorev, Petr; Matveev, Dmitry; Bakaeva, Anastasiia; Terentyev, Dmitry; Zhurkin, Evgeny E.; Van Oost, Guido; Noterdaeme, Jean-Marie

2016-12-01

Tungsten is a primary candidate for plasma facing materials for future fusion devices. An important safety concern in the design of plasma facing components is the retention of hydrogen isotopes. Available experimental data is vast and scattered, and a consistent physical model of retention of hydrogen isotopes in tungsten is still missing. In this work we propose a model of non-equilibrium hydrogen isotopes trapping under fusion relevant plasma exposure conditions. The model is coupled to a diffusion-trapping simulation tool and is used to interpret recent experiments involving high plasma flux exposures. From the computational analysis performed, it is concluded that high flux high temperature exposures (T = 1000 K, flux = 1024 D/m2/s and fluence of 1026 D/m2) result in generation of sub-surface damage and bulk diffusion, so that the retention is driven by both sub-surface plasma-induced defects (bubbles) and trapping at natural defects. On the basis of the non-equilibrium trapping model we have estimated the amount of H stored in the sub-surface region to be ∼10-5 at-1, while the bulk retention is about 4 × 10-7 at-1, calculated by assuming the sub-surface layer thickness of about 10 μm and adjusting the trap concentration to comply with the experimental results for the integral retention.

The Abundance of Molecular Hydrogen and Its Correlation with Midplane Pressure in Galaxies: Non-equilibrium, Turbulent, Chemical Models

NASA Astrophysics Data System (ADS)

Mac Low, Mordecai-Mark; Glover, Simon C. O.

2012-02-01

Observations of spiral galaxies show a strong linear correlation between the ratio of molecular to atomic hydrogen surface density R mol and midplane pressure. To explain this, we simulate three-dimensional, magnetized turbulence, including simplified treatments of non-equilibrium chemistry and the propagation of dissociating radiation, to follow the formation of H2 from cold atomic gas. The formation timescale for H2 is sufficiently long that equilibrium is not reached within the 20-30 Myr lifetimes of molecular clouds. The equilibrium balance between radiative dissociation and H2 formation on dust grains fails to predict the time-dependent molecular fractions we find. A simple, time-dependent model of H2 formation can reproduce the gross behavior, although turbulent density perturbations increase molecular fractions by a factor of few above it. In contradiction to equilibrium models, radiative dissociation of molecules plays little role in our model for diffuse radiation fields with strengths less than 10 times that of the solar neighborhood, because of the effective self-shielding of H2. The observed correlation of R mol with pressure corresponds to a correlation with local gas density if the effective temperature in the cold neutral medium of galactic disks is roughly constant. We indeed find such a correlation of R mol with density. If we examine the value of R mol in our local models after a free-fall time at their average density, as expected for models of molecular cloud formation by large-scale gravitational instability, our models reproduce the observed correlation over more than an order-of-magnitude range in density.

Increased Accuracy of Ligand Sensing by Receptor Internalization and Lateral Receptor Diffusion

NASA Astrophysics Data System (ADS)

Aquino, Gerardo; Endres, Robert

2010-03-01

Many types of cells can sense external ligand concentrations with cell-surface receptors at extremely high accuracy. Interestingly, ligand-bound receptors are often internalized, a process also known as receptor-mediated endocytosis. While internalization is involved in a vast number of important functions for the life of a cell, it was recently also suggested to increase the accuracy of sensing ligand as overcounting of the same ligand molecules is reduced. A similar role may be played by receptor diffusion om the cell membrane. Fast, lateral receptor diffusion is known to be relevant in neurotransmission initiated by release of neurotransmitter glutamate in the synaptic cleft between neurons. By binding ligand and removal by diffusion from the region of release of the neurotransmitter, diffusing receptors can be reasonably expected to reduce the local overcounting of the same ligand molecules in the region of signaling. By extending simple ligand-receptor models to out-of-equilibrium thermodynamics, we show that both receptor internalization and lateral diffusion increase the accuracy with which cells can measure ligand concentrations in the external environment. We confirm this with our model and give quantitative predictions for experimental parameters values. We give quantitative predictions, which compare favorably to experimental data of real receptors.

Ion exchange of several radionuclides on the hydrous crystalline silicotitanate, UOP IONSIV IE-911

DOE Office of Scientific and Technical Information (OSTI.GOV)

Huckman, M.E.; Latheef, I.M.; Anthony, R.G.

1999-04-01

The crystalline silicotitanate, UOP IONSIV IE-911, is a proven material for removing radionuclides from a wide variety of waste streams. It is superior for removing several radionuclides from the highly alkaline solutions typical of DOE wastes. This laboratory previously developed an equilibrium model applicable to complex solutions for IE-910 (the power form of the granular IE-911), and more recently, the authors have developed several single component ion-exchange kinetic models for predicting column breakthrough curves and batch reactor concentration histories. In this paper, the authors model ion-exchange column performance using effective diffusivities determined from batch kinetic experiments. This technique is preferablemore » because the batch experiments are easier, faster, and cheaper to perform than column experiments. They also extend these ideas to multicomponent systems. Finally, they evaluate the ability of the equilibrium model to predict data for IE-911.« less

Equilibrium and Kinetic Studies of Cd2+ Biosorption by the Brown Algae Sargassum fusiforme

PubMed Central

Zou, Hui-Xi; Li, Nan; Wang, Li-Hua; Yu, Ping; Yan, Xiu-Feng

2014-01-01

A fundamental investigation of the biosorption of Cd2+ from aqueous solution by the edible seaweed Sargassum fusiforme was performed under batch conditions. The influences of experimental parameters, such as the initial pH, sorption time, temperature, and initial Cd2+ concentration, on Cd2+ uptake by S. fusiforme were evaluated. The results indicated that the biosorption of Cd2+ depended on the initial Cd2+ concentration, as well as the pH. The uptake of Cd2+ could be described by the Langmuir isotherm model, and both the Langmuir biosorption equilibrium constant and the maximum biosorption capacity of the monolayer decreased with increasing temperature, thereby confirming the exothermic character of the sorption process. The biosorption kinetics follows the pseudo-second-order kinetic model, and intraparticle diffusion is the sole rate-limiting step for the entire biosorption period. These fundamental equilibrium and kinetic results can support further studies to the removal of cadmium from S. fusiforme harvested from cadmium-polluted waters. PMID:24736449

Dynamic Analysis of a Reaction-Diffusion Rumor Propagation Model

NASA Astrophysics Data System (ADS)

Zhao, Hongyong; Zhu, Linhe

2016-06-01

The rapid development of the Internet, especially the emergence of the social networks, leads rumor propagation into a new media era. Rumor propagation in social networks has brought new challenges to network security and social stability. This paper, based on partial differential equations (PDEs), proposes a new SIS rumor propagation model by considering the effect of the communication between the different rumor infected users on rumor propagation. The stabilities of a nonrumor equilibrium point and a rumor-spreading equilibrium point are discussed by linearization technique and the upper and lower solutions method, and the existence of a traveling wave solution is established by the cross-iteration scheme accompanied by the technique of upper and lower solutions and Schauder’s fixed point theorem. Furthermore, we add the time delay to rumor propagation and deduce the conditions of Hopf bifurcation and stability switches for the rumor-spreading equilibrium point by taking the time delay as the bifurcation parameter. Finally, numerical simulations are performed to illustrate the theoretical results.

Determination of the equilibrium constant of C60 fullerene binding with drug molecules.

PubMed

Mosunov, Andrei A; Pashkova, Irina S; Sidorova, Maria; Pronozin, Artem; Lantushenko, Anastasia O; Prylutskyy, Yuriy I; Parkinson, John A; Evstigneev, Maxim P

2017-03-01

We report a new analytical method that allows the determination of the magnitude of the equilibrium constant of complexation, K h , of small molecules to C 60 fullerene in aqueous solution. The developed method is based on the up-scaled model of C 60 fullerene-ligand complexation and contains the full set of equations needed to fit titration datasets arising from different experimental methods (UV-Vis spectroscopy, 1 H NMR spectroscopy, diffusion ordered NMR spectroscopy, DLS). The up-scaled model takes into consideration the specificity of C 60 fullerene aggregation in aqueous solution and allows the highly dispersed nature of C 60 fullerene cluster distribution to be accounted for. It also takes into consideration the complexity of fullerene-ligand dynamic equilibrium in solution, formed by various types of self- and hetero-complexes. These features make the suggested method superior to standard Langmuir-type analysis, the approach used to date for obtaining quantitative information on ligand binding with different nanoparticles.

Nonequilibrium radiation and chemistry models for aerocapture vehicle flowfields

NASA Technical Reports Server (NTRS)

Carlson, Leland A.

1994-01-01

The primary accomplishments of the project were as follows: (1) From an overall standpoint, the primary accomplishment of this research was the development of a complete gasdynamic-radiatively coupled nonequilibrium viscous shock layer solution method for axisymmetric blunt bodies. This method can be used for rapid engineering modeling of nonequilibrium re-entry flowfields over a wide range of conditions. (2) Another significant accomplishment was the development of an air radiation model that included local thermodynamic nonequilibrium (LTNE) phenomena. (3) As part of this research, three electron-electronic energy models were developed. The first was a quasi-equilibrium electron (QEE) model which determined an effective free electron temperature and assumed that the electronic states were in equilibrium with the free electrons. The second was a quasi-equilibrium electron-electronic (QEEE) model which computed an effective electron-electronic temperature. The third model was a full electron-electronic (FEE) differential equation model which included convective, collisional, viscous, conductive, vibrational coupling, and chemical effects on electron-electronic energy. (4) Since vibration-dissociation coupling phenomena as well as vibrational thermal nonequilibrium phenomena are important in the nonequilibrium zone behind a shock front, a vibrational energy and vibration-dissociation coupling model was developed and included in the flowfield model. This model was a modified coupled vibrational dissociation vibrational (MCVDV) model and also included electron-vibrational coupling. (5) Another accomplishment of the project was the usage of the developed models to investigate radiative heating. (6) A multi-component diffusion model which properly models the multi-component nature of diffusion in complex gas mixtures such as air, was developed and incorporated into the blunt body model. (7) A model was developed to predict the magnitude and characteristics of the shock wave precursor ahead of vehicles entering the Earth's atmosphere. (8) Since considerable data exists for radiating nonequilibrium flow behind normal shock waves, a normal shock wave version of the blunt body code was developed. (9) By comparing predictions from the models and codes with available normal shock data and the flight data of Fire II, it is believed that the developed flowfield and nonequilibrium radiation models have been essentially validated for engineering applications.

Brownian ratchets: How stronger thermal noise can reduce diffusion

NASA Astrophysics Data System (ADS)

Spiechowicz, Jakub; Kostur, Marcin; Łuczka, Jerzy

2017-02-01

We study diffusion properties of an inertial Brownian motor moving on a ratchet substrate, i.e., a periodic structure with broken reflection symmetry. The motor is driven by an unbiased time-periodic symmetric force that takes the system out of thermal equilibrium. For selected parameter sets, the system is in a non-chaotic regime in which we can identify a non-monotonic dependence of the diffusion coefficient on temperature: for low temperature, it initially increases as the temperature grows, passes through its local maximum, next starts to diminish reaching its local minimum, and finally it monotonically increases in accordance with the Einstein linear relation. Particularly interesting is the temperature interval in which diffusion is suppressed by the thermal noise, and we explain this effect in terms of transition rates of a three-state stochastic model.

Brownian ratchets: How stronger thermal noise can reduce diffusion.

PubMed

Spiechowicz, Jakub; Kostur, Marcin; Łuczka, Jerzy

2017-02-01

We study diffusion properties of an inertial Brownian motor moving on a ratchet substrate, i.e., a periodic structure with broken reflection symmetry. The motor is driven by an unbiased time-periodic symmetric force that takes the system out of thermal equilibrium. For selected parameter sets, the system is in a non-chaotic regime in which we can identify a non-monotonic dependence of the diffusion coefficient on temperature: for low temperature, it initially increases as the temperature grows, passes through its local maximum, next starts to diminish reaching its local minimum, and finally it monotonically increases in accordance with the Einstein linear relation. Particularly interesting is the temperature interval in which diffusion is suppressed by the thermal noise, and we explain this effect in terms of transition rates of a three-state stochastic model.

Thermal equilibrium concentrations and effects of negatively charged Ga vacancies in n-type GaAs

NASA Astrophysics Data System (ADS)

Tan, T. Y.; You, H.-M.; Gösele, U. M.

1993-03-01

We have calculated the thermal equilibrium concentrations of the various negatively charged Ga vacancy species in GaAs. The triply-negatively-charged Ga vacancy, V {Ga/3-}, has been emphasized, since it dominates Ga self-diffusion and Ga-Al interdiffusion under intrinsic and n-doping conditions, as well as the diffusion of Si donor atoms occupying Ga sites. Under strong n-doping conditions, the thermal equilibrium V {Ga/3-}concentration, C_{V_{_{Ga} }^{3 - } }^{eq} (n), has been found to exhibit a temperature independence or a negative temperature dependence, i.e., the C_{V_{_{Ga} }^{3 - } }^{eq} (n) value is either unchanged or increases as the temperature is lowered. This is quite contrary to the normal point defect behavior for which the point defect thermal equilibrium concentration decreases as the temperature is lowered. This C_{V_{_{Ga} }^{3 - } }^{eq} (n) property provides explanations to a number of outstanding experimental results, either requiring the interpretation that V {Ga/3-}has attained its thermal equilibrium concentration at the onset of each experiment, or requiring mechanisms involving point defect non-equilibrium phenomena.

Anomalous versus Slowed-Down Brownian Diffusion in the Ligand-Binding Equilibrium

PubMed Central

Soula, Hédi; Caré, Bertrand; Beslon, Guillaume; Berry, Hugues

2013-01-01

Measurements of protein motion in living cells and membranes consistently report transient anomalous diffusion (subdiffusion) that converges back to a Brownian motion with reduced diffusion coefficient at long times after the anomalous diffusion regime. Therefore, slowed-down Brownian motion could be considered the macroscopic limit of transient anomalous diffusion. On the other hand, membranes are also heterogeneous media in which Brownian motion may be locally slowed down due to variations in lipid composition. Here, we investigate whether both situations lead to a similar behavior for the reversible ligand-binding reaction in two dimensions. We compare the (long-time) equilibrium properties obtained with transient anomalous diffusion due to obstacle hindrance or power-law-distributed residence times (continuous-time random walks) to those obtained with space-dependent slowed-down Brownian motion. Using theoretical arguments and Monte Carlo simulations, we show that these three scenarios have distinctive effects on the apparent affinity of the reaction. Whereas continuous-time random walks decrease the apparent affinity of the reaction, locally slowed-down Brownian motion and local hindrance by obstacles both improve it. However, only in the case of slowed-down Brownian motion is the affinity maximal when the slowdown is restricted to a subregion of the available space. Hence, even at long times (equilibrium), these processes are different and exhibit irreconcilable behaviors when the area fraction of reduced mobility changes. PMID:24209851

Noise-induced symmetry breaking far from equilibrium and the emergence of biological homochirality

NASA Astrophysics Data System (ADS)

Jafarpour, Farshid; Biancalani, Tommaso; Goldenfeld, Nigel

2017-03-01

The origin of homochirality, the observed single-handedness of biological amino acids and sugars, has long been attributed to autocatalysis, a frequently assumed precursor for early life self-replication. However, the stability of homochiral states in deterministic autocatalytic systems relies on cross-inhibition of the two chiral states, an unlikely scenario for early life self-replicators. Here we present a theory for a stochastic individual-level model of autocatalytic prebiotic self-replicators that are maintained out of thermal equilibrium. Without chiral inhibition, the racemic state is the global attractor of the deterministic dynamics, but intrinsic multiplicative noise stabilizes the homochiral states. Moreover, we show that this noise-induced bistability is robust with respect to diffusion of molecules of opposite chirality, and systems of diffusively coupled autocatalytic chemical reactions synchronize their final homochiral states when the self-replication is the dominant production mechanism for the chiral molecules. We conclude that nonequilibrium autocatalysis is a viable mechanism for homochirality, without imposing additional nonlinearities such as chiral inhibition.

Non-monotonic temperature dependence of chaos-assisted diffusion in driven periodic systems

NASA Astrophysics Data System (ADS)

Spiechowicz, J.; Talkner, P.; Hänggi, P.; Łuczka, J.

2016-12-01

The spreading of a cloud of independent Brownian particles typically proceeds more effectively at higher temperatures, as it derives from the commonly known Sutherland-Einstein relation for systems in thermal equilibrium. Here, we report on a non-equilibrium situation in which the diffusion of a periodically driven Brownian particle moving in a periodic potential decreases with increasing temperature within a finite temperature window. We identify as the cause for this non-intuitive behaviour a dominant deterministic mechanism consisting of a few unstable periodic orbits embedded into a chaotic attractor together with thermal noise-induced dynamical changes upon varying temperature. The presented analysis is based on extensive numerical simulations of the corresponding Langevin equation describing the studied setup as well as on a simplified stochastic model formulated in terms of a three-state Markovian process. Because chaos exists in many natural as well as in artificial systems representing abundant areas of contemporary knowledge, the described mechanism may potentially be discovered in plentiful different contexts.

Space-time models based on random fields with local interactions

NASA Astrophysics Data System (ADS)

Hristopulos, Dionissios T.; Tsantili, Ivi C.

2016-08-01

The analysis of space-time data from complex, real-life phenomena requires the use of flexible and physically motivated covariance functions. In most cases, it is not possible to explicitly solve the equations of motion for the fields or the respective covariance functions. In the statistical literature, covariance functions are often based on mathematical constructions. In this paper, we propose deriving space-time covariance functions by solving “effective equations of motion”, which can be used as statistical representations of systems with diffusive behavior. In particular, we propose to formulate space-time covariance functions based on an equilibrium effective Hamiltonian using the linear response theory. The effective space-time dynamics is then generated by a stochastic perturbation around the equilibrium point of the classical field Hamiltonian leading to an associated Langevin equation. We employ a Hamiltonian which extends the classical Gaussian field theory by including a curvature term and leads to a diffusive Langevin equation. Finally, we derive new forms of space-time covariance functions.

Impact of density-dependent migration flows on epidemic outbreaks in heterogeneous metapopulations

NASA Astrophysics Data System (ADS)

Ripoll, J.; Avinyó, A.; Pellicer, M.; Saldaña, J.

2015-08-01

We investigate the role of migration patterns on the spread of epidemics in complex networks. We enhance the SIS-diffusion model on metapopulations to a nonlinear diffusion. Specifically, individuals move randomly over the network but at a rate depending on the population of the departure patch. In the absence of epidemics, the migration-driven equilibrium is described by quantifying the total number of individuals living in heavily or lightly populated areas. Our analytical approach reveals that strengthening the migration from populous areas contains the infection at the early stage of the epidemic. Moreover, depending on the exponent of the nonlinear diffusion rate, epidemic outbreaks do not always occur in the most populated areas as one might expect.

Pattern dynamics of the reaction-diffusion immune system.

PubMed

Zheng, Qianqian; Shen, Jianwei; Wang, Zhijie

2018-01-01

In this paper, we will investigate the effect of diffusion, which is ubiquitous in nature, on the immune system using a reaction-diffusion model in order to understand the dynamical behavior of complex patterns and control the dynamics of different patterns. Through control theory and linear stability analysis of local equilibrium, we obtain the optimal condition under which the system loses stability and a Turing pattern occurs. By combining mathematical analysis and numerical simulation, we show the possible patterns and how these patterns evolve. In addition, we establish a bridge between the complex patterns and the biological mechanism using the results from a previous study in Nature Cell Biology. The results in this paper can help us better understand the biological significance of the immune system.

Transport coefficients in high-temperature ionized air flows with electronic excitation

NASA Astrophysics Data System (ADS)

Istomin, V. A.; Oblapenko, G. P.

2018-01-01

Transport coefficients are studied in high-temperature ionized air mixtures using the modified Chapman-Enskog method. The 11-component mixture N2/N2+/N /N+/O2/O2+/O /O+/N O /N O+/e- , taking into account the rotational and vibrational degrees of freedom of molecules and electronic degrees of freedom of both atomic and molecular species, is considered. Using the PAINeT software package, developed by the authors of the paper, in wide temperature range calculations of the thermal conductivity, thermal diffusion, diffusion, and shear viscosity coefficients for an equilibrium ionized air mixture and non-equilibrium flow conditions for mixture compositions, characteristic of those in shock tube experiments and re-entry conditions, are performed. For the equilibrium air case, the computed transport coefficients are compared to those obtained using simplified kinetic theory algorithms. It is shown that neglecting electronic excitation leads to a significant underestimation of the thermal conductivity coefficient at temperatures higher than 25 000 K. For non-equilibrium test cases, it is shown that the thermal diffusion coefficients of neutral species and the self-diffusion coefficients of all species are strongly affected by the mixture composition, while the thermal conductivity coefficient is most strongly influenced by the degree of ionization of the flow. Neglecting electronic excitation causes noticeable underestimation of the thermal conductivity coefficient at temperatures higher than 20 000 K.

Monte Carlo analysis of neutron diffuse scattering data

NASA Astrophysics Data System (ADS)

Goossens, D. J.; Heerdegen, A. P.; Welberry, T. R.; Gutmann, M. J.

2006-11-01

This paper presents a discussion of a technique developed for the analysis of neutron diffuse scattering data. The technique involves processing the data into reciprocal space sections and modelling the diffuse scattering in these sections. A Monte Carlo modelling approach is used in which the crystal energy is a function of interatomic distances between molecules and torsional rotations within molecules. The parameters of the model are the spring constants governing the interactions, as they determine the correlations which evolve when the model crystal structure is relaxed at finite temperature. When the model crystal has reached equilibrium its diffraction pattern is calculated and a χ2 goodness-of-fit test between observed and calculated data slices is performed. This allows a least-squares refinement of the fit parameters and so automated refinement can proceed. The first application of this methodology to neutron, rather than X-ray, data is outlined. The sample studied was deuterated benzil, d-benzil, C14D10O2, for which data was collected using time-of-flight Laue diffraction on SXD at ISIS.

Biosorption of metal ions using a low cost modified adsorbent (Mauritia flexuosa): experimental design and mathematical modeling.

PubMed

Melo, Diego de Quadros; Vidal, Carla Bastos; Medeiros, Thiago Coutinho; Raulino, Giselle Santiago Cabral; Dervanoski, Adriana; Pinheiro, Márcio do Carmo; Nascimento, Ronaldo Ferreira do

2016-09-01

Buriti fibers were subjected to an alkaline pre-treatment and tested as an adsorbent to investigate the adsorption of copper, cadmium, lead and nickel in mono- and multi-element aqueous solutions, the results showed an increase in the adsorption capacity compared to the unmodified Buriti fiber. The effects of pH, adsorbent mass, agitation rate and initial metal ions concentration on the efficiency of the adsorption process were studied using a fractional 2(4-1) factorial design, and the results showed that all four parameters influenced metal adsorption differently. Fourier transform infrared spectrometry and X-ray fluorescence analysis were used to identify the groups that participated in the adsorption process and suggest its mechanisms and they indicated the probable mechanisms involved in the adsorption process are mainly ion exchange. Kinetic and thermodynamic equilibrium parameters were determined. The adsorption kinetics were adjusted to the homogeneous diffusion model. The adsorption equilibrium was reached in 30 min for Cu(2+) and Pb(2+), 20 min for Ni(2+) and instantaneously for Cd(2+). The results showed a significant difference was found in the competitiveness for the adsorption sites. A mathematical model was used to simulate the breakthrough curves in multi-element column adsorption considering the influences of external mass transfer and intraparticle diffusion resistance.

Stochastic dynamics and non-equilibrium thermodynamics of a bistable chemical system: the Schlögl model revisited.

PubMed

Vellela, Melissa; Qian, Hong

2009-10-06

Schlögl's model is the canonical example of a chemical reaction system that exhibits bistability. Because the biological examples of bistability and switching behaviour are increasingly numerous, this paper presents an integrated deterministic, stochastic and thermodynamic analysis of the model. After a brief review of the deterministic and stochastic modelling frameworks, the concepts of chemical and mathematical detailed balances are discussed and non-equilibrium conditions are shown to be necessary for bistability. Thermodynamic quantities such as the flux, chemical potential and entropy production rate are defined and compared across the two models. In the bistable region, the stochastic model exhibits an exchange of the global stability between the two stable states under changes in the pump parameters and volume size. The stochastic entropy production rate shows a sharp transition that mirrors this exchange. A new hybrid model that includes continuous diffusion and discrete jumps is suggested to deal with the multiscale dynamics of the bistable system. Accurate approximations of the exponentially small eigenvalue associated with the time scale of this switching and the full time-dependent solution are calculated using Matlab. A breakdown of previously known asymptotic approximations on small volume scales is observed through comparison with these and Monte Carlo results. Finally, in the appendix section is an illustration of how the diffusion approximation of the chemical master equation can fail to represent correctly the mesoscopically interesting steady-state behaviour of the system.

Anatomy of particle diffusion

NASA Astrophysics Data System (ADS)

Bringuier, E.

2009-11-01

The paper analyses particle diffusion from a thermodynamic standpoint. The main goal of the paper is to highlight the conceptual connection between particle diffusion, which belongs to non-equilibrium statistical physics, and mechanics, which deals with particle motion, at the level of third-year university courses. We start out from the fact that, near equilibrium, particle transport should occur down the gradient of the chemical potential. This yields Fick's law with two additional advantages. First, splitting the chemical potential into 'mechanical' and 'chemical' contributions shows how transport and mechanics are linked through the diffusivity-mobility relationship. Second, splitting the chemical potential into entropic and energetic contributions discloses the respective roles of entropy maximization and energy minimization in driving diffusion. The paper addresses first unary diffusion, where there is only one mobile species in an immobile medium, and next turns to binary diffusion, where two species are mobile with respect to each other in a fluid medium. The interrelationship between unary and binary diffusivities is brought out and it is shown how binary diffusion reduces to unary diffusion in the limit of high dilution of one species amidst the other one. Self- and mutual diffusion are considered and contrasted within the thermodynamic framework; self-diffusion is a time-dependent manifestation of the Gibbs paradox of mixing.

Efficient estimation of diffusion during dendritic solidification

NASA Technical Reports Server (NTRS)

Yeum, K. S.; Poirier, D. R.; Laxmanan, V.

1989-01-01

A very efficient finite difference method has been developed to estimate the solute redistribution during solidification with diffusion in the solid. This method is validated by comparing the computed results with the results of an analytical solution derived by Kobayashi (1988) for the assumptions of a constant diffusion coefficient, a constant equilibrium partition ratio, and a parabolic rate of the advancement of the solid/liquid interface. The flexibility of the method is demonstrated by applying it to the dendritic solidification of a Pb-15 wt pct Sn alloy, for which the equilibrium partition ratio and diffusion coefficient vary substantially during solidification. The fraction eutectic at the end of solidification is also obtained by estimating the fraction solid, in greater resolution, where the concentration of solute in the interdendritic liquid reaches the eutectic composition of the alloy.

Grain size distribution in sheared polycrystals

NASA Astrophysics Data System (ADS)

Sarkar, Tanmoy; Biswas, Santidan; Chaudhuri, Pinaki; Sain, Anirban

2017-12-01

Plastic deformation in solids induced by external stresses is of both fundamental and practical interest. Using both phase field crystal modeling and molecular dynamics simulations, we study the shear response of monocomponent polycrystalline solids. We subject mesocale polycrystalline samples to constant strain rates in a planar Couette flow geometry for studying its plastic flow, in particular its grain deformation dynamics. As opposed to equilibrium solids where grain dynamics is mainly driven by thermal diffusion, external stress/strain induce a much higher level of grain deformation activity in the form of grain rotation, coalescence, and breakage, mediated by dislocations. Despite this, the grain size distribution of this driven system shows only a weak power-law correction to its equilibrium log-normal behavior. We interpret the grain reorganization dynamics using a stochastic model.

Does shaking increase the pressure inside a bottle of champagne?

PubMed

Vreme, A; Pouligny, B; Nadal, F; Liger-Belair, G

2015-02-01

Colas, beers and sparkling wines are all concentrated solutions of carbon dioxide in aqueous solvents. Any such carbonated liquid is ordinarily conditioned inside a closed bottle or a metal can as a liquid-gas 2-phase system. At thermodynamic equilibrium, the partial pressure of carbon-dioxide in the gas phase and its concentration in the liquid are proportional (Henry's law). In practical conditions and use (transport, opening of the container, exterior temperature change, etc.), Henry's equilibrium can be perturbed. The goal of this paper is to describe and understand how the system responds to such perturbations and evolves towards a new equilibrium state. Formally, we investigate the dynamics around Henry's equilibrium of a closed system, through dedicated experiments and modeling. We focus on the response to a sudden pressure change and to mechanical shaking (the latter point inspired the article's title). Observations are rationalized through basic considerations including molecular diffusion, bubble dynamics (based on Epstein-Plesset theory) and chemi-convective hydrodynamic instabilities. Copyright © 2014 Elsevier Inc. All rights reserved.

The rate of equilibration of viscous aerosol particles

NASA Astrophysics Data System (ADS)

O'Meara, Simon; Topping, David O.; McFiggans, Gordon

2016-04-01

The proximity of atmospheric aerosol particles to equilibrium with their surrounding condensable vapours can substantially impact their transformations, fate and impacts and is the subject of vibrant research activity. In this study we first compare equilibration timescales estimated by three different models for diffusion through aerosol particles to assess any sensitivity to choice of model framework. Equilibration times for diffusion coefficients with varying dependencies on composition are compared for the first time. We show that even under large changes in the saturation ratio of a semi-volatile component (es) of 1-90 % predicted equilibration timescales are in agreement, including when diffusion coefficients vary with composition. For condensing water and a diffusion coefficient dependent on composition, a plasticising effect is observed, leading to a decreased estimated equilibration time with increasing final es. Above 60 % final es maximum equilibration times of around 1 s are estimated for comparatively large particles (10 µm) containing a relatively low diffusivity component (1 × 10-25 m2 s-1 in pure form). This, as well as other results here, questions whether particle-phase diffusion through water-soluble particles can limit hygroscopic growth in the ambient atmosphere. In the second part of this study, we explore sensitivities associated with the use of particle radius measurements to infer diffusion coefficient dependencies on composition using a diffusion model. Given quantified similarities between models used in this study, our results confirm considerations that must be taken into account when designing such experiments. Although quantitative agreement of equilibration timescales between models is found, further work is necessary to determine their suitability for assessing atmospheric impacts, such as their inclusion in polydisperse aerosol simulations.

Diffusion of cations in chromia layers grown on iron-base alloys

DOE Office of Scientific and Technical Information (OSTI.GOV)

Lobnig, R.E.; Hennesen, K.; Grabke, H.J.

Diffusion of the cations Cr, Fe, Mn, and Ni in Cr{sub 2}O{sub 3} has been investigated at 1,173 K. The diffusion measurements were performed on chromia layers grown on the model alloys Fe-20Cr and Fe-20Cr-12Ni in order to consider effects of small amounts of dissolved alien cations in Cr{sub 2}O{sub 3}. The samples were diffusion annealed in H{sub 2}-H{sub 2}O at an oxygen partial pressure close to the Cr{sub 2}O{sub 3}/Cr equilibrium. For all tracers the lattice-diffusion coefficients are 3-5 orders of magnitude smaller than the grain-boundary diffusion coefficients. The lattice diffusivity of Mn is about two orders of magnitudemore » greater than the other lattice-diffusion coefficients, especially in Cr{sub 2}O{sub 3} grown on Fe-20Cr-12Ni. The values of the diffusion coefficients for Cr, Fe, and Ni are in the same range. Diffusion of the tracers in Cr{sub 2}O{sub 3} grown on different alloys did not show significant differences with the exception of Mn.« less

Inhibitory effect on the uptake and diffusion of Cd(2+) onto soybean hull sorbent in Cd-Pb binary sorption systems.

PubMed

Módenes, Aparecido N; Espinoza-Quiñones, Fernando R; Colombo, Andréia; Geraldi, Claudinéia L; Trigueros, Daniela E G

2015-05-01

The uptake of Cd(2+) and Pb(2+) ions by a soybean hull (SH) biosorbent in single and binary systems has been investigated. Sorption tests regarding SH in natura and chemically treated were carried out testing a suitable value range of solution pH, sorption temperature and shaking velocity. Sorption capacity is improved at pH 4, 30 °C temperature and 100 rpm. When a strong base is applied, a related-to-untreated SH increasing of 20% in the sorption capacity of Pb(2+) ions was observed, but with poor results for Cd(2+) uptake. Additionally, a relatively strong decreasing in both sorption capacities of Pb(2+) and Cd(2+) ions was evidenced for all acidic treatments. Regarding untreated SH, kinetic sorption data of both metals were well-interpreted by a pseudo second-order model and a rate-limiting step on the basis of an intra-particle diffusion model was suggested to occur. An inhibitory effect of Pb(2+) diffusion over Cd(2+) one was observed, limiting to reach the obtained maximum sorption capacity in single system. Maximum adsorption capacities of 0.49 and 0.67mequivg(-1) for Cd(2+) and Pb(2+), respectively, were predicted by the Langmuir isotherm model that reproduced well the equilibrium sorption data for single systems. The inhibitory effect of one metal over the other one was verified in equilibrium sorption data for binary systems interpreted on the basis of a modified extended Langmuir isotherm model, predicting changes in metal affinity onto the SH surface. Finally, SH is an alternative biosorbent with a great potential for the wastewater treatment containing cadmium and lead ions. Copyright © 2015 Elsevier Ltd. All rights reserved.

Coupling of phytoplankton uptake and air-water exchange of persistent organic pollutants

DOE Office of Scientific and Technical Information (OSTI.GOV)

Dachs, J.; Eisenreich, S.J.; Baker, J.E.

1999-10-15

A dynamic model that couples air-water exchange and phytoplankton uptake of persistent organic pollutants has been developed and then applied to PCB data from a small experimental lake. A sensitivity analysis of the model, taking into account the influence of physical environmental conditions such as temperature, wind speed, and mixing depth as well as plankton-related parameters such as biomass and growth rate was carried out for a number of PCBs with different physical-chemical properties. The results indicate that air-water exchange dynamics are influenced not only by physical parameters but also by phytoplankton biomass and growth rate. New phytoplankton production resultsmore » in substantially longer times to reach equilibrium. Phytoplankton uptake-induced depletion of the dissolved phase concentration maintains air and water phases out of equilibrium. Furthermore, PCBs in phytoplankton also take longer times to reach equilibrium with the dissolved water phase when the latter is supported by diffusive air-water exchange. However, both model analysis and model application to the Experimental Lakes Area of northwestern Ontario (Canada) suggest that the gas phase supports the concentrations of persistent organic pollutants, such as PCBs, in atmospherically driven aquatic environments.« less

Bursting Regimes in a Reaction-Diffusion System with Action Potential-Dependent Equilibrium

PubMed Central

Meier, Stephen R.; Lancaster, Jarrett L.; Starobin, Joseph M.

2015-01-01

The equilibrium Nernst potential plays a critical role in neural cell dynamics. A common approximation used in studying electrical dynamics of excitable cells is that the ionic concentrations inside and outside the cell membranes act as charge reservoirs and remain effectively constant during excitation events. Research into brain electrical activity suggests that relaxing this assumption may provide a better understanding of normal and pathophysiological functioning of the brain. In this paper we explore time-dependent ionic concentrations by allowing the ion-specific Nernst potentials to vary with developing transmembrane potential. As a specific implementation, we incorporate the potential-dependent Nernst shift into a one-dimensional Morris-Lecar reaction-diffusion model. Our main findings result from a region in parameter space where self-sustaining oscillations occur without external forcing. Studying the system close to the bifurcation boundary, we explore the vulnerability of the system with respect to external stimulations which disrupt these oscillations and send the system to a stable equilibrium. We also present results for an extended, one-dimensional cable of excitable tissue tuned to this parameter regime and stimulated, giving rise to complex spatiotemporal pattern formation. Potential applications to the emergence of neuronal bursting in similar two-variable systems and to pathophysiological seizure-like activity are discussed. PMID:25823018

Diffusion modelling of metamorphic layered coronas with stability criterion and consideration of affinity

NASA Astrophysics Data System (ADS)

Ashworth, J. R.; Sheplev, V. S.

1997-09-01

Layered coronas between two reactant minerals can, in many cases, be attributed to diffusion-controlled growth with local equilibrium. This paper clarifies and unifies the previous approaches of various authors to the simplest form of modelling, which uses no assumed values for thermochemical quantities. A realistic overall reaction must be estimated from measured overall proportions of minerals and their major element compositions. Modelling is not restricted to a particular number of components S, relative to the number of phases Φ. IfΦ > S + 1, the overall reaction is a combination of simultaneous reactions. The stepwise method, solving for the local reaction at each boundary in turn, is extended to allow for recurrence of a mineral (its presence in two parts of the layer structure separated by a gap). The equations are also given in matrix form. A thermodynamic stability criterion is derived, determining which layer sequence is truly stable if several are computable from the same inputs. A layer structure satisfying the stability criterion has greater growth rate (and greater rate of entropy production) than the other computable layer sequences. This criterion of greatest entropy production is distinct from Prigogine's theorem of minimum entropy production, which distinguishes the stationary or quasi-stationary state from other states of the same layer sequence. The criterion leads to modification of previous results for coronas comprising hornblende, spinel, and orthopyroxene between olivine (Ol) and plagioclase (Pl). The outcome supports the previous inference that Si, and particularly Al, commonly behave as immobile relative to other cation-forming major elements. The affinity (-ΔG) of a corona-forming reaction is estimated, using previous estimates of diffusion coefficient and the duration t of reaction, together with a new model quantity (-ΔG) *. For an example of the Ol + Pl reaction, a rough calculation gives (-ΔG) > 1.7RT (per mole of P1 consumed, based on a 24-oxygen formula for Pl). At 600-700°C, this represents (-ΔG) > 10kJ mol -1 and departure from equilibrium temperature by at least ˜ 100°C. The lower end of this range is petrologically reasonable and, for t < 100Ma, corresponds to a Fick's-law diffusion coefficient for Al, DAl > 10 -25m 2s -1, larger than expected for lattice diffusion but consistent with fluid-absent grain-boundary diffusion and small concentration gradients.

Dynamics and profiles of a diffusive host-pathogen system with distinct dispersal rates

NASA Astrophysics Data System (ADS)

Wu, Yixiang; Zou, Xingfu

2018-04-01

In this paper, we investigate a diffusive host-pathogen model with heterogeneous parameters and distinct dispersal rates for the susceptible and infected hosts. We first prove that the solution of the model exists globally and the model system possesses a global attractor. We then identify the basic reproduction number R0 for the model and prove its threshold role: if R0 ≤ 1, the disease free equilibrium is globally asymptotically stable; if R0 > 1, the solution of the model is uniformly persistent and there exists a positive (pathogen persistent) steady state. Finally, we study the asymptotic profiles of the positive steady state as the dispersal rate of the susceptible or infected hosts approaches zero. Our result suggests that the infected hosts concentrate at certain points which can be characterized as the pathogen's most favoured sites when the mobility of the infected host is limited.

Non-equilibrium steady-state distributions of colloids in a tilted periodic potential

NASA Astrophysics Data System (ADS)

Ma, Xiaoguang; Lai, Pik-Yin; Ackerson, Bruce; Tong, Penger

A two-layer colloidal system is constructed to study the effects of the external force F on the non-equilibrium steady-state (NESS) dynamics of the diffusing particles over a tilted periodic potential, in which detailed balance is broken due to the presence of a steady particle flux. The periodic potential is provided by the bottom layer colloidal spheres forming a fixed crystalline pattern on a glass substrate. The corrugated surface of the bottom colloidal crystal provides a gravitational potential field for the top layer diffusing particles. By tilting the sample with respect to gravity, a tangential component F is applied to the diffusing particles. The measured NESS probability density function Pss (x , y) of the particles is found to deviate from the equilibrium distribution depending on the driving or distance from equilibrium. The experimental results are compared with the exact solution of the 1D Smoluchowski equation and the numerical results of the 2D Smoluchowski equation. Moreover, from the obtained exact 1D solution, we develop an analytical method to accurately extract the 1D potential U0 (x) from the measured Pss (x) . Work supported in part by the Research Grants Council of Hong Kong SAR.

Fresh clouds: A parameterized updraft method for calculating cloud densities in one-dimensional models

NASA Astrophysics Data System (ADS)

Wong, Michael H.; Atreya, Sushil K.; Kuhn, William R.; Romani, Paul N.; Mihalka, Kristen M.

2015-01-01

Models of cloud condensation under thermodynamic equilibrium in planetary atmospheres are useful for several reasons. These equilibrium cloud condensation models (ECCMs) calculate the wet adiabatic lapse rate, determine saturation-limited mixing ratios of condensing species, calculate the stabilizing effect of latent heat release and molecular weight stratification, and locate cloud base levels. Many ECCMs trace their heritage to Lewis (Lewis, J.S. [1969]. Icarus 10, 365-378) and Weidenschilling and Lewis (Weidenschilling, S.J., Lewis, J.S. [1973]. Icarus 20, 465-476). Calculation of atmospheric structure and gas mixing ratios are correct in these models. We resolve errors affecting the cloud density calculation in these models by first calculating a cloud density rate: the change in cloud density with updraft length scale. The updraft length scale parameterizes the strength of the cloud-forming updraft, and converts the cloud density rate from the ECCM into cloud density. The method is validated by comparison with terrestrial cloud data. Our parameterized updraft method gives a first-order prediction of cloud densities in a “fresh” cloud, where condensation is the dominant microphysical process. Older evolved clouds may be better approximated by another 1-D method, the diffusive-precipitative Ackerman and Marley (Ackerman, A.S., Marley, M.S. [2001]. Astrophys. J. 556, 872-884) model, which represents a steady-state equilibrium between precipitation and condensation of vapor delivered by turbulent diffusion. We re-evaluate observed cloud densities in the Galileo Probe entry site (Ragent, B. et al. [1998]. J. Geophys. Res. 103, 22891-22910), and show that the upper and lower observed clouds at ∼0.5 and ∼3 bars are consistent with weak (cirrus-like) updrafts under conditions of saturated ammonia and water vapor, respectively. The densest observed cloud, near 1.3 bar, requires unexpectedly strong updraft conditions, or higher cloud density rates. The cloud density rate in this layer may be augmented by a composition with non-NH4SH components (possibly including adsorbed NH3).

Adaptive Implicit Non-Equilibrium Radiation Diffusion

DOE Office of Scientific and Technical Information (OSTI.GOV)

Philip, Bobby; Wang, Zhen; Berrill, Mark A

2013-01-01

We describe methods for accurate and efficient long term time integra- tion of non-equilibrium radiation diffusion systems: implicit time integration for effi- cient long term time integration of stiff multiphysics systems, local control theory based step size control to minimize the required global number of time steps while control- ling accuracy, dynamic 3D adaptive mesh refinement (AMR) to minimize memory and computational costs, Jacobian Free Newton-Krylov methods on AMR grids for efficient nonlinear solution, and optimal multilevel preconditioner components that provide level independent solver convergence.

Ion Layer Separation and Equilibrium Zonal Winds in Midlatitude Sporadic E

NASA Technical Reports Server (NTRS)

Earle, G. D.; Kane, T. J.; Pfaff, R. F.; Bounds, S. R.

2000-01-01

In-situ observations of a moderately strong mid-latitude sporadic-E layer show a separation in altitude between distinct sublayers composed of Fe(+), Mg(+), and NO(+). From these observations it is possible to estimate the zonal wind field consistent with diffusive equilibrium near the altitude of the layer. The amplitude of the zonal wind necessary to sustain the layer against diffusive effects is less than 10 meters per second, and the vertical wavelength is less than 10 km.

Equilibrium and kinetics study on hexavalent chromium adsorption onto diethylene triamine grafted glycidyl methacrylate based copolymers.

PubMed

Maksin, Danijela D; Nastasović, Aleksandra B; Milutinović-Nikolić, Aleksandra D; Suručić, Ljiljana T; Sandić, Zvjezdana P; Hercigonja, Radmila V; Onjia, Antonije E

2012-03-30

Two porous and one non-porous crosslinked poly(glycidyl methacrylate-co-ethylene glycol dimethacrylate) [abbreviated PGME] were prepared by suspension copolymerization and functionalized with diethylene triamine [abbreviated PGME-deta]. Samples were characterized by elemental analysis, mercury porosimetry, scanning electron microscopy with energy-dispersive X-ray spectroscopy, and transmission electron microscopy. Kinetics of Cr(VI) sorption by PGME-deta were investigated in batch static experiments, in the temperature range 25-70°C. Sorption was rapid, with the uptake capacity higher than 80% after 30 min. Sorption behavior and rate-controlling mechanisms were analyzed using five kinetic models (pseudo-first order, pseudo-second order, Elovich, intraparticle diffusion and Bangham model). Kinetic studies showed that Cr(VI) adsorption adhered to the pseudo-second-order model, with definite influence of pore diffusion. Equilibrium data was tested with Langmuir, Freundlich and Tempkin adsorption isotherm models. Langmuir model was the most suitable indicating homogeneous distribution of active sites on PGME-deta and monolayer sorption. The maximum adsorption capacity from the Langmuir model, Q(max), at pH 1.8 and 25°C was 143 mg g(-1) for PGME2-deta (sample with the highest amino group concentration) while at 70°C Q(max) reached the high value of 198 mg g(-1). Thermodynamic parameters revealed spontaneous and endothermic nature of Cr(VI) adsorption onto PGME-deta. Copyright © 2012 Elsevier B.V. All rights reserved.

Plasma Equilibrium in a Magnetic Field with Stochastic Field-Line Trajectories

NASA Astrophysics Data System (ADS)

Krommes, J. A.; Reiman, A. H.

2008-11-01

The nature of plasma equilibrium in a magnetic field with stochastic field lines is examined, expanding upon the ideas first described by Reiman et al. The magnetic partial differential equation (PDE) that determines the equilibrium Pfirsch-Schlüter currents is treated as a passive stochastic PDE for μj/B. Renormalization leads to a stochastic Langevin equation for μ in which the resonances at the rational surfaces are broadened by the stochastic diffusion of the field lines; even weak radial diffusion can significantly affect the equilibrium, which need not be flattened in the stochastic region. Particular attention is paid to satisfying the periodicity constraints in toroidal configurations with sheared magnetic fields. A numerical scheme that couples the renormalized Langevin equation to Ampere's law is described. A. Reiman et al, Nucl. Fusion 47, 572--8 (2007). J. A. Krommes, Phys. Reports 360, 1--351.

Langevin equation with fluctuating diffusivity: A two-state model

NASA Astrophysics Data System (ADS)

Miyaguchi, Tomoshige; Akimoto, Takuma; Yamamoto, Eiji

2016-07-01

Recently, anomalous subdiffusion, aging, and scatter of the diffusion coefficient have been reported in many single-particle-tracking experiments, though the origins of these behaviors are still elusive. Here, as a model to describe such phenomena, we investigate a Langevin equation with diffusivity fluctuating between a fast and a slow state. Namely, the diffusivity follows a dichotomous stochastic process. We assume that the sojourn time distributions of these two states are given by power laws. It is shown that, for a nonequilibrium ensemble, the ensemble-averaged mean-square displacement (MSD) shows transient subdiffusion. In contrast, the time-averaged MSD shows normal diffusion, but an effective diffusion coefficient transiently shows aging behavior. The propagator is non-Gaussian for short time and converges to a Gaussian distribution in a long-time limit; this convergence to Gaussian is extremely slow for some parameter values. For equilibrium ensembles, both ensemble-averaged and time-averaged MSDs show only normal diffusion and thus we cannot detect any traces of the fluctuating diffusivity with these MSDs. Therefore, as an alternative approach to characterizing the fluctuating diffusivity, the relative standard deviation (RSD) of the time-averaged MSD is utilized and it is shown that the RSD exhibits slow relaxation as a signature of the long-time correlation in the fluctuating diffusivity. Furthermore, it is shown that the RSD is related to a non-Gaussian parameter of the propagator. To obtain these theoretical results, we develop a two-state renewal theory as an analytical tool.

The elimination of siloxanes from the biogas of a wastewater treatment plant by means of an adsorption process.

PubMed

Trapote, Arturo; García, Mariano; Prats, Daniel

2016-12-01

Siloxanes present in the biogas produced during anaerobic digestion in wastewater treatment plants (WWTPs) can damage the mechanism of cogeneration heat engines and obstruct the process of energy valorization. The objective of this research is to detect the presence of siloxanes in the biogas and evaluate a procedure for their elimination. A breakthrough curve of a synthetic decamethylcyclopentasiloxane on an experimental bed of activated carbon was modeled and the theoretical mathematical model of the adsorption process was adjusted. As a result, the constants of the model were obtained: the mass transfer constant, Henry's equilibrium constant, and the Eddy diffusion. The procedure developed allows the adsorption equilibrium of siloxanes on activated carbon to be predicted, and makes it possible to lay the basis for the design of an appropriate activated carbon module for the elimination of siloxanes in a WWTP.

Diagnostic analysis of two-dimensional monthly average ozone balance with Chapman chemistry

NASA Technical Reports Server (NTRS)

Stolarski, Richard S.; Jackman, Charles H.; Kaye, Jack A.

1986-01-01

Chapman chemistry has been used in a two-dimensional model to simulate ozone balance phenomenology. The similarity between regions of ozone production and loss calculated using Chapman chemistry and those computed using LIMS and SAMS data with a photochemical equilibrium model indicate that such simplified chemistry is useful in studying gross features in stratospheric ozone balance. Net ozone production or loss rates are brought about by departures from the photochemical equilibrium (PCE) condition. If transport drives ozone above its PCE condition, then photochemical loss dominates production. If transport drives ozone below its PCE condition, then photochemical production dominates loss. Gross features of ozone loss/production (L/P) inferred for the real atmosphere from data are also simulated using only eddy diffusion. This indicates that one must be careful in assigning a transport scheme for a two-dimensional model that mimics only behavior of the observed ozone L/P.

A statistical mechanics approach to computing rare transitions in multi-stable turbulent geophysical flows

NASA Astrophysics Data System (ADS)

Laurie, J.; Bouchet, F.

2012-04-01

Many turbulent flows undergo sporadic random transitions, after long periods of apparent statistical stationarity. For instance, paths of the Kuroshio [1], the Earth's magnetic field reversal, atmospheric flows [2], MHD experiments [3], 2D turbulence experiments [4,5], 3D flows [6] show this kind of behavior. The understanding of this phenomena is extremely difficult due to the complexity, the large number of degrees of freedom, and the non-equilibrium nature of these turbulent flows. It is however a key issue for many geophysical problems. A straightforward study of these transitions, through a direct numerical simulation of the governing equations, is nearly always impracticable. This is mainly a complexity problem, due to the large number of degrees of freedom involved for genuine turbulent flows, and the extremely long time between two transitions. In this talk, we consider two-dimensional and geostrophic turbulent models, with stochastic forces. We consider regimes where two or more attractors coexist. As an alternative to direct numerical simulation, we propose a non-equilibrium statistical mechanics approach to the computation of this phenomenon. Our strategy is based on large deviation theory [7], derived from a path integral representation of the stochastic process. Among the trajectories connecting two non-equilibrium attractors, we determine the most probable one. Moreover, we also determine the transition rates, and in which cases this most probable trajectory is a typical one. Interestingly, we prove that in the class of models we consider, a mechanism exists for diffusion over sets of connected attractors. For the type of stochastic forces that allows this diffusion, the transition between attractors is not a rare event. It is then very difficult to characterize the flow as bistable. However for another class of stochastic forces, this diffusion mechanism is prevented, and genuine bistability or multi-stability is observed. We discuss how these results are probably connected to the long debated existence of multi-stability in the atmosphere and oceans.

Cow bones char as a green sorbent for fluorides removal from aqueous solutions: batch and fixed-bed studies.

PubMed

Nigri, Elbert M; Cechinel, Maria Alice P; Mayer, Diego A; Mazur, Luciana P; Loureiro, José M; Rocha, Sônia D F; Vilar, Vítor J P

2017-01-01

Cow bone char was investigated as sorbent for the defluoridation of aqueous solutions. The cow bone char was characterized in terms of its morphology, chemical composition, and functional groups present on the bone char surface using different analytical techniques: SEM, EDS, N 2 -BET method, and FTIR. Batch equilibrium studies were performed for the bone chars prepared using different procedures. The highest sorption capacities for fluoride were obtained for the acid washed (q = 6.2 ± 0.5 mg/g) and Al-doped (q = 6.4 ± 0.3 mg/g) bone chars. Langmuir and Freundlich models fitted well the equilibrium sorption data. Fluoride removal rate in batch system is fast in the first 5 h, decreasing after this time until achieving equilibrium due to pore diffusion. The presence of carbonate and bicarbonate ions in the aqueous solution contributes to a decrease of the fluoride sorption capacity of the bone char by 79 and 31 %, respectively. Regeneration of the F-loaded bone char using 0.5 M NaOH solution leads to a sorption capacity for fluoride of 3.1 mg/g in the second loading cycle. Fluoride breakthrough curve obtained in a fixed-bed column presents an asymmetrical S-shaped form, with a slow approach of C/C 0  → 1.0 due to pore diffusion phenomena. Considering the guideline value for drinking water of 1.5 mg F - /L, as recommended by World Health Organization, the service cycle for fluoride removal was of 71.0 h ([F - ] feed  ∼ 9 mg/L; flow rate = 1 mL/min; m sorbent  = 12.6 g). A mass transfer model considering the pore diffusion was able to satisfactorily describe the experimental data obtained in batch and continuous systems.

Diffusive-convective physical vapor transport of PbTe from a Te-rich solid source

NASA Technical Reports Server (NTRS)

Zoutendyk, J.; Akutagawa, W.

1982-01-01

Crystal growth of PbTe by physical vapor transport (sublimation) in a closed ampoule is governed by the vapor species in thermal equilibrium with the solid compound. Deviations from stoichiometry in the source material cause diffusion limitation of the transport rate, which can be modified by natural (gravity-driven) convection. Mass-transport experiments have been performed using Te-rich material wherein sublimation rates have been measured in order to study the effects of natural convection in diffusion-limited vapor transport. Linear velocities for both crystal growth and evaporation (back sublimation) have been measured for transport in the direction of gravity, horizontally, and opposite to gravity. The experimental results are discussed in terms of both the one-dimensional diffusive-advective model and current, more sophisticated theory which includes natural convection. There is some evidence that convection effects from radial temperature gradients and solutal density gradients have been observed.

Massively Parallel Simulations of Diffusion in Dense Polymeric Structures

DOE Office of Scientific and Technical Information (OSTI.GOV)

Faulon, Jean-Loup, Wilcox, R.T.

1997-11-01

An original computational technique to generate close-to-equilibrium dense polymeric structures is proposed. Diffusion of small gases are studied on the equilibrated structures using massively parallel molecular dynamics simulations running on the Intel Teraflops (9216 Pentium Pro processors) and Intel Paragon(1840 processors). Compared to the current state-of-the-art equilibration methods this new technique appears to be faster by some orders of magnitude.The main advantage of the technique is that one can circumvent the bottlenecks in configuration space that inhibit relaxation in molecular dynamics simulations. The technique is based on the fact that tetravalent atoms (such as carbon and silicon) fit in themore » center of a regular tetrahedron and that regular tetrahedrons can be used to mesh the three-dimensional space. Thus, the problem of polymer equilibration described by continuous equations in molecular dynamics is reduced to a discrete problem where solutions are approximated by simple algorithms. Practical modeling applications include the constructing of butyl rubber and ethylene-propylene-dimer-monomer (EPDM) models for oxygen and water diffusion calculations. Butyl and EPDM are used in O-ring systems and serve as sealing joints in many manufactured objects. Diffusion coefficients of small gases have been measured experimentally on both polymeric systems, and in general the diffusion coefficients in EPDM are an order of magnitude larger than in butyl. In order to better understand the diffusion phenomena, 10, 000 atoms models were generated and equilibrated for butyl and EPDM. The models were submitted to a massively parallel molecular dynamics simulation to monitor the trajectories of the diffusing species.« less

Anatomy of Particle Diffusion

ERIC Educational Resources Information Center

Bringuier, E.

2009-01-01

The paper analyses particle diffusion from a thermodynamic standpoint. The main goal of the paper is to highlight the conceptual connection between particle diffusion, which belongs to non-equilibrium statistical physics, and mechanics, which deals with particle motion, at the level of third-year university courses. We start out from the fact…

A 3D model for rain-induced landslides based on molecular dynamics with fractal and fractional water diffusion

NASA Astrophysics Data System (ADS)

Martelloni, Gianluca; Bagnoli, Franco; Guarino, Alessio

2017-09-01

We present a three-dimensional model of rain-induced landslides, based on cohesive spherical particles. The rainwater infiltration into the soil follows either the fractional or the fractal diffusion equations. We analytically solve the fractal partial differential equation (PDE) for diffusion with particular boundary conditions to simulate a rainfall event. We developed a numerical integration scheme for the PDE, compared with the analytical solution. We adapt the fractal diffusion equation obtaining the gravimetric water content that we use as input of a triggering scheme based on Mohr-Coulomb limit-equilibrium criterion. This triggering is then complemented by a standard molecular dynamics algorithm, with an interaction force inspired by the Lennard-Jones potential, to update the positions and velocities of particles. We present our results for homogeneous and heterogeneous systems, i.e., systems composed by particles with same or different radius, respectively. Interestingly, in the heterogeneous case, we observe segregation effects due to the different volume of the particles. Finally, we analyze the parameter sensibility both for the triggering and the propagation phases. Our simulations confirm the results of a previous two-dimensional model and therefore the feasible applicability to real cases.

Anomalous versus slowed-down Brownian diffusion in the ligand-binding equilibrium.

PubMed

Soula, Hédi; Caré, Bertrand; Beslon, Guillaume; Berry, Hugues

2013-11-05

Measurements of protein motion in living cells and membranes consistently report transient anomalous diffusion (subdiffusion) that converges back to a Brownian motion with reduced diffusion coefficient at long times after the anomalous diffusion regime. Therefore, slowed-down Brownian motion could be considered the macroscopic limit of transient anomalous diffusion. On the other hand, membranes are also heterogeneous media in which Brownian motion may be locally slowed down due to variations in lipid composition. Here, we investigate whether both situations lead to a similar behavior for the reversible ligand-binding reaction in two dimensions. We compare the (long-time) equilibrium properties obtained with transient anomalous diffusion due to obstacle hindrance or power-law-distributed residence times (continuous-time random walks) to those obtained with space-dependent slowed-down Brownian motion. Using theoretical arguments and Monte Carlo simulations, we show that these three scenarios have distinctive effects on the apparent affinity of the reaction. Whereas continuous-time random walks decrease the apparent affinity of the reaction, locally slowed-down Brownian motion and local hindrance by obstacles both improve it. However, only in the case of slowed-down Brownian motion is the affinity maximal when the slowdown is restricted to a subregion of the available space. Hence, even at long times (equilibrium), these processes are different and exhibit irreconcilable behaviors when the area fraction of reduced mobility changes. Copyright © 2013 Biophysical Society. Published by Elsevier Inc. All rights reserved.

Excitation of the Magnetospheric Cavity

DTIC Science & Technology

2007-06-16

gyrofrequency of 880 kHz at the ground at the equator, and uses a diffusive equilibrium model [ Angerami and Thomas, 1964] to calculate charged particle...significantly damped [Smith and Angerami , 1968; Edgar, 1976; Gurnett and Inan, 1988], resonantly interacting with, and pitch angle scattering...2429, 1999. Angerami , J. J., and J. O. Thomas, Studies of planetary Atmospheres, 1, The distribution of electrons and ions in the Earth’s

Ablation and radiation coupled viscous hypersonic shock layers, volume 1

NASA Technical Reports Server (NTRS)

Engel, C. D.

1971-01-01

The results for a stagnation-line analysis of the radiative heating of a phenolic-nylon ablator are presented. The analysis includes flow field coupling with the ablator surface, equilibrium chemistry, a step-function diffusion model and a coupled line and continuum radiation calculation. This report serves as the documentation, i e. users manual and operating instructions for the computer programs listed in the report.

The soft X-ray diffuse background observed with the HEAO 1 low-energy detectors

NASA Technical Reports Server (NTRS)

Garmire, G. P.; Nousek, J. A.; Apparao, K. M. V.; Burrows, D. N.; Fink, R. L.; Kraft, R. P.

1992-01-01

Results of a study of the diffuse soft-X-ray background as observed by the low-energy detectors of the A-2 experiment aboard the HEAO 1 satellite are reported. The observed sky intensities are presented as maps of the diffuse X-ray background sky in several energy bands covering the energy range 0.15-2.8 keV. It is found that the soft X-ray diffuse background (SXDB) between 1.5 and 2.8 keV, assuming a power law form with photon number index 1.4, has a normalization constant of 10.5 +/- 1.0 photons/sq cm s sr keV. Below 1.5 keV the spectrum of the SXDB exceeds the extrapolation of this power law. The low-energy excess for the NEP can be fitted with emission from a two-temperature equilibrium plasma model with the temperatures given by log I1 = 6.16 and log T2 = 6.33. It is found that this model is able to account for the spectrum below 1 keV, but fails to yield the observed Galactic latitude variation.

Sustained Release of Naproxen in a New Kind Delivery System of Carbon Nanotubes Hydrogel

PubMed Central

Peng, Xiahui; Zhuang, Qiang; Peng, Dongming; Dong, Qiuli; Tan, Lini; Jiao, Feipeng; Liu, Linqi; Liu, jingyu; Zhao, Chenxi; Wang, Xiaomei

2013-01-01

In this paper, carbon nanotubes (CNTs) were added into chitosan (CS) hydrogels in the form of chitosan modified CNTs (CS-CNTs) composites to prepare carbon nanotubes hydrogels (CNTs-GEL). The products, named CS-MWCNTs, were characterized by scanning electron microscope (SEM) and Fourier transform infrared (FTIR) spectroscopy. Swelling properties and effect of pH on controlled release performance of the two kinds of hydrogels, CNTs- GEL and pure chitosan hydrogels without CNTs (GEL), were investigated respectively. The results showed that CNTs-GEL possess better controlled release performance than GEL. The releasing equilibrium time of CNTs-GEL was longer than that of GEL in both pH = w7.4 and pH=1.2 conditions, although the release ratios of the model drug are similar in the same pH buffer solutions. It is found that release kinetics is better fitted Ritger-Peppas empirical model indicating a fick-diffusion process in pH = 1.2, while in pH = 7.4 it was non-fick diffusion involving surface diffusion and corrosion diffusion processes. PMID:24523738

Nonequilibrium Fluctuations and Enhanced Diffusion of a Driven Particle in a Dense Environment

NASA Astrophysics Data System (ADS)

Illien, Pierre; Bénichou, Olivier; Oshanin, Gleb; Sarracino, Alessandro; Voituriez, Raphaël

2018-05-01

We study the diffusion of a tracer particle driven out of equilibrium by an external force and traveling in a dense environment of arbitrary density. The system evolves on a discrete lattice and its stochastic dynamics is described by a master equation. Relying on a decoupling approximation that goes beyond the naive mean-field treatment of the problem, we calculate the fluctuations of the position of the tracer around its mean value on a lattice of arbitrary dimension, and with different boundary conditions. We reveal intrinsically nonequilibrium effects, such as enhanced diffusivity of the tracer induced by both the crowding interactions and the external driving. We finally consider the high-density and low-density limits of the model and show that our approximation scheme becomes exact in these limits.

Communication: Influence of external static and alternating electric fields on water from long-time non-equilibrium ab initio molecular dynamics

NASA Astrophysics Data System (ADS)

Futera, Zdenek; English, Niall J.

2017-07-01

The response of water to externally applied electric fields is of central relevance in the modern world, where many extraneous electric fields are ubiquitous. Historically, the application of external fields in non-equilibrium molecular dynamics has been restricted, by and large, to relatively inexpensive, more or less sophisticated, empirical models. Here, we report long-time non-equilibrium ab initio molecular dynamics in both static and oscillating (time-dependent) external electric fields, therefore opening up a new vista in rigorous studies of electric-field effects on dynamical systems with the full arsenal of electronic-structure methods. In so doing, we apply this to liquid water with state-of-the-art non-local treatment of dispersion, and we compute a range of field effects on structural and dynamical properties, such as diffusivities and hydrogen-bond kinetics.

Assortative mating and mutation diffusion in spatial evolutionary systems

NASA Astrophysics Data System (ADS)

Paley, C. J.; Taraskin, S. N.; Elliott, S. R.

2010-04-01

The influence of spatial structure on the equilibrium properties of a sexual population model defined on networks is studied numerically. Using a small-world-like topology of the networks as an investigative tool, the contributions to the fitness of assortative mating and of global mutant spread properties are considered. Simple measures of nearest-neighbor correlations and speed of spread of mutants through the system have been used to confirm that both of these dynamics are important contributory factors to the fitness. It is found that assortative mating increases the fitness of populations. Quick global spread of favorable mutations is shown to be a key factor increasing the equilibrium fitness of populations.

Flat-roof phenomenon of dynamic equilibrium phase in the negative bias temperature instability effect on a power MOSFET

NASA Astrophysics Data System (ADS)

Zhang, Yue; Zhuo, Qing-Qing; Liu, Hong-Xia; Ma, Xiao-Hua; Hao, Yue

2014-05-01

The effect of the static negative bias temperature (NBT) stress on a p-channel power metal—oxide—semiconductor field-effect transistor (MOSFET) is investigated by experiment and simulation. The time evolution of the negative bias temperature instability (NBTI) degradation has the trend predicted by the reaction—diffusion (R—D) model but with an exaggerated time scale. The phenomena of the flat-roof section are observed under various stress conditions, which can be considered as the dynamic equilibrium phase in the R—D process. Based on the simulated results, the variation of the flat-roof section with the stress condition can be explained.

The Kirkendall and Frenkel effects during 2D diffusion process

NASA Astrophysics Data System (ADS)

Wierzba, Bartek

2014-11-01

The two-dimensional approach for inter-diffusion and voids generation is presented. The voids evolution and growth is discussed. This approach is based on the bi-velocity (Darken) method which combines the Darken and Brenner concepts that the volume velocity is essential in defining the local material velocity in multi-component mixture at non-equilibrium. The model is formulated for arbitrary multi-component two-dimensional systems. It is shown that the voids growth is due to the drift velocity and vacancy migration. The radius of the void can be easily estimated. The distributions of (1) components, (2) vacancy and (3) voids radius over the distance is presented.

Application of the Hilbert space average method on heat conduction models.

PubMed

Michel, Mathias; Gemmer, Jochen; Mahler, Günter

2006-01-01

We analyze closed one-dimensional chains of weakly coupled many level systems, by means of the so-called Hilbert space average method (HAM). Subject to some concrete conditions on the Hamiltonian of the system, our theory predicts energy diffusion with respect to a coarse-grained description for almost all initial states. Close to the respective equilibrium, we investigate this behavior in terms of heat transport and derive the heat conduction coefficient. Thus, we are able to show that both heat (energy) diffusive behavior as well as Fourier's law follows from and is compatible with a reversible Schrödinger dynamics on the complete level of description.

Ballistic and diffusive dynamics in a two-dimensional ideal gas of macroscopic chaotic Faraday waves.

PubMed

Welch, Kyle J; Hastings-Hauss, Isaac; Parthasarathy, Raghuveer; Corwin, Eric I

2014-04-01

We have constructed a macroscopic driven system of chaotic Faraday waves whose statistical mechanics, we find, are surprisingly simple, mimicking those of a thermal gas. We use real-time tracking of a single floating probe, energy equipartition, and the Stokes-Einstein relation to define and measure a pseudotemperature and diffusion constant and then self-consistently determine a coefficient of viscous friction for a test particle in this pseudothermal gas. Because of its simplicity, this system can serve as a model for direct experimental investigation of nonequilibrium statistical mechanics, much as the ideal gas epitomizes equilibrium statistical mechanics.

Ordering phase transition in the one-dimensional Axelrod model

NASA Astrophysics Data System (ADS)

Vilone, D.; Vespignani, A.; Castellano, C.

2002-12-01

We study the one-dimensional behavior of a cellular automaton aimed at the description of the formation and evolution of cultural domains. The model exhibits a non-equilibrium transition between a phase with all the system sharing the same culture and a disordered phase of coexisting regions with different cultural features. Depending on the initial distribution of the disorder the transition occurs at different values of the model parameters. This phenomenology is qualitatively captured by a mean-field approach, which maps the dynamics into a multi-species reaction-diffusion problem.

A Lagrangian model for soil water dynamics: can we step beyond Richard's equation while preserving capillarity as first order control?

NASA Astrophysics Data System (ADS)

Zehe, Erwin; Jackisch, Conrad

2016-04-01

Water storage in the unsaturated zone is controlled by capillary forces which increase nonlinearly with decreasing pore size, because water acts as a wetting fluid in soil. The standard approach to represent capillary and gravity controlled soil water dynamics is the Darcy-Richards equation in combination with suitable soil water characteristics. This continuum model essentially assumes capillarity controlled diffusive fluxes to dominate soil water dynamics under local thermodynamic equilibrium conditions. Today we know that the assumptions of local equilibrium conditions e.g. and a mainly diffusive flow are often not appropriate, particularly during rainfall events in structured soils. Rapid or preferential flow imply a strong local disequilibrium and imperfect mixing between a fast fraction of soil water, traveling in interconnected coarse pores or non-capillary macropores, and the slower diffusive flow in finer fractions of the pore space. Although various concepts have been proposed to overcome the inability of the Darcy - Richards concept to cope with not-well mixed preferential flow, we still lack an approach that is commonly accepted. Notwithstanding the listed short comings, one should not mistake the limitations of the Richards equation with non-importance of capillary forces in soil. Without capillarity infiltrating rainfall would drain into groundwater bodies, leaving an empty soil as the local equilibrium state - there would be no soil water dynamics at all, probably even no terrestrial vegetation without capillary forces. Better alternatives for the Darcy-Richards approach are thus highly desirable, as long they preserve the grain of "truth" about capillarity as first order control. Here we propose such an alternative approach to simulate soil moisture dynamics in a stochastic and yet physical way. Soil water is represented by particles of constant mass, which travel according to the Itô form of the Fokker Planck equation. The model concept builds on established soil physics by estimating the drift velocity and the diffusion term based on the soil water characteristics. A naive random walk, which assumes all water particles to move at the same drift velocity and diffusivity, overestimated depletion of soil moisture gradients compared to a Richards' solver within three distinctly different soils. This is because soil water and hence the corresponding water particles in smaller pores size fractions, are, due to the non-linear decrease of soil hydraulic conductivity with decreasing soil moisture, much less mobile. After accounting for this subscale variability of particle mobility, the particle model and a Richards' solver performed highly similar during simulated wetting and drying circles in three distinctly different soils. Alternatively, we tested a computational less approach, assuming only the 10 or 20% of the fastest particles as mobile, while treating the remaining particles located in smaller pores sizes as immobile. For instance in a sandy soil a mobile fraction of 20% revealed almost identical results as the full mobility model and performed even closer to the Richards solver. In this context we also compared the cases of perfect mixing and no mixing between mobile and immobile water particles between different time steps. The second option was clearly superior with respect to match simulations with the Richards' solver. The particle model is hence a suitable tool to "unmask" a) inherent implications of the Darcy-Richards concept on the fraction of soil water that actually contributes to soil water dynamics and b) the inherent very limited degrees of freedom for mixing between mobile and immobile water fractions. A main asset of the particle based approach is that the assumption of local equilibrium equation during infiltration may be easily released. We tested this idea in a straight forward manner, by treating infiltrating event water particles as second particle type which travel initially, mainly gravity driven, in the largest pore fraction at maximum drift, and yet experience a slow diffusive mixing with the pre-event water particles within a characteristic mixing time. Simulations with the particle model in the non-equilibrium mode were a) rather sensitive to the coefficient describing mixing of event water particles and b) clearly outperformed the Richards model with respect to match observed soil dynamics in a real world benchmark. The proposed non-linear random walk of water particles is, hence, an easy to implement alternative for simulating soil moisture dynamics in the unsaturated, which preserves the influence of capillarity and makes use of established soil physics. The approach is particularly promising to deal with preferential flow and transport of solutes and to explore transit time distributions.

Monitoring equilibrium reaction dynamics of a nearly barrierless molecular rotor using ultrafast vibrational echoes

NASA Astrophysics Data System (ADS)

Nilsen, Ian A.; Osborne, Derek G.; White, Aaron M.; Anna, Jessica M.; Kubarych, Kevin J.

2014-10-01

Using rapidly acquired spectral diffusion, a recently developed variation of heterodyne detected infrared photon echo spectroscopy, we observe ˜3 ps solvent independent spectral diffusion of benzene chromium tricarbonyl (C6H6Cr(CO)3, BCT) in a series of nonpolar linear alkane solvents. The spectral dynamics is attributed to low-barrier internal torsional motion. This tripod complex has two stable minima corresponding to staggered and eclipsed conformations, which differ in energy by roughly half of kBT. The solvent independence is due to the relative size of the rotor compared with the solvent molecules, which create a solvent cage in which torsional motion occurs largely free from solvent damping. Since the one-dimensional transition state is computed to be only 0.03 kBT above the higher energy eclipsed conformation, this model system offers an unusual, nearly barrierless reaction, which nevertheless is characterized by torsional coordinate dependent vibrational frequencies. Hence, by studying the spectral diffusion of the tripod carbonyls, it is possible to gain insight into the fundamental dynamics of internal rotational motion, and we find some evidence for the importance of non-diffusive ballistic motion even in the room-temperature liquid environment. Using several different approaches to describe equilibrium kinetics, as well as the influence of reactive dynamics on spectroscopic observables, we provide evidence that the low-barrier torsional motion of BCT provides an excellent test case for detailed studies of the links between chemical exchange and linear and nonlinear vibrational spectroscopy.

Modeling studies of gas movement and moisture migration at Yucca Mountain, Nevada

DOE Office of Scientific and Technical Information (OSTI.GOV)

Tsang, Y.W.; Pruess, K.

1991-06-01

Modeling studies on moisture redistribution processes that are mediated by gas phase flow and diffusion have been carried out. The problem addressed is the effect of a lowered humidity of the soil gas at the land surface on moisture removal from Yucca Mountain, the potential site for a high-level nuclear waste repository. At the land surface, humid formation gas contacts much drier atmospheric air. Near this contact, the humidity of the soil gas may be considerably lower than at greater depth, where the authors expect equilibrium with the liquid phase and close to 100% humidity. The lower relative humidity ofmore » the soil gas may be modeled by imposing, at the land surface, an additional negative capillary suction corresponding to vapor pressure lowering according to Kelvin`s Equation, thus providing a driving force for the upward movement of moisture in both the vapor and liquid phases. Sensitivity studies show that moisture removal from Yucca Mountain arising from the lowered-relative-humidity boundary condition is controlled by vapor diffusion. There is much experimental evidence in the soil literature that diffusion of vapor is enhanced due to pore-level phase change effects by a few orders of magnitude. Modeling results presented here will account for this enhancement in vapor diffusion.« less

A collisional-radiative model of iron vapour in a thermal arc plasma

NASA Astrophysics Data System (ADS)

Baeva, M.; Uhrlandt, D.; Murphy, A. B.

2017-06-01

A collisional-radiative model for the ground state and fifty effective excited levels of atomic iron, and one level for singly-ionized iron, is set up for technological plasmas. Attention is focused on the population of excited states of atomic iron as a result of excitation, de-excitation, ionization, recombination and spontaneous emission. Effective rate coefficients for ionization and recombination, required in non-equilibrium plasma transport models, are also obtained. The collisional-radiative model is applied to a thermal arc plasma. Input parameters for the collisional-radiative model are provided by a magnetohydrodynamic simulation of a gas-metal welding arc, in which local thermodynamic equilibrium is assumed and the treatment of the transport of metal vapour is based on combined diffusion coefficients. The results clearly identify the conditions in the arc, under which the atomic state distribution satisfies the Boltzmann distribution, with an excitation temperature equal to the plasma temperature. These conditions are met in the central part of the arc, even though a local temperature minimum occurs here. This provides assurance that diagnostic methods based on local thermodynamic equilibrium, in particular those of optical emission spectroscopy, are reliable here. In contrast, deviations from the equilibrium atomic-state distribution are obtained in the near-electrode and arc fringe regions. As a consequence, the temperatures determined from the ratio of line intensities and number densities obtained from the emission coefficient in these regions are questionable. In this situation, the collisional-radiative model can be used as a diagnostic tool to assist in the interpretation of spectroscopic measurements.

Coarse-grained model of water diffusion and proton conductivity in hydrated polyelectrolyte membrane

DOE Office of Scientific and Technical Information (OSTI.GOV)

Lee, Ming-Tsung; Vishnyakov, Aleksey; Neimark, Alexander V., E-mail: aneimark@rutgers.edu

2016-01-07

Using dissipative particle dynamics (DPD), we simulate nanoscale segregation, water diffusion, and proton conductivity in hydrated sulfonated polystyrene (sPS). We employ a novel model [Lee et al. J. Chem. Theory Comput. 11(9), 4395-4403 (2015)] that incorporates protonation/deprotonation equilibria into DPD simulations. The polymer and water are modeled by coarse-grained beads interacting via short-range soft repulsion and smeared charge electrostatic potentials. The proton is introduced as a separate charged bead that forms dissociable Morse bonds with the base beads representing water and sulfonate anions. Morse bond formation and breakup artificially mimics the Grotthuss mechanism of proton hopping between the bases. Themore » DPD model is parameterized by matching the proton mobility in bulk water, dissociation constant of benzenesulfonic acid, and liquid-liquid equilibrium of water-ethylbenzene solutions. The DPD simulations semi-quantitatively predict nanoscale segregation in the hydrated sPS into hydrophobic and hydrophilic subphases, water self-diffusion, and proton mobility. As the hydration level increases, the hydrophilic subphase exhibits a percolation transition from isolated water clusters to a 3D network. The analysis of hydrophilic subphase connectivity and water diffusion demonstrates the importance of the dynamic percolation effect of formation and breakup of temporary junctions between water clusters. The proposed DPD model qualitatively predicts the ratio of proton to water self-diffusion and its dependence on the hydration level that is in reasonable agreement with experiments.« less

Particle-Size-Grouping Model of Precipitation Kinetics in Microalloyed Steels

NASA Astrophysics Data System (ADS)

Xu, Kun; Thomas, Brian G.

2012-03-01

The formation, growth, and size distribution of precipitates greatly affects the microstructure and properties of microalloyed steels. Computational particle-size-grouping (PSG) kinetic models based on population balances are developed to simulate precipitate particle growth resulting from collision and diffusion mechanisms. First, the generalized PSG method for collision is explained clearly and verified. Then, a new PSG method is proposed to model diffusion-controlled precipitate nucleation, growth, and coarsening with complete mass conservation and no fitting parameters. Compared with the original population-balance models, this PSG method saves significant computation and preserves enough accuracy to model a realistic range of particle sizes. Finally, the new PSG method is combined with an equilibrium phase fraction model for plain carbon steels and is applied to simulate the precipitated fraction of aluminum nitride and the size distribution of niobium carbide during isothermal aging processes. Good matches are found with experimental measurements, suggesting that the new PSG method offers a promising framework for the future development of realistic models of precipitation.

Modelling element distributions in the atmospheres of magnetic Ap stars

NASA Astrophysics Data System (ADS)

Alecian, G.; Stift, M. J.

2007-11-01

Context: In recent papers convincing evidence has been presented for chemical stratification in Ap star atmospheres, and surface abundance maps have been shown to correlate with the magnetic field direction. Radiatively driven diffusion, which is known to be sensitive to the magnetic field strength and direction, is among the processes responsible for these inhomogeneities. Aims: Here we explore the hypothesis that equilibrium stratifications - such that the diffusive particle flux is close to zero throughout the atmosphere - can, in a number of cases, explain the observed abundance maps and vertical distributions of the various elements. Methods: An iterative scheme adjusts the abundances in such a way as to achieve either zero particle flux or zero effective acceleration throughout the atmosphere, taking strength and direction of the magnetic field into account. Results: The investigation of equilibrium stratifications in stellar atmospheres with temperatures from 8500 to 12 000 K and fields up to 10 kG reveals considerable variations in the vertical distribution of the 5 elements studied (Mg, Si, Ca, Ti, Fe), often with zones of large over- or under-abundances and with indications of other competing processes (such as mass loss). Horizontal magnetic fields can be very efficient in helping the accumulation of elements in higher layers. Conclusions: A comparison between our calculations and the vertical abundance profiles and surface maps derived by magnetic Doppler imaging reveals that equilibrium stratifications are in a number of cases consistent with the main trends inferred from observed spectra. However, it is not clear whether such equilibrium solutions will ever be reached during the evolution of an Ap star.

Relativistic diffusive motion in random electromagnetic fields

NASA Astrophysics Data System (ADS)

Haba, Z.

2011-08-01

We show that the relativistic dynamics in a Gaussian random electromagnetic field can be approximated by the relativistic diffusion of Schay and Dudley. Lorentz invariant dynamics in the proper time leads to the diffusion in the proper time. The dynamics in the laboratory time gives the diffusive transport equation corresponding to the Jüttner equilibrium at the inverse temperature β-1 = mc2. The diffusion constant is expressed by the field strength correlation function (Kubo's formula).

Sediment Equilibrium and Diffusive Fluxes in Relation to Phosphorus Dynamics in the Turbid Minnesota River

DTIC Science & Technology

2009-01-01

extractable P and K in a sandy clay loam soil under continuous corn ( Zea mays L .). Can J Soil Sci 75:361-367. Zhang, T. Q., A. F. MacKenzie, B. C...diffusive P flux from deposited sediment stored in river channels may also play a role in soluble P control. Ranges in equilibrium partitioning between...largest plants in the State of Minnesota, discharge (average discharge = 1.8 m3 s-1) at effluent P concentrations of 1.5 mg L -1 or less. A 538-megawatt

Novel non-equilibrium modelling of a DC electric arc in argon

NASA Astrophysics Data System (ADS)

Baeva, M.; Benilov, M. S.; Almeida, N. A.; Uhrlandt, D.

2016-06-01

A novel non-equilibrium model has been developed to describe the interplay of heat and mass transfer and electric and magnetic fields in a DC electric arc. A complete diffusion treatment of particle fluxes, a generalized form of Ohm’s law, and numerical matching of the arc plasma with the space-charge sheaths adjacent to the electrodes are applied to analyze in detail the plasma parameters and the phenomena occurring in the plasma column and the near-electrode regions of a DC arc generated in atmospheric pressure argon for current levels from 20 A up to 200 A. Results comprising electric field and potential, current density, heating of the electrodes, and effects of thermal and chemical non-equilibrium are presented and discussed. The current-voltage characteristic obtained is in fair agreement with known experimental data. It indicates a minimum for arc current of about 80 A. For all current levels, a field reversal in front of the anode accompanied by a voltage drop of (0.7-2.6) V is observed. Another field reversal is observed near the cathode for arc currents below 80 A.

Symmetry, Hopf bifurcation, and the emergence of cluster solutions in time delayed neural networks.

PubMed

Wang, Zhen; Campbell, Sue Ann

2017-11-01

We consider the networks of N identical oscillators with time delayed, global circulant coupling, modeled by a system of delay differential equations with Z N symmetry. We first study the existence of Hopf bifurcations induced by the coupling time delay and then use symmetric Hopf bifurcation theory to determine how these bifurcations lead to different patterns of symmetric cluster oscillations. We apply our results to a case study: a network of FitzHugh-Nagumo neurons with diffusive coupling. For this model, we derive the asymptotic stability, global asymptotic stability, absolute instability, and stability switches of the equilibrium point in the plane of coupling time delay (τ) and excitability parameter (a). We investigate the patterns of cluster oscillations induced by the time delay and determine the direction and stability of the bifurcating periodic orbits by employing the multiple timescales method and normal form theory. We find that in the region where stability switching occurs, the dynamics of the system can be switched from the equilibrium point to any symmetric cluster oscillation, and back to equilibrium point as the time delay is increased.

Income, Inequality, Market Potential, and Diffusion of Mobile Telephony

ERIC Educational Resources Information Center

Kim, Sungjoong

2009-01-01

The diffusion of many previous innovations eventually slowed down and reached an equilibrium level. Despite continued rapid growth, it is possible that the diffusion of mobile telephony will also begin to decelerate and reach a saturation level. Whether universal service can be achieved with the help of mobile telephony will therefore depend…

Diffusion relaxation times of nonequilibrium isolated small bodies and their solid phase ensembles to equilibrium states

NASA Astrophysics Data System (ADS)

Tovbin, Yu. K.

2017-08-01

The possibility of obtaining analytical estimates in a diffusion approximation of the times needed by nonequilibrium small bodies to relax to their equilibrium states based on knowledge of the mass transfer coefficient is considered. This coefficient is expressed as the product of the self-diffusion coefficient and the thermodynamic factor. A set of equations for the diffusion transport of mixture components is formulated, characteristic scales of the size of microheterogeneous phases are identified, and effective mass transfer coefficients are constructed for them. Allowing for the developed interface of coexisting and immiscible phases along with the porosity of solid phases is discussed. This approach can be applied to the diffusion equalization of concentrations of solid mixture components in many physicochemical systems: the mutual diffusion of components in multicomponent systems (alloys, semiconductors, solid mixtures of inert gases) and the mass transfer of an absorbed mobile component in the voids of a matrix consisting of slow components or a mixed composition of mobile and slow components (e.g., hydrogen in metals, oxygen in oxides, and the transfer of molecules through membranes of different natures, including polymeric).

Fluorescence Correlation Spectroscopy and Nonlinear Stochastic Reaction-Diffusion

DOE Office of Scientific and Technical Information (OSTI.GOV)

Del Razo, Mauricio; Pan, Wenxiao; Qian, Hong

2014-05-30

The currently existing theory of fluorescence correlation spectroscopy (FCS) is based on the linear fluctuation theory originally developed by Einstein, Onsager, Lax, and others as a phenomenological approach to equilibrium fluctuations in bulk solutions. For mesoscopic reaction-diffusion systems with nonlinear chemical reactions among a small number of molecules, a situation often encountered in single-cell biochemistry, it is expected that FCS time correlation functions of a reaction-diffusion system can deviate from the classic results of Elson and Magde [Biopolymers (1974) 13:1-27]. We first discuss this nonlinear effect for reaction systems without diffusion. For nonlinear stochastic reaction-diffusion systems there are no closedmore » solutions; therefore, stochastic Monte-Carlo simulations are carried out. We show that the deviation is small for a simple bimolecular reaction; the most significant deviations occur when the number of molecules is small and of the same order. Extending Delbrück-Gillespie’s theory for stochastic nonlinear reactions with rapidly stirring to reaction-diffusion systems provides a mesoscopic model for chemical and biochemical reactions at nanometric and mesoscopic level such as a single biological cell.« less

Mathematical Model for the Mineralization of Bone

NASA Technical Reports Server (NTRS)

Martin, Bruce

1994-01-01

A mathematical model is presented for the transport and precipitation of mineral in refilling osteons. One goal of this model was to explain calcification 'halos,' in which the bone near the haversian canal is more highly mineralized than the more peripheral lamellae, which have been mineralizing longer. It was assumed that the precipitation rate of mineral is proportional to the difference between the local concentration of calcium ions and an equilibrium concentration and that the transport of ions is by either diffusion or some other concentration gradient-dependent process. Transport of ions was assumed to be slowed by the accumulation of mineral in the matrix along the transport path. ne model also mimics bone apposition, slowing of apposition during refilling, and mineralization lag time. It was found that simple diffusion cannot account for the transport of calcium ions into mineralizing bone, because the diffusion coefficient is two orders of magnitude too low. If a more rapid concentration gradient-driven means of transport exists, the model demonstrates that osteonal geometry and variable rate of refilling work together to produce calcification halos, as well as the primary and secondary calcification effect reported in the literature.

Mineral paragenesis on Mars: The roles of reactive surface area and diffusion

PubMed Central

Gil‐Lozano, Carolina; Uceda, Esther R.; Losa‐Adams, Elisabeth; Davila, Alfonso F.; Gago‐Duport, Luis

2017-01-01

Abstract Geochemical models of secondary mineral precipitation on Mars generally assume semiopen systems (open to the atmosphere but closed at the water‐sediment interface) and equilibrium conditions. However, in natural multicomponent systems, the reactive surface area of primary minerals controls the dissolution rate and affects the precipitation sequences of secondary phases, and simultaneously, the transport of dissolved species may occur through the atmosphere‐water and water‐sediment interfaces. Here we present a suite of geochemical models designed to analyze the formation of secondary minerals in basaltic sediments on Mars, evaluating the role of (i) reactive surface areas and (ii) the transport of ions through a basalt sediment column. We consider fully open conditions, both to the atmosphere and to the sediment, and a kinetic approach for mineral dissolution and precipitation. Our models consider a geochemical scenario constituted by a basin (i.e., a shallow lake) where supersaturation is generated by evaporation/cooling and the starting point is a solution in equilibrium with basaltic sediments. Our results show that cation removal by diffusion, along with the input of atmospheric volatiles and the influence of the reactive surface area of primary minerals, plays a central role in the evolution of the secondary mineral sequences formed. We conclude that precipitation of evaporites finds more restrictions in basaltic sediments of small grain size than in basaltic sediments of greater grain size. PMID:29104844

Mineral paragenesis on Mars: The roles of reactive surface area and diffusion.

PubMed

Fairén, Alberto G; Gil-Lozano, Carolina; Uceda, Esther R; Losa-Adams, Elisabeth; Davila, Alfonso F; Gago-Duport, Luis

2017-09-01

Geochemical models of secondary mineral precipitation on Mars generally assume semiopen systems (open to the atmosphere but closed at the water-sediment interface) and equilibrium conditions. However, in natural multicomponent systems, the reactive surface area of primary minerals controls the dissolution rate and affects the precipitation sequences of secondary phases, and simultaneously, the transport of dissolved species may occur through the atmosphere-water and water-sediment interfaces. Here we present a suite of geochemical models designed to analyze the formation of secondary minerals in basaltic sediments on Mars, evaluating the role of (i) reactive surface areas and (ii) the transport of ions through a basalt sediment column. We consider fully open conditions, both to the atmosphere and to the sediment, and a kinetic approach for mineral dissolution and precipitation. Our models consider a geochemical scenario constituted by a basin (i.e., a shallow lake) where supersaturation is generated by evaporation/cooling and the starting point is a solution in equilibrium with basaltic sediments. Our results show that cation removal by diffusion, along with the input of atmospheric volatiles and the influence of the reactive surface area of primary minerals, plays a central role in the evolution of the secondary mineral sequences formed. We conclude that precipitation of evaporites finds more restrictions in basaltic sediments of small grain size than in basaltic sediments of greater grain size.

Computation of thermodynamic and transport properties to predict thermophoretic effects in an argon-krypton mixture

NASA Astrophysics Data System (ADS)

Miller, Nicholas A. T.; Daivis, Peter J.; Snook, Ian K.; Todd, B. D.

2013-10-01

Thermophoresis is the movement of molecules caused by a temperature gradient. Here we report the results of a study of thermophoresis using non-equilibrium molecular dynamics simulations of a confined argon-krypton fluid subject to two different temperatures at thermostated walls. The resulting temperature profile between the walls is used along with the Soret coefficient to predict the concentration profile that develops across the channel. We obtain the Soret coefficient by calculating the mutual diffusion and thermal diffusion coefficients. We report an appropriate method for calculating the transport coefficients for binary systems, using the Green-Kubo integrals and radial distribution functions obtained from equilibrium molecular dynamics simulations of the bulk fluid. Our method has the unique advantage of separating the mutual diffusion and thermal diffusion coefficients, and calculating the sign and magnitude of their individual contributions to thermophoresis in binary mixtures.

Effects of g-Jitter on Diffusion in Binary Liquids

NASA Technical Reports Server (NTRS)

Duval, Walter M. B.

1999-01-01

The microgravity environment offers the potential to measure the binary diffusion coefficients in liquids without the masking effects introduced by buoyancy-induced flows due to Earth s gravity. However, the background g-jitter (vibrations from the shuttle, onboard machinery, and crew) normally encountered in many shuttle experiments may alter the benefits of the microgravity environment and introduce vibrations that could offset its intrinsic advantages. An experiment during STS-85 (August 1997) used the Microgravity Vibration Isolation Mount (MIM) to isolate and introduce controlled vibrations to two miscible liquids inside a cavity to study the effects of g-jitter on liquid diffusion. Diffusion in a nonhomogeneous liquid system is caused by a nonequilibrium condition that results in the transport of mass (dispersion of the different kinds of liquid molecules) to approach equilibrium. The dynamic state of the system tends toward equilibrium such that the system becomes homogeneous. An everyday example is the mixing of cream and coffee (a nonhomogeneous system) via stirring. The cream diffuses into the coffee, thus forming a homogeneous system. At equilibrium the system is said to be mixed. However, during stirring, simple observations show complex flow field dynamics-stretching and folding of material interfaces, thinning of striation thickness, self-similar patterns, and so on. This example illustrates that, even though mixing occurs via mass diffusion, stirring to enhance transport plays a major role. Stirring can be induced either by mechanical means (spoon or plastic stirrer) or via buoyancy-induced forces caused by Earth s gravity. Accurate measurements of binary diffusion coefficients are often inhibited by buoyancy-induced flows. The microgravity environment minimizes the effect of buoyancy-induced flows and allows the true diffusion limit to be achieved. One goal of this experiment was to show that the microgravity environment suppresses buoyancy-induced convection, thereby mass diffusion becomes the dominant mechanism for transport. Since g-jitter transmitted by the shuttle to the experiment can potentially excite buoyancy-induced flows, we also studied the effects of controlled vibrations on the system.

Diffusion-plus-drift models for the mass leakage from centrifugal magnetospheres of magnetic hot-stars

NASA Astrophysics Data System (ADS)

Owocki, Stanley P.; Cranmer, Steven R.

2018-03-01

In the subset of luminous, early-type stars with strong, large-scale magnetic fields and moderate to rapid rotation, material from the star's radiatively driven stellar wind outflow becomes trapped by closed magnetic loops, forming a centrifugally supported, corotating magnetosphere. We present here a semi-analytic analysis of how this quasi-steady accumulation of wind mass can be balanced by losses associated with a combination of an outward, centrifugally driven drift in the region beyond the Kepler co-rotation radius, and an inward/outward diffusion near this radius. We thereby derive scaling relations for the equilibrium spatial distribution of mass, and the associated emission measure for observational diagnostics like Balmer line emission. We discuss the potential application of these relations for interpreting surveys of the emission line diagnostics for OB stars with centrifugally supported magnetospheres. For a specific model of turbulent field-line-wandering rooted in surface motions associated with the iron opacity bump, we estimate values for the associated diffusion and drift coefficients.

Phonon Mapping in Flowing Equilibrium

NASA Astrophysics Data System (ADS)

Ruff, J. P. C.

2015-03-01

When a material conducts heat, a modification of the phonon population occurs. The equilibrium Bose-Einstein distribution is perturbed towards flowing-equilibrium, for which the distribution function is not analytically known. Here I argue that the altered phonon population can be efficiently mapped over broad regions of reciprocal space, via diffuse x-ray scattering or time-of-flight neutron scattering, while a thermal gradient is applied across a single crystal sample. When compared to traditional transport measurements, this technique offers a superior, information-rich new perspective on lattice thermal conductivity, wherein the band and momentum dependences of the phonon thermal current are directly resolved. The proposed method is benchmarked using x-ray thermal diffuse scattering measurements of single crystal diamond under transport conditions. CHESS is supported by the NSF & NIH/NIGMS via NSF Award DMR-1332208.

Thermal conductance at the interface between crystals using equilibrium and nonequilibrium molecular dynamics

NASA Astrophysics Data System (ADS)

Merabia, Samy; Termentzidis, Konstantinos

2012-09-01

In this article, we compare the results of nonequilibrium (NEMD) and equilibrium (EMD) molecular dynamics methods to compute the thermal conductance at the interface between solids. We propose to probe the thermal conductance using equilibrium simulations measuring the decay of the thermally induced energy fluctuations of each solid. We also show that NEMD and EMD give generally speaking inconsistent results for the thermal conductance: Green-Kubo simulations probe the Landauer conductance between two solids which assumes phonons on both sides of the interface to be at equilibrium. On the other hand, we show that NEMD give access to the out-of-equilibrium interfacial conductance consistent with the interfacial flux describing phonon transport in each solid. The difference may be large and reaches typically a factor 5 for interfaces between usual semiconductors. We analyze finite size effects for the two determinations of the interfacial thermal conductance, and show that the equilibrium simulations suffer from severe size effects as compared to NEMD. We also compare the predictions of the two above-mentioned methods—EMD and NEMD—regarding the interfacial conductance of a series of mass mismatched Lennard-Jones solids. We show that the Kapitza conductance obtained with EMD can be well described using the classical diffuse mismatch model (DMM). On the other hand, NEMD simulation results are consistent with an out-of-equilibrium generalization of the acoustic mismatch model (AMM). These considerations are important in rationalizing previous results obtained using molecular dynamics, and help in pinpointing the physical scattering mechanisms taking place at atomically perfect interfaces between solids, which is a prerequisite to understand interfacial heat transfer across real interfaces.

Characterization of the atrazine sorption process on Andisol and Ultisol volcanic ash-derived soils: kinetic parameters and the contribution of humic fractions.

PubMed

Báez, María E; Fuentes, Edwar; Espinoza, Jeannette

2013-07-03

Atrazine sorption was studied in six Andisol and Ultisol soils. Humic and fulvic acids and humin contributions were established. Sorption on soils was well described by the Freundlich model. Kf values ranged from 2.2-15.6 μg(1-1/n)mL(1/n)g⁻¹. The relevance of humic acid and humin was deduced from isotherm and kinetics experiments. KOC values varied between 221 and 679 mLg⁻¹ for these fractions. Fulvic acid presented low binding capacity. Sorption was controlled by instantaneous equilibrium followed by a time-dependent phase. The Elovich equation, intraparticle diffusion model, and a two-site nonequilibrium model allowed us to conclude that (i) there are two rate-limited phases in Andisols related to intrasorbent diffusion in organic matter and retarded intraparticle diffusion in the organo-mineral complex and that (ii) there is one rate-limited phase in Ultisols attributed to the mineral composition. The lower organic matter content of Ultisols and the slower sorption rate and mechanisms involved must be considered to assess the leaching behavior of atrazine.

Modeling of diffusive plasmas in local thermodynamic equilibrium with integral constraints: application to mercury-free high pressure discharge lamp mixtures

NASA Astrophysics Data System (ADS)

Janssen, J. F. J.; Suijker, J. L. G.; Peerenboom, K. S. C.; van Dijk, J.

2017-03-01

The mercury free lamp model previously discussed in Gnybida et al (2014 J. Phys. D: Appl. Phys. 47 125201) did not account for self-consistent diffusion and only included two molecular transitions. In this paper we apply, for the first time, a self-consistent diffusion algorithm that features (1) species/mass conservation up to machine accuracy and (2) an arbitrary mix of integral (total mass) and local (cold spot) constraints on the composition. Another advantage of this model is that the total pressure of the gas is calculated self consistently. Therefore, the usage of a predetermined pressure is no longer required. Additionally, the number of association processes has been increased from 2 to 6. The population as a function of interatomic separation determines the spectrum of the emitted continuum radiation. Previously, this population was calculated using the limit of low densities. In this work an expression is used that removes this limitation. The result of these improvements is that the agreement between the simulated and measured spectra has improved considerably.

A nonlinear dynamic age-structured model of e-commerce in spain: Stability analysis of the equilibrium by delay and stochastic perturbations

NASA Astrophysics Data System (ADS)

Burgos, C.; Cortés, J.-C.; Shaikhet, L.; Villanueva, R.-J.

2018-11-01

First, we propose a deterministic age-structured epidemiological model to study the diffusion of e-commerce in Spain. Afterwards, we determine the parameters (death, birth and growth rates) of the underlying demographic model as well as the parameters (transmission of the use of e-commerce rates) of the proposed epidemiological model that best fit real data retrieved from the Spanish National Statistical Institute. Motivated by the two following facts: first the dynamics of acquiring the use of a new technology as e-commerce is mainly driven by the feedback after interacting with our peers (family, friends, mates, mass media, etc.), hence having a certain delay, and second the inherent uncertainty of sampled real data and the social complexity of the phenomena under analysis, we introduce aftereffect and stochastic perturbations in the initial deterministic model. This leads to a delayed stochastic model for e-commerce. We then investigate sufficient conditions in order to guarantee the stability in probability of the equilibrium point of the dynamic e-commerce delayed stochastic model. Our theoretical findings are numerically illustrated using real data.

A novel Kinetic Monte Carlo algorithm for Non-Equilibrium Simulations

NASA Astrophysics Data System (ADS)

Jha, Prateek; Kuzovkov, Vladimir; Grzybowski, Bartosz; Olvera de La Cruz, Monica

2012-02-01

We have developed an off-lattice kinetic Monte Carlo simulation scheme for reaction-diffusion problems in soft matter systems. The definition of transition probabilities in the Monte Carlo scheme are taken identical to the transition rates in a renormalized master equation of the diffusion process and match that of the Glauber dynamics of Ising model. Our scheme provides several advantages over the Brownian dynamics technique for non-equilibrium simulations. Since particle displacements are accepted/rejected in a Monte Carlo fashion as opposed to moving particles following a stochastic equation of motion, nonphysical movements (e.g., violation of a hard core assumption) are not possible (these moves have zero acceptance). Further, the absence of a stochastic ``noise'' term resolves the computational difficulties associated with generating statistically independent trajectories with definitive mean properties. Finally, since the timestep is independent of the magnitude of the interaction forces, much longer time-steps can be employed than Brownian dynamics. We discuss the applications of this scheme for dynamic self-assembly of photo-switchable nanoparticles and dynamical problems in polymeric systems.

Modeling uptake of hydrophobic organic contaminants into polyethylene passive samplers.

PubMed

Thompson, Jay M; Hsieh, Ching-Hong; Luthy, Richard G

2015-02-17

Single-phase passive samplers are gaining acceptance as a method to measure hydrophobic organic contaminant (HOC) concentration in water. Although the relationship between the HOC concentration in water and passive sampler is linear at equilibrium, mass transfer models are needed for nonequilibrium conditions. We report measurements of organochlorine pesticide diffusion and partition coefficients with respect to polyethylene (PE), and present a Fickian approach to modeling HOC uptake by PE in aqueous systems. The model is an analytic solution to Fick's second law applied through an aqueous diffusive boundary layer and a polyethylene layer. Comparisons of the model with existing methods indicate agreement at appropriate boundary conditions. Laboratory release experiments on the organochlorine pesticides DDT, DDE, DDD, and chlordane in well-mixed slurries support the model's applicability to aqueous systems. In general, the advantage of the model is its application in the cases of well-agitated systems, low values of polyethylene-water partioning coefficients, thick polyethylene relative to the boundary layer thickness, and/or short exposure times. Another significant advantage is the ability to estimate, or at least bound, the needed exposure time to reach a desired CPE without empirical model inputs. A further finding of this work is that polyethylene diffusivity does not vary by transport direction through the sampler thickness.

Donnan membrane technique (DMT) for anion measurement.

PubMed

Vega, Flora Alonso; Weng, Liping; Temminghoff, Erwin J M; Van Riemsdijk, Willem H

2010-04-01

Donnan membrane technique (DMT) is developed and tested for determination of free anion concentrations. Time needed to reach the Donnan membrane equilibrium depends on type of ions and the background. The Donnan membrane equilibrium is reached in 1 day for Cl(-), 1-2 days for NO(3)(-), 1-4 days for SO(4)(2-) and SeO(4)(2-), and 1-14 days for H(2)PO(4)(-) in a background of 2-200 mM KCl or K(2)SO(4). The strongest effect of ionic strength on equilibrium time is found for H(2)PO(4)(-), followed by SO(4)(2-) and SeO(4)(2-), and then by Cl(-) and NO(3)(-). The negatively charged organic particles of fulvic and humic acids do not pass the membrane. Two approaches for the measurement of different anion species of the same element, such as SeO(4)(2-) and HSeO(3)(-), using DMT are proposed and tested. These two approaches are based on transport kinetics or response to ionic strength difference. A transport model that was developed previously for cation DMT is applied in this work to analyze the rate-limiting step in the anion DMT. In the absence of mobile/labile complexes, transport tends to be controlled by diffusion in solution at a low ionic strength, whereas at a higher ionic strength, diffusion in the membrane starts to control the transport.

Impact of biochar produced from post-harvest residue on the adsorption behavior of diesel oil on loess soil.

PubMed

Jiang, Yu Feng; Sun, Hang; Yves, Uwamungu J; Li, Hong; Hu, Xue Fei

2016-02-01

The primary objective of this study was to investigate the effect of biochar, produced from wheat residue at different temperatures, on the adsorption of diesel oil by loess soil. Kinetic and equilibrium data were processed to understand the adsorption mechanism of diesel by biochar-affected loess soil; dynamic and thermodynamic adsorption experiments were conducted to characterize this adsorption. The surface features and chemical structure of biochar, modified at varying pyrolytic temperatures, were investigated using surface scanning electron microscopy and Fourier transform infrared analysis. The kinetic data showed that the adsorption of diesel oil onto loess soil could be described by a pseudo-second-order kinetic model, with the rate-controlling step being intraparticle diffusion. However, in the presence of biochar, boundary layer control and intraparticle diffusion were both involved in the adsorption. Besides, the adsorption equilibrium data were well described by the Freundlich isothermal model. The saturated adsorption capacity weakened as temperature increased, suggesting a spontaneous exothermic process. Thermodynamic parameter analysis showed that adsorption was mainly a physical process and was enhanced by chemical adsorption. The adsorption capacity of loess soil for diesel oil was weakened with increasing pH. The biochar produced by pyrolytic wheat residue increased the adsorption behavior of petroleum pollutants in loess soil.

Modeling the reversible, diffusive sink effect in response to transient contaminant sources.

PubMed

Zhao, D; Little, J C; Hodgson, A T

2002-09-01

A physically based diffusion model is used to evaluate the sink effect of diffusion-controlled indoor materials and to predict the transient contaminant concentration in indoor air in response to several time-varying contaminant sources. For simplicity, it is assumed the predominant indoor material is a homogeneous slab, initially free of contaminant, and the air within the room is well mixed. The model enables transient volatile organic compound (VOC) concentrations to be predicted based on the material/air partition coefficient (K) and the material-phase diffusion coefficient (D) of the sink. Model predictions are made for three scenarios, each mimicking a realistic situation in a building. Styrene, phenol, and naphthalene are used as representative VOCs. A styrene butadiene rubber (SBR) backed carpet, vinyl flooring (VF), and a polyurethane foam (PUF) carpet cushion are considered as typical indoor sinks. In scenarios involving a sinusoidal VOC input and a double exponential decaying input, the model predicts the sink has a modest impact for SBR/styrene, but the effect increases for VF/phenol and PUF/naphthalene. In contrast, for an episodic chemical spill, SBR is predicted to reduce the peak styrene concentration considerably. A parametric study reveals for systems involving a large equilibrium constant (K), the kinetic constant (D) will govern the shape of the resulting gasphase concentration profile. On the other hand, for systems with a relaxed mass transfer resistance, K will dominate the profile.

Statistical mechanics of shell models for two-dimensional turbulence

NASA Astrophysics Data System (ADS)

Aurell, E.; Boffetta, G.; Crisanti, A.; Frick, P.; Paladin, G.; Vulpiani, A.

1994-12-01

We study shell models that conserve the analogs of energy and enstrophy and hence are designed to mimic fluid turbulence in two-dimensions (2D). The main result is that the observed state is well described as a formal statistical equilibrium, closely analogous to the approach to two-dimensional ideal hydrodynamics of Onsager [Nuovo Cimento Suppl. 6, 279 (1949)], Hopf [J. Rat. Mech. Anal. 1, 87 (1952)], and Lee [Q. Appl. Math. 10, 69 (1952)]. In the presence of forcing and dissipation we observe a forward flux of enstrophy and a backward flux of energy. These fluxes can be understood as mean diffusive drifts from a source to two sinks in a system which is close to local equilibrium with Lagrange multipliers (``shell temperatures'') changing slowly with scale. This is clear evidence that the simplest shell models are not adequate to reproduce the main features of two-dimensional turbulence. The dimensional predictions on the power spectra from a supposed forward cascade of enstrophy and from one branch of the formal statistical equilibrium coincide in these shell models in contrast to the corresponding predictions for the Navier-Stokes and Euler equations in 2D. This coincidence has previously led to the mistaken conclusion that shell models exhibit a forward cascade of enstrophy. We also study the dynamical properties of the models and the growth of perturbations.

Sedimentation dynamics and equilibrium profiles in multicomponent mixtures of colloidal particles.

PubMed

Spruijt, E; Biesheuvel, P M

2014-02-19

In this paper we give a general theoretical framework that describes the sedimentation of multicomponent mixtures of particles with sizes ranging from molecules to macroscopic bodies. Both equilibrium sedimentation profiles and the dynamic process of settling, or its converse, creaming, are modeled. Equilibrium profiles are found to be in perfect agreement with experiments. Our model reconciles two apparently contradicting points of view about buoyancy, thereby resolving a long-lived paradox about the correct choice of the buoyant density. On the one hand, the buoyancy force follows necessarily from the suspension density, as it relates to the hydrostatic pressure gradient. On the other hand, sedimentation profiles of colloidal suspensions can be calculated directly using the fluid density as apparent buoyant density in colloidal systems in sedimentation-diffusion equilibrium (SDE) as a result of balancing gravitational and thermodynamic forces. Surprisingly, this balance also holds in multicomponent mixtures. This analysis resolves the ongoing debate of the correct choice of buoyant density (fluid or suspension): both approaches can be used in their own domain. We present calculations of equilibrium sedimentation profiles and dynamic sedimentation that show the consequences of these insights. In bidisperse mixtures of colloids, particles with a lower mass density than the homogeneous suspension will first cream and then settle, whereas particles with a suspension-matched mass density form transient, bimodal particle distributions during sedimentation, which disappear when equilibrium is reached. In all these cases, the centers of the distributions of the particles with the lowest mass density of the two, regardless of their actual mass, will be located in equilibrium above the so-called isopycnic point, a natural consequence of their hard-sphere interactions. We include these interactions using the Boublik-Mansoori-Carnahan-Starling-Leland (BMCSL) equation of state. Finally, we demonstrate that our model is not limited to hard spheres, by extending it to charged spherical particles, and to dumbbells, trimers and short chains of connected beads.

Neutral solute transport across osteochondral interface: A finite element approach.

PubMed

Arbabi, Vahid; Pouran, Behdad; Weinans, Harrie; Zadpoor, Amir A

2016-12-08

Investigation of the solute transfer across articular cartilage and subchondral bone plate could nurture the understanding of the mechanisms of osteoarthritis (OA) progression. In the current study, we approached the transport of neutral solutes in human (slight OA) and equine (healthy) samples using both computed tomography and biphasic-solute finite element modeling. We developed a multi-zone biphasic-solute finite element model (FEM) accounting for the inhomogeneity of articular cartilage (superficial, middle and deep zones) and subchondral bone plate. Fitting the FEM model to the concentration-time curves of the cartilage and the equilibrium concentration of the subchondral plate/calcified cartilage enabled determination of the diffusion coefficients in the superficial, middle and deep zones of cartilage and subchondral plate. We found slightly higher diffusion coefficients for all zones in the human samples as compared to the equine samples. Generally the diffusion coefficient in the superficial zone of human samples was about 3-fold higher than the middle zone, the diffusion coefficient of the middle zone was 1.5-fold higher than that of the deep zone, and the diffusion coefficient of the deep zone was 1.5-fold higher than that of the subchondral plate/calcified cartilage. Those ratios for equine samples were 9, 2 and 1.5, respectively. Regardless of the species considered, there is a gradual decrease of the diffusion coefficient as one approaches the subchondral plate, whereas the rate of decrease is dependent on the type of species. Copyright © 2016 Elsevier Ltd. All rights reserved.

Entropy-based artificial viscosity stabilization for non-equilibrium Grey Radiation-Hydrodynamics

DOE Office of Scientific and Technical Information (OSTI.GOV)

Delchini, Marc O., E-mail: delchinm@email.tamu.edu; Ragusa, Jean C., E-mail: jean.ragusa@tamu.edu; Morel, Jim, E-mail: jim.morel@tamu.edu

2015-09-01

The entropy viscosity method is extended to the non-equilibrium Grey Radiation-Hydrodynamic equations. The method employs a viscous regularization to stabilize the numerical solution. The artificial viscosity coefficient is modulated by the entropy production and peaks at shock locations. The added dissipative terms are consistent with the entropy minimum principle. A new functional form of the entropy residual, suitable for the Radiation-Hydrodynamic equations, is derived. We demonstrate that the viscous regularization preserves the equilibrium diffusion limit. The equations are discretized with a standard Continuous Galerkin Finite Element Method and a fully implicit temporal integrator within the MOOSE multiphysics framework. The methodmore » of manufactured solutions is employed to demonstrate second-order accuracy in both the equilibrium diffusion and streaming limits. Several typical 1-D radiation-hydrodynamic test cases with shocks (from Mach 1.05 to Mach 50) are presented to establish the ability of the technique to capture and resolve shocks.« less

The dependence of the oceans MOC on mesoscale eddy diffusivities: A model study

NASA Technical Reports Server (NTRS)

Marshall, John; Scott, Jeffery R.; Romanou, Anastasia; Kelley, Maxwell; Leboissetier, Anthony

2017-01-01

The dependence of the depth and strength of the ocean's global meridional overturning cells (MOC) on the specification of mesoscale eddy diffusivity (K) is explored in two ocean models. The GISS and MIT ocean models are driven by the same prescribed forcing fields, configured in similar ways, spun up to equilibrium for a range of K 's and the resulting MOCs mapped and documented. Scaling laws implicit in modern theories of the MOC are used to rationalize the results. In all calculations the K used in the computation of eddy-induced circulation and that used in the representation of eddy stirring along neutral surfaces, is set to the same value but is changed across experiments. We are able to connect changes in the strength and depth of the Atlantic MOC, the southern ocean upwelling MOC, and the deep cell emanating from Antarctica, to changes in K.

Thermodynamic Model Formulations for Inhomogeneous Solids with Application to Non-isothermal Phase Field Modelling

NASA Astrophysics Data System (ADS)

Gladkov, Svyatoslav; Kochmann, Julian; Reese, Stefanie; Hütter, Markus; Svendsen, Bob

2016-04-01

The purpose of the current work is the comparison of thermodynamic model formulations for chemically and structurally inhomogeneous solids at finite deformation based on "standard" non-equilibrium thermodynamics [SNET: e. g. S. de Groot and P. Mazur, Non-equilibrium Thermodynamics, North Holland, 1962] and the general equation for non-equilibrium reversible-irreversible coupling (GENERIC) [H. C. Öttinger, Beyond Equilibrium Thermodynamics, Wiley Interscience, 2005]. In the process, non-isothermal generalizations of standard isothermal conservative [e. g. J. W. Cahn and J. E. Hilliard, Free energy of a non-uniform system. I. Interfacial energy. J. Chem. Phys. 28 (1958), 258-267] and non-conservative [e. g. S. M. Allen and J. W. Cahn, A macroscopic theory for antiphase boundary motion and its application to antiphase domain coarsening. Acta Metall. 27 (1979), 1085-1095; A. G. Khachaturyan, Theory of Structural Transformations in Solids, Wiley, New York, 1983] diffuse interface or "phase-field" models [e. g. P. C. Hohenberg and B. I. Halperin, Theory of dynamic critical phenomena, Rev. Modern Phys. 49 (1977), 435-479; N. Provatas and K. Elder, Phase Field Methods in Material Science and Engineering, Wiley-VCH, 2010.] for solids are obtained. The current treatment is consistent with, and includes, previous works [e. g. O. Penrose and P. C. Fife, Thermodynamically consistent models of phase-field type for the kinetics of phase transitions, Phys. D 43 (1990), 44-62; O. Penrose and P. C. Fife, On the relation between the standard phase-field model and a "thermodynamically consistent" phase-field model. Phys. D 69 (1993), 107-113] on non-isothermal systems as a special case. In the context of no-flux boundary conditions, the SNET- and GENERIC-based approaches are shown to be completely consistent with each other and result in equivalent temperature evolution relations.

Measuring internal friction of an ultrafast-folding protein.

PubMed

Cellmer, Troy; Henry, Eric R; Hofrichter, James; Eaton, William A

2008-11-25

Nanosecond laser T-jump was used to measure the viscosity dependence of the folding kinetics of the villin subdomain under conditions where the viscogen has no effect on its equilibrium properties. The dependence of the unfolding/refolding relaxation time on solvent viscosity indicates a major contribution to the dynamics from internal friction. The internal friction increases with increasing temperature, suggesting a shift in the transition state along the reaction coordinate toward the native state with more compact structures, and therefore, a smaller diffusion coefficient due to increased landscape roughness. Fitting the data with an Ising-like model yields a relatively small position dependence for the diffusion coefficient. This finding is consistent with the excellent correlation found between experimental and calculated folding rates based on free energy barrier heights using the same diffusion coefficient for every protein.

Fibonacci family of dynamical universality classes.

PubMed

Popkov, Vladislav; Schadschneider, Andreas; Schmidt, Johannes; Schütz, Gunter M

2015-10-13

Universality is a well-established central concept of equilibrium physics. However, in systems far away from equilibrium, a deeper understanding of its underlying principles is still lacking. Up to now, a few classes have been identified. Besides the diffusive universality class with dynamical exponent [Formula: see text], another prominent example is the superdiffusive Kardar-Parisi-Zhang (KPZ) class with [Formula: see text]. It appears, e.g., in low-dimensional dynamical phenomena far from thermal equilibrium that exhibit some conservation law. Here we show that both classes are only part of an infinite discrete family of nonequilibrium universality classes. Remarkably, their dynamical exponents [Formula: see text] are given by ratios of neighboring Fibonacci numbers, starting with either [Formula: see text] (if a KPZ mode exist) or [Formula: see text] (if a diffusive mode is present). If neither a diffusive nor a KPZ mode is present, all dynamical modes have the Golden Mean [Formula: see text] as dynamical exponent. The universal scaling functions of these Fibonacci modes are asymmetric Lévy distributions that are completely fixed by the macroscopic current density relation and compressibility matrix of the system and hence accessible to experimental measurement.

A Simplified Model of Moisture Transport in Hydrophilic Porous Media With Applications to Pharmaceutical Tablets.

PubMed

Klinzing, Gerard R; Zavaliangos, Antonios

2016-08-01

This work establishes a predictive model that explicitly recognizes microstructural parameters in the description of the overall mass uptake and local gradients of moisture into tablets. Model equations were formulated based on local tablet geometry to describe the transient uptake of moisture. An analytical solution to a simplified set of model equations was solved to predict the overall mass uptake and moisture gradients with the tablets. The analytical solution takes into account individual diffusion mechanisms in different scales of porosity and diffusion into the solid phase. The time constant of mass uptake was found to be a function of several key material properties, such as tablet relative density, pore tortuosity, and equilibrium moisture content of the material. The predictions of the model are in excellent agreement with experimental results for microcrystalline cellulose tablets without the need for parameter fitting. The model presented provides a new method to analyze the transient uptake of moisture into hydrophilic materials with the knowledge of only a few fundamental material and microstructural parameters. In addition, the model allows for quick and insightful predictions of moisture diffusion for a variety of practical applications including pharmaceutical tablets, porous polymer systems, or cementitious materials. Copyright © 2016 American Pharmacists Association®. Published by Elsevier Inc. All rights reserved.

Long-term aging behaviors in a model soft colloidal system.

PubMed

Li, Qi; Peng, Xiaoguang; McKenna, Gregory B

2017-02-15

Colloidal and molecular systems share similar behaviors near to the glass transition volume fraction or temperature. Here, aging behaviors after volume fraction up-jump (induced by performing temperature down-jumps) conditions for a PS-PNIPAM/AA soft colloidal system were investigated using light scattering (diffusing wave spectroscopy, DWS). Both aging responses and equilibrium dynamics were investigated. For the aging responses, long-term experiments (100 000 s) were performed, and both equilibrium and non-equilibrium behaviors of the system were obtained. In the equilibrium state, as effective volume fraction increases (or temperature decreases), the colloidal dispersion displays a transition from the liquid to a glassy state. The equilibrium α-relaxation dynamics strongly depend on both the effective volume fraction and the initial mass concentration for the studied colloidal systems. Compared with prior results from our lab [X. Di, X. Peng and G. B. McKenna, J. Chem. Phys., 2014, 140, 054903], the effective volume fractions investigated spanned a wider range, to deeper into the glassy domain. The results show that the α-relaxation time τ α of the samples aged into equilibrium deviate from the classical Vogel-Fulcher-Tammann (VFT)-type expectations and the super-Arrhenius signature disappears above the glass transition volume fraction. The non-equilibrium aging response shows that the time for the structural evolution into equilibrium and the α-relaxation time are decoupled. The DWS investigation of the aging behavior after different volume fraction jumps reveals a different non-equilibrium or aging behavior for the considered colloidal systems compared with either molecular glasses or the macroscopic rheology of a similar colloidal dispersions.

Fate of polychlorinated biphenyls in a contaminated lake ecosystem: combining equilibrium passive sampling of sediment and water with total concentration measurements of biota.

PubMed

Mäenpää, Kimmo; Leppänen, Matti T; Figueiredo, Kaisa; Mayer, Philipp; Gilbert, Dorothea; Jahnke, Annika; Gil-Allué, Carmen; Akkanen, Jarkko; Nybom, Inna; Herve, Sirpa

2015-11-01

Equilibrium sampling devices can be applied to study and monitor the exposure and fate of hydrophobic organic chemicals on a thermodynamic basis. They can be used to determine freely dissolved concentrations and chemical activity ratios and to predict equilibrium partitioning concentrations of hydrophobic organic chemicals in biota lipids. The authors' aim was to assess the equilibrium status of polychlorinated biphenyls (PCBs) in a contaminated lake ecosystem and along its discharge course using equilibrium sampling devices for measurements in sediment and water and by also analyzing biota. The authors used equilibrium sampling devices (silicone rubber and polyethylene [PE]) to determine freely dissolved concentrations and chemical activities of PCBs in the water column and sediment porewater and calculated for both phases the corresponding equilibrium concentrations and chemical activities in model lipids. Overall, the studied ecosystem appeared to be in disequilibrium for the studied phases: sediment, water, and biota. Chemical activities of PCBs were higher in sediment than in water, which implies that the sediment functioned as a partitioning source of PCBs and that net diffusion occurred from the sediment to the water column. Measured lipid-normalized PCB concentrations in biota were generally below equilibrium lipid concentrations relative to the sediment (CLip ⇌Sed ) or water (CLip ⇌W ), indicating that PCB levels in the organisms were below the maximum partitioning levels. The present study shows the application versatility of equilibrium sampling devices in the field and facilitates a thermodynamic understanding of exposure and fate of PCBs in a contaminated lake and its discharge course. © 2015 SETAC.

The effect of non-equilibrium metal cooling on the interstellar medium

NASA Astrophysics Data System (ADS)

Capelo, Pedro R.; Bovino, Stefano; Lupi, Alessandro; Schleicher, Dominik R. G.; Grassi, Tommaso

2018-04-01

By using a novel interface between the modern smoothed particle hydrodynamics code GASOLINE2 and the chemistry package KROME, we follow the hydrodynamical and chemical evolution of an isolated galaxy. In order to assess the relevance of different physical parameters and prescriptions, we constructed a suite of 10 simulations, in which we vary the chemical network (primordial and metal species), how metal cooling is modelled (non-equilibrium versus equilibrium; optically thin versus thick approximation), the initial gas metallicity (from 10 to 100 per cent solar), and how molecular hydrogen forms on dust. This is the first work in which metal injection from supernovae, turbulent metal diffusion, and a metal network with non-equilibrium metal cooling are self-consistently included in a galaxy simulation. We find that properly modelling the chemical evolution of several metal species and the corresponding non-equilibrium metal cooling has important effects on the thermodynamics of the gas, the chemical abundances, and the appearance of the galaxy: the gas is typically warmer, has a larger molecular-gas mass fraction, and has a smoother disc. We also conclude that, at relatively high metallicity, the choice of molecular-hydrogen formation rates on dust is not crucial. Moreover, we confirm that a higher initial metallicity produces a colder gas and a larger fraction of molecular gas, with the low-metallicity simulation best matching the observed molecular Kennicutt-Schmidt relation. Finally, our simulations agree quite well with observations that link star formation rate to metal emission lines.

Application of activated carbon derived from scrap tires for adsorption of Rhodamine B.

PubMed

Li, Li; Liu, Shuangxi; Zhu, Tan

2010-01-01

Activated carbon derived from solid hazardous waste scrap tires was evaluated as a potential adsorbent for cationic dye removal. The adsorption process with respect to operating parameters was investigated to evaluate the adsorption characteristics of the activated pyrolytic tire char (APTC) for Rhodamine B (RhB). Systematic research including equilibrium, kinetics and thermodynamic studies was performed. The results showed that APTC was a potential adsorbent for RhB with a higher adsorption capacity than most adsorbents. Solution pH and temperature exert significant influence while ionic strength showed little effect on the adsorption process. The adsorption equilibrium data obey Langmuir isotherm and the kinetic data were well described by the pseudo second-order kinetic model. The adsorption process followed intra-particle diffusion model with more than one process affecting the adsorption process. Thermodynamic study confirmed that the adsorption was a physisorption process with spontaneous, endothermic and random characteristics.

Increases to Inferred Rates of Planetesimal Accretion due to Thermohaline Mixing in Metal-accreting White Dwarfs

NASA Astrophysics Data System (ADS)

Bauer, Evan B.; Bildsten, Lars

2018-06-01

Many isolated, old white dwarfs (WDs) show surprising evidence of metals in their photospheres. Given that the timescale for gravitational sedimentation is astronomically short, this is taken as evidence for ongoing accretion, likely of tidally disrupted planetesimals. The rate of such accretion, {\\dot{M}}acc}, is important to constrain, and most modeling of this process relies on assuming an equilibrium between diffusive sedimentation and metal accretion supplied to the WD’s surface convective envelope. Building on the earlier work of Deal and collaborators, we show that high {\\dot{M}}acc} models with only diffusive sedimentation are unstable to thermohaline mixing and that models that account for the enhanced mixing from the active thermohaline instability require larger accretion rates, sometimes reaching {\\dot{M}}acc}≈ {10}13 {{g}} {{{s}}}-1 to explain observed calcium abundances. We present results from a grid of MESA models that include both diffusion and thermohaline mixing. These results demonstrate that both mechanisms are essential for understanding metal pollution across the range of polluted WDs with hydrogen atmospheres. Another consequence of active thermohaline mixing is that the observed metal abundance ratios are identical to accreted material.

Measurement of the neutral composition of the lower thermosphere above Fort Churchill by rocket-borne mass spectrometer.

NASA Technical Reports Server (NTRS)

Hickman, D. R.; Nier, A. O.

1972-01-01

Measurement of the neutral atmospheric composition above Fort Churchill, Canada (59 N, 94 W), by mass spectrometers in two rocket flights at 0835 CST on Feb. 4 and 6, 1969. A quantitative measure for the extent of agreement with static diffusive equilibrium is introduced, and substantial agreement with profiles predicted when static diffusive equilibrium was assumed is found for all constituents including helium. A sensitive search for atomic nitrogen yielded upper limits of a few per cent for one flight and of 0.2% for the other.

Measurement of steady-state minority-carrier transport parameters in heavily doped n-type silicon

NASA Technical Reports Server (NTRS)

Del Alamo, Jesus A.; Swanson, Richard M.

1987-01-01

The relevant hole transport and recombination parameters in heavily doped n-type silicon under steady state are the hole diffusion length and the product of the hole diffusion coefficient times the hole equilibrium concentration. These parameters have measured in phosphorus-doped silicon grown by epitaxy throughout nearly two orders of magnitude of doping level. Both parameters are found to be strong functions of donor concentration. The equilibrium hole concentration can be deduced from the measurement. A rigid shrinkage of the forbidden gap appears as the dominant heavy doping mechanism in phosphorus-doped silicon.

Equilibrium and kinetic modelling of Cd(II) biosorption by algae Gelidium and agar extraction algal waste.

PubMed

Vilar, Vítor J P; Botelho, Cidália M S; Boaventura, Rui A R

2006-01-01

In this study an industrial algal waste from agar extraction has been used as an inexpensive and effective biosorbent for cadmium (II) removal from aqueous solutions. This biosorbent was compared with the algae Gelidium itself, which is the raw material for agar extraction. Equilibrium data follow both Langmuir and Redlich-Peterson models. The parameters of Langmuir equilibrium model are q(max)=18.0 mgg(-1), b=0.19 mgl(-1) and q(max)=9.7 mgg(-1), b=0.16 mgl(-1), respectively for Gelidium and the algal waste. Kinetic experiments were conducted at initial Cd(II) concentrations in the range 6-91 mgl(-1). Data were fitted to pseudo-first- and second-order Lagergren models. For an initial Cd(II) concentration of 91 mgl(-1) the parameters of the pseudo-first-order Lagergren model are k(1,ads)=0.17 and 0.87 min(-1); q(eq)=16.3 and 8.7 mgg(-1), respectively, for Gelidium and algal waste. Kinetic constants vary with the initial metal concentration. The adsorptive behaviour of biosorbent particles was modelled using a batch reactor mass transfer kinetic model. The model successfully predicts Cd(II) concentration profiles and provides significant insights on the biosorbents performance. The homogeneous diffusivity, D(h), is in the range 0.5-2.2 x10(-8) and 2.1-10.4 x10(-8)cm(2)s(-1), respectively, for Gelidium and algal waste.

A 3-Component System of Competition and Diffusion.

DTIC Science & Technology

1983-08-01

assume * that the distribution of the populations are determined by competition of’ Lotka - Volterra - * Gause type and simple diffusion. Suppose ui(t,x...diffusive Lotka - Volterra system with three species can have a stable non-constant equilibrium solutions. J. Math. Biol., (in press). [7] Kishimoto, K., Mimura...M. and Yoshida, K., Stable spatlo-temporal oscillations of diffusive Lotka - Volterra systems with three or more species, to appear in J. Math. Biol

Bistability: Requirements on Cell-Volume, Protein Diffusion, and Thermodynamics

PubMed Central

Endres, Robert G.

2015-01-01

Bistability is considered wide-spread among bacteria and eukaryotic cells, useful e.g. for enzyme induction, bet hedging, and epigenetic switching. However, this phenomenon has mostly been described with deterministic dynamic or well-mixed stochastic models. Here, we map known biological bistable systems onto the well-characterized biochemical Schlögl model, using analytical calculations and stochastic spatiotemporal simulations. In addition to network architecture and strong thermodynamic driving away from equilibrium, we show that bistability requires fine-tuning towards small cell volumes (or compartments) and fast protein diffusion (well mixing). Bistability is thus fragile and hence may be restricted to small bacteria and eukaryotic nuclei, with switching triggered by volume changes during the cell cycle. For large volumes, single cells generally loose their ability for bistable switching and instead undergo a first-order phase transition. PMID:25874711

Ehrenfest's Lottery--Time and Entropy Maximization

ERIC Educational Resources Information Center

Ashbaugh, Henry S.

2010-01-01

Successful teaching of the Second Law of Thermodynamics suffers from limited simple examples linking equilibrium to entropy maximization. I describe a thought experiment connecting entropy to a lottery that mixes marbles amongst a collection of urns. This mixing obeys diffusion-like dynamics. Equilibrium is achieved when the marble distribution is…

Fisher-Wright model with deterministic seed bank and selection.

PubMed

Koopmann, Bendix; Müller, Johannes; Tellier, Aurélien; Živković, Daniel

2017-04-01

Seed banks are common characteristics to many plant species, which allow storage of genetic diversity in the soil as dormant seeds for various periods of time. We investigate an above-ground population following a Fisher-Wright model with selection coupled with a deterministic seed bank assuming the length of the seed bank is kept constant and the number of seeds is large. To assess the combined impact of seed banks and selection on genetic diversity, we derive a general diffusion model. The applied techniques outline a path of approximating a stochastic delay differential equation by an appropriately rescaled stochastic differential equation. We compute the equilibrium solution of the site-frequency spectrum and derive the times to fixation of an allele with and without selection. Finally, it is demonstrated that seed banks enhance the effect of selection onto the site-frequency spectrum while slowing down the time until the mutation-selection equilibrium is reached. Copyright © 2016 Elsevier Inc. All rights reserved.

Electrical characteristics of TIG arcs in argon from non-equilibrium modelling and experiment

NASA Astrophysics Data System (ADS)

Baeva, Margarita; Uhrlandt, Dirk; Siewert, Erwan

2016-09-01

Electric arcs are widely used in industrial processes so that a thorough understanding of the arc characteristics is highly important to industrial research and development. TIG welding arcs operated with pointed electrodes made of tungsten, doped with cerium oxide, have been studied in order to analyze in detail the electric field and the arc voltage. Newly developed non-equilibrium model of the arc is based on a complete diffusion treatment of particle fluxes, a generalized form of Ohm's law, and boundary conditions accounting for the space-charge sheaths within the magneto-hydrodynamic approach. Experiments have been carried out for electric currents in the range 5-200 A. The electric arc has been initiated between a WC20 cathode and a water-cooled copper plate placed 0.8 mm from each other. The arc length has been continuously increased by 0.1 mm up to 15 mm and the arc voltage has been simultaneously recorded. Modelling and experimental results will be presented and discussed.

Adsorption isotherms and kinetics of activated carbons produced from coals of different ranks.

PubMed

Purevsuren, B; Lin, Chin-Jung; Davaajav, Y; Ariunaa, A; Batbileg, S; Avid, B; Jargalmaa, S; Huang, Yu; Liou, Sofia Ya-Hsuan

2015-01-01

Activated carbons (ACs) from six coals, ranging from low-rank lignite brown coal to high-rank stone coal, were utilized as adsorbents to remove basic methylene blue (MB) from an aqueous solution. The surface properties of the obtained ACs were characterized via thermal analysis, N2 isothermal sorption, scanning electron microscopy, Fourier transform infrared spectroscopy, X-ray photoelectron spectroscopy and Boehm titration. As coal rank decreased, an increase in the heterogeneity of the pore structures and abundance of oxygen-containing functional groups increased MB coverage on its surface. The equilibrium data fitted well with the Langmuir model, and adsorption capacity of MB ranged from 51.8 to 344.8 mg g⁻¹. Good correlation coefficients were obtained using the intra-particle diffusion model, indicating that the adsorption of MB onto ACs is diffusion controlled. The values of the effective diffusion coefficient ranged from 0.61 × 10⁻¹⁰ to 7.1 × 10⁻¹⁰ m² s⁻¹, indicating that ACs from lower-rank coals have higher effective diffusivities. Among all the ACs obtained from selected coals, the AC from low-rank lignite brown coal was the most effective in removing MB from an aqueous solution.

Predictive modeling of CO2 sequestration in deep saline sandstone reservoirs: Impacts of geochemical kinetics

DOE Office of Scientific and Technical Information (OSTI.GOV)

Balashov, Victor N.; Guthrie, George D.; Hakala, J. Alexandra

2013-03-01

One idea for mitigating the increase in fossil-fuel generated CO{sub 2} in the atmosphere is to inject CO{sub 2} into subsurface saline sandstone reservoirs. To decide whether to try such sequestration at a globally significant scale will require the ability to predict the fate of injected CO{sub 2}. Thus, models are needed to predict the rates and extents of subsurface rock-water-gas interactions. Several reactive transport models for CO{sub 2} sequestration created in the last decade predicted sequestration in sandstone reservoirs of ~17 to ~90 kg CO{sub 2} m{sup -3|. To build confidence in such models, a baseline problem including rockmore » + water chemistry is proposed as the basis for future modeling so that both the models and the parameterizations can be compared systematically. In addition, a reactive diffusion model is used to investigate the fate of injected supercritical CO{sub 2} fluid in the proposed baseline reservoir + brine system. In the baseline problem, injected CO{sub 2} is redistributed from the supercritical (SC) free phase by dissolution into pore brine and by formation of carbonates in the sandstone. The numerical transport model incorporates a full kinetic description of mineral-water reactions under the assumption that transport is by diffusion only. Sensitivity tests were also run to understand which mineral kinetics reactions are important for CO{sub 2} trapping. The diffusion transport model shows that for the first ~20 years after CO{sub 2} diffusion initiates, CO{sub 2} is mostly consumed by dissolution into the brine to form CO{sub 2,aq} (solubility trapping). From 20-200 years, both solubility and mineral trapping are important as calcite precipitation is driven by dissolution of oligoclase. From 200 to 1000 years, mineral trapping is the most important sequestration mechanism, as smectite dissolves and calcite precipitates. Beyond 2000 years, most trapping is due to formation of aqueous HCO{sub 3}{sup -}. Ninety-seven percent of the maximum CO{sub 2} sequestration, 34.5 kg CO{sub 2} per m{sup 3} of sandstone, is attained by 4000 years even though the system does not achieve chemical equilibrium until ~25,000 years. This maximum represents about 20% CO{sub 2} dissolved as CO{sub 2},aq, 50% dissolved as HCO{sub 3}{sup -}{sub ,aq}, and 30% precipitated as calcite. The extent of sequestration as HCO{sub 3}{sup -} at equilibrium can be calculated from equilibrium thermodynamics and is roughly equivalent to the amount of Na+ in the initial sandstone in a soluble mineral (here, oligoclase). Similarly, the extent of trapping in calcite is determined by the amount of Ca2+ in the initial oligoclase and smectite. Sensitivity analyses show that the rate of CO{sub 2} sequestration is sensitive to the mineral-water reaction kinetic constants between approximately 10 and 4000 years. The sensitivity of CO{sub 2} sequestration to the rate constants decreases in magnitude respectively from oligoclase to albite to smectite.« less

Effect of the Lateral Exospheric Transport on the Horizontal Hydrogen Distribution Near the Exobase of Mars

NASA Astrophysics Data System (ADS)

Chaufray, J.-Y.; Yelle, R. V.; Gonzalez-Galindo, F.; Forget, F.; Lopez-Valverde, M.; Leblanc, F.; Modolo, R.

2018-03-01

We simulate the hydrogen density near the exobase of Mars, using the 3-D Martian Global Circulation Model of Laboratoire de Météorologie Dynamique, coupled to an exospheric ballistic model to compute the downward ballistic flux. The simulated hydrogen distribution near the exobase obtained at two different seasons—Ls = 180° and Ls = 270°—is close to Zero Net Ballistic Flux equilibrium. In other words, the hydrogen density near the exobase adjusts to have a balance between the local upward ballistic and the downward ballistic flux due to a short lateral migration time in the exosphere compared to the vertical diffusion time. This equilibrium leads to a hydrogen density n near the exobase directly controlled by the exospheric temperature T by the relation nT5/2 = constant. This relation could be used to extend 1-D hydrogen exospheric model of Mars used to derive the hydrogen density and escape flux at Mars from Lyman-α observations to 3-D model based on observed or modeled exospheric temperature near the exobase, without increasing the number of free parameters.

Radial Distribution Functions of Strongly Coupled Two-Temperature Plasmas

NASA Astrophysics Data System (ADS)

Shaffer, Nathaniel R.; Tiwari, Sanat Kumar; Baalrud, Scott D.

2017-10-01

We present tests of three theoretical models for the radial distribution functions (RDFs) in two-temperature strongly coupled plasmas. RDFs are useful in extending plasma thermodynamics and kinetic theory to strong coupling, but they are usually known only for thermal equilibrium or for approximate one-component model plasmas. Accurate two-component modeling is necessary to understand the impact of strong coupling on inter-species transport, e.g., ambipolar diffusion and electron-ion temperature relaxation. We demonstrate that the Seuferling-Vogel-Toeppfer (SVT) extension of the hypernetted chain equations not only gives accurate RDFs (as compared with classical molecular dynamics simulations), but also has a simple connection with the Yukawa OCP model. This connection gives a practical means to recover the structure of the electron background from knowledge of the ion-ion RDF alone. Using the model RDFs in Effective Potential Theory, we report the first predictions of inter-species transport coefficients of strongly coupled plasmas far from equilibrium. This work is supported by NSF Grant No. PHY-1453736, AFSOR Award No. FA9550-16-1-0221, and used XSEDE computational resources.

A moving mesh finite difference method for equilibrium radiation diffusion equations

DOE Office of Scientific and Technical Information (OSTI.GOV)

Yang, Xiaobo, E-mail: xwindyb@126.com; Huang, Weizhang, E-mail: whuang@ku.edu; Qiu, Jianxian, E-mail: jxqiu@xmu.edu.cn

2015-10-01

An efficient moving mesh finite difference method is developed for the numerical solution of equilibrium radiation diffusion equations in two dimensions. The method is based on the moving mesh partial differential equation approach and moves the mesh continuously in time using a system of meshing partial differential equations. The mesh adaptation is controlled through a Hessian-based monitor function and the so-called equidistribution and alignment principles. Several challenging issues in the numerical solution are addressed. Particularly, the radiation diffusion coefficient depends on the energy density highly nonlinearly. This nonlinearity is treated using a predictor–corrector and lagged diffusion strategy. Moreover, the nonnegativitymore » of the energy density is maintained using a cutoff method which has been known in literature to retain the accuracy and convergence order of finite difference approximation for parabolic equations. Numerical examples with multi-material, multiple spot concentration situations are presented. Numerical results show that the method works well for radiation diffusion equations and can produce numerical solutions of good accuracy. It is also shown that a two-level mesh movement strategy can significantly improve the efficiency of the computation.« less

Influence of Liquid Structure on Fickian Diffusion in Binary Mixtures of n-Hexane and Carbon Dioxide Probed by Dynamic Light Scattering, Raman Spectroscopy, and Molecular Dynamics Simulations.

PubMed

Klein, Tobias; Wu, Wenchang; Rausch, Michael Heinrich; Giraudet, Cédric; Koller, Thomas M; Fröba, Andreas Paul

2018-06-11

This study contributes to a fundamental understanding how the liquid structure in a model system consisting of weakly associative n-hexane ( n-C 6 H 14 ) and carbon dioxide (CO 2 ) influences the Fickian diffusion process. For this, the benefits of light scattering experiments and molecular dynamics (MD) simulations at macroscopic thermodynamic equilibrium were combined synergistically. Our reference Fickian diffusivities measured by dynamic light scattering (DLS) revealed an unusual trend with increasing CO 2 mole fractions up to a CO 2 concentration of about 70 mol%, which agrees with our simulation results. The molecular impacts on the Fickian diffusion were analyzed by MD simulations, where kinetic contributions related to the Maxwell-Stefan (MS) diffusivity and structural contributions quantified by the thermodynamic factor were studied separately. Both the MS diffusivity and the thermodynamic factor indicate the deceleration of Fickian diffusion compared to an ideal mixture behavior. Computed radial distribution functions as well as a significant blue-shift of the CH-stretching modes of n-C 6 H 14 identified by Raman spectroscopy show that the slowing-down of the diffusion is caused by a structural organization in the binary mixtures over a broad concentration range in the form of self-associated n-C 6 H 14 and CO 2 domains. These networks start to form close to the infinite dilution limits and seem to have their largest extent at a solute-solvent transition point at about 70 mol% of CO 2 . The current results not only improve the general understanding of mass diffusion in liquids, but also serve to develop sound prediction models for Fick diffusivities.

Instabilities and diffusion in a hydrodynamic model of a fluid membrane coupled to a thin active fluid layer.

PubMed

Sarkar, N; Basu, A

2012-11-01

We construct a coarse-grained effective two-dimensional (2d hydrodynamic theory as a theoretical model for a coupled system of a fluid membrane and a thin layer of a polar active fluid in its ordered state that is anchored to the membrane. We show that such a system is prone to generic instabilities through the interplay of nonequilibrium drive, polar order and membrane fluctuation. We use our model equations to calculate diffusion coefficients of an inclusion in the membrane and show that their values depend strongly on the system size, in contrast to their equilibrium values. Our work extends the work of S. Sankararaman and S. Ramaswamy (Phys. Rev. Lett., 102, 118107 (2009)) to a coupled system of a fluid membrane and an ordered active fluid layer. Our model is broadly inspired by and should be useful as a starting point for theoretical descriptions of the coupled dynamics of a cell membrane and a cortical actin layer anchored to it.

PolyPole-1: An accurate numerical algorithm for intra-granular fission gas release

DOE Office of Scientific and Technical Information (OSTI.GOV)

Pizzocri, D.; Rabiti, C.; Luzzi, L.

2016-09-01

This paper describes the development of a new numerical algorithm (called PolyPole-1) to efficiently solve the equation for intra-granular fission gas release in nuclear fuel. The work was carried out in collaboration with Politecnico di Milano and Institute for Transuranium Elements. The PolyPole-1 algorithms is being implemented in INL's fuels code BISON code as part of BISON's fission gas release model. The transport of fission gas from within the fuel grains to the grain boundaries (intra-granular fission gas release) is a fundamental controlling mechanism of fission gas release and gaseous swelling in nuclear fuel. Hence, accurate numerical solution of themore » corresponding mathematical problem needs to be included in fission gas behaviour models used in fuel performance codes. Under the assumption of equilibrium between trapping and resolution, the process can be described mathematically by a single diffusion equation for the gas atom concentration in a grain. In this work, we propose a new numerical algorithm (PolyPole-1) to efficiently solve the fission gas diffusion equation in time-varying conditions. The PolyPole-1 algorithm is based on the analytic modal solution of the diffusion equation for constant conditions, with the addition of polynomial corrective terms that embody the information on the deviation from constant conditions. The new algorithm is verified by comparing the results to a finite difference solution over a large number of randomly generated operation histories. Furthermore, comparison to state-of-the-art algorithms used in fuel performance codes demonstrates that the accuracy of the PolyPole-1 solution is superior to other algorithms, with similar computational effort. Finally, the concept of PolyPole-1 may be extended to the solution of the general problem of intra-granular fission gas diffusion during non-equilibrium trapping and resolution, which will be the subject of future work.« less

Stochastic simulation of reaction-diffusion systems: A fluctuating-hydrodynamics approach

NASA Astrophysics Data System (ADS)

Kim, Changho; Nonaka, Andy; Bell, John B.; Garcia, Alejandro L.; Donev, Aleksandar

2017-03-01

We develop numerical methods for stochastic reaction-diffusion systems based on approaches used for fluctuating hydrodynamics (FHD). For hydrodynamic systems, the FHD formulation is formally described by stochastic partial differential equations (SPDEs). In the reaction-diffusion systems we consider, our model becomes similar to the reaction-diffusion master equation (RDME) description when our SPDEs are spatially discretized and reactions are modeled as a source term having Poisson fluctuations. However, unlike the RDME, which becomes prohibitively expensive for an increasing number of molecules, our FHD-based description naturally extends from the regime where fluctuations are strong, i.e., each mesoscopic cell has few (reactive) molecules, to regimes with moderate or weak fluctuations, and ultimately to the deterministic limit. By treating diffusion implicitly, we avoid the severe restriction on time step size that limits all methods based on explicit treatments of diffusion and construct numerical methods that are more efficient than RDME methods, without compromising accuracy. Guided by an analysis of the accuracy of the distribution of steady-state fluctuations for the linearized reaction-diffusion model, we construct several two-stage (predictor-corrector) schemes, where diffusion is treated using a stochastic Crank-Nicolson method, and reactions are handled by the stochastic simulation algorithm of Gillespie or a weakly second-order tau leaping method. We find that an implicit midpoint tau leaping scheme attains second-order weak accuracy in the linearized setting and gives an accurate and stable structure factor for a time step size of an order of magnitude larger than the hopping time scale of diffusing molecules. We study the numerical accuracy of our methods for the Schlögl reaction-diffusion model both in and out of thermodynamic equilibrium. We demonstrate and quantify the importance of thermodynamic fluctuations to the formation of a two-dimensional Turing-like pattern and examine the effect of fluctuations on three-dimensional chemical front propagation. By comparing stochastic simulations to deterministic reaction-diffusion simulations, we show that fluctuations accelerate pattern formation in spatially homogeneous systems and lead to a qualitatively different disordered pattern behind a traveling wave.

Stochastic simulation of reaction-diffusion systems: A fluctuating-hydrodynamics approach

DOE PAGES

Kim, Changho; Nonaka, Andy; Bell, John B.; ...

2017-03-24

Here, we develop numerical methods for stochastic reaction-diffusion systems based on approaches used for fluctuating hydrodynamics (FHD). For hydrodynamic systems, the FHD formulation is formally described by stochastic partial differential equations (SPDEs). In the reaction-diffusion systems we consider, our model becomes similar to the reaction-diffusion master equation (RDME) description when our SPDEs are spatially discretized and reactions are modeled as a source term having Poisson fluctuations. However, unlike the RDME, which becomes prohibitively expensive for an increasing number of molecules, our FHD-based description naturally extends from the regime where fluctuations are strong, i.e., each mesoscopic cell has few (reactive) molecules,more » to regimes with moderate or weak fluctuations, and ultimately to the deterministic limit. By treating diffusion implicitly, we avoid the severe restriction on time step size that limits all methods based on explicit treatments of diffusion and construct numerical methods that are more efficient than RDME methods, without compromising accuracy. Guided by an analysis of the accuracy of the distribution of steady-state fluctuations for the linearized reaction-diffusion model, we construct several two-stage (predictor-corrector) schemes, where diffusion is treated using a stochastic Crank-Nicolson method, and reactions are handled by the stochastic simulation algorithm of Gillespie or a weakly second-order tau leaping method. We find that an implicit midpoint tau leaping scheme attains second-order weak accuracy in the linearized setting and gives an accurate and stable structure factor for a time step size of an order of magnitude larger than the hopping time scale of diffusing molecules. We study the numerical accuracy of our methods for the Schlögl reaction-diffusion model both in and out of thermodynamic equilibrium. We demonstrate and quantify the importance of thermodynamic fluctuations to the formation of a two-dimensional Turing-like pattern and examine the effect of fluctuations on three-dimensional chemical front propagation. Furthermore, by comparing stochastic simulations to deterministic reaction-diffusion simulations, we show that fluctuations accelerate pattern formation in spatially homogeneous systems and lead to a qualitatively different disordered pattern behind a traveling wave.« less

Binding equilibrium and kinetics of membrane-anchored receptors and ligands in cell adhesion: Insights from computational model systems and theory.

PubMed

Weikl, Thomas R; Hu, Jinglei; Xu, Guang-Kui; Lipowsky, Reinhard

2016-09-02

The adhesion of cell membranes is mediated by the binding of membrane-anchored receptor and ligand proteins. In this article, we review recent results from simulations and theory that lead to novel insights on how the binding equilibrium and kinetics of these proteins is affected by the membranes and by the membrane anchoring and molecular properties of the proteins. Simulations and theory both indicate that the binding equilibrium constant [Formula: see text] and the on- and off-rate constants of anchored receptors and ligands in their 2-dimensional (2D) membrane environment strongly depend on the membrane roughness from thermally excited shape fluctuations on nanoscales. Recent theory corroborated by simulations provides a general relation between [Formula: see text] and the binding constant [Formula: see text] of soluble variants of the receptors and ligands that lack the membrane anchors and are free to diffuse in 3 dimensions (3D).

Binding equilibrium and kinetics of membrane-anchored receptors and ligands in cell adhesion: Insights from computational model systems and theory

PubMed Central

Weikl, Thomas R.; Hu, Jinglei; Xu, Guang-Kui; Lipowsky, Reinhard

2016-01-01

ABSTRACT The adhesion of cell membranes is mediated by the binding of membrane-anchored receptor and ligand proteins. In this article, we review recent results from simulations and theory that lead to novel insights on how the binding equilibrium and kinetics of these proteins is affected by the membranes and by the membrane anchoring and molecular properties of the proteins. Simulations and theory both indicate that the binding equilibrium constant K2D and the on- and off-rate constants of anchored receptors and ligands in their 2-dimensional (2D) membrane environment strongly depend on the membrane roughness from thermally excited shape fluctuations on nanoscales. Recent theory corroborated by simulations provides a general relation between K2D and the binding constant K3D of soluble variants of the receptors and ligands that lack the membrane anchors and are free to diffuse in 3 dimensions (3D). PMID:27294442

Diffusion coefficients in systems with inclusion compounds. 1. alpha. -Cyclodextrin-L-phenylalanine-water at 25 degree C

DOE Office of Scientific and Technical Information (OSTI.GOV)

Paduano, L.; Sartorio, R.; Vitagliano, V.

Diffusion coefficients in the ternary system {alpha}-cyclodextrin (at one concentration)-L-phenylalanine (at four concentrations)-water have been measured by using the Gouy interferometric technique. The effect of the inclusion equilibrium on the cross-term diffusion coefficients was observed. The measured diffusion coefficients in the ternary systems were used to calculate values of the binding constants. These values are in good agreement with the value obtained from calorimetric studies.

Boron diffusion in bcc-Fe studied by first-principles calculations

NASA Astrophysics Data System (ADS)

Xianglong, Li; Ping, Wu; Ruijie, Yang; Dan, Yan; Sen, Chen; Shiping, Zhang; Ning, Chen

2016-03-01

The diffusion mechanism of boron in bcc-Fe has been studied by first-principles calculations. The diffusion coefficients of the interstitial mechanism, the B-monovacancy complex mechanism, and the B-divacancy complex mechanism have been calculated. The calculated diffusion coefficient of the interstitial mechanism is D0 = 1.05 × 10-7 exp (-0.75 eV/kT) m2 · s-1, while the diffusion coefficients of the B-monovacancy and the B-divacancy complex mechanisms are D1 = 1.22 × 10-6 f1 exp (-2.27 eV/kT) m2 · s-1 and D2 ≈ 8.36 × 10-6 exp (-4.81 eV/kT) m2 · s-1, respectively. The results indicate that the dominant diffusion mechanism in bcc-Fe is the interstitial mechanism through an octahedral interstitial site instead of the complex mechanism. The calculated diffusion coefficient is in accordance with the reported experiment results measured in Fe-3%Si-B alloy (bcc structure). Since the non-equilibrium segregation of boron is based on the diffusion of the complexes as suggested by the theory, our calculation reasonably explains why the non-equilibrium segregation of boron is not observed in bcc-Fe in experiments. Project supported by the National Natural Science Foundation of China (Grant No. 51276016) and the National Basic Research Program of China (Grant No. 2012CB720406).

HELIOS: An Open-source, GPU-accelerated Radiative Transfer Code for Self-consistent Exoplanetary Atmospheres

NASA Astrophysics Data System (ADS)

Malik, Matej; Grosheintz, Luc; Mendonça, João M.; Grimm, Simon L.; Lavie, Baptiste; Kitzmann, Daniel; Tsai, Shang-Min; Burrows, Adam; Kreidberg, Laura; Bedell, Megan; Bean, Jacob L.; Stevenson, Kevin B.; Heng, Kevin

2017-02-01

We present the open-source radiative transfer code named HELIOS, which is constructed for studying exoplanetary atmospheres. In its initial version, the model atmospheres of HELIOS are one-dimensional and plane-parallel, and the equation of radiative transfer is solved in the two-stream approximation with nonisotropic scattering. A small set of the main infrared absorbers is employed, computed with the opacity calculator HELIOS-K and combined using a correlated-k approximation. The molecular abundances originate from validated analytical formulae for equilibrium chemistry. We compare HELIOS with the work of Miller-Ricci & Fortney using a model of GJ 1214b, and perform several tests, where we find: model atmospheres with single-temperature layers struggle to converge to radiative equilibrium; k-distribution tables constructed with ≳ 0.01 cm-1 resolution in the opacity function (≲ {10}3 points per wavenumber bin) may result in errors ≳ 1%-10% in the synthetic spectra; and a diffusivity factor of 2 approximates well the exact radiative transfer solution in the limit of pure absorption. We construct “null-hypothesis” models (chemical equilibrium, radiative equilibrium, and solar elemental abundances) for six hot Jupiters. We find that the dayside emission spectra of HD 189733b and WASP-43b are consistent with the null hypothesis, while the latter consistently underpredicts the observed fluxes of WASP-8b, WASP-12b, WASP-14b, and WASP-33b. We demonstrate that our results are somewhat insensitive to the choice of stellar models (blackbody, Kurucz, or PHOENIX) and metallicity, but are strongly affected by higher carbon-to-oxygen ratios. The code is publicly available as part of the Exoclimes Simulation Platform (exoclime.net).

Venus ionosphere: photochemical and thermal diffusion control of ion composition.

PubMed

Bauer, S J; Donahue, T M; Hartle, R E; Taylor, H A

1979-07-06

The major photochemical sources and sinks for ten of the ions measured by the ion mass spectrometer on the Pioneer Venus bus and orbiter spacecraft that are consistent with the neutral gas composition measured on the same spacecraft have been identified. The neutral gas temperature (Tn) as a function of solar zenith angle (chi) derived from measured ion distributions in photochemical equilibrium is given by Tn (K) = 323 cos(1/5)chi. Above 200 kilometers, the altitude behavior of ions is generally controlled by plasma diffusion, with important modifications for minor ions due to thermal diffusion resulting from the observed gradients of plasma temperatures. The dayside equilibrium distributions of ions are sometimes perturbed by plasma convection, while lateral transport of ions from the dayside seems to be a major source of the nightside ionosphere.

Thermodynamic analysis of Cr(VI) extraction using TOPO impregnated membranes.

PubMed

Praveen, Prashant; Loh, Kai-Chee

2016-08-15

Solid/liquid extraction of Cr(VI) was accomplished using trioctylphosphine oxide impregnated polypropylene hollow fiber membranes. Extraction of 100-500mg/L Cr(VI) by the extractant impregnated membranes (EIM) was characterized by high uptake rate and capacity, and equilibrium was attained within 45min of contact. Extraction equilibrium was pH-dependent (at an optimal pH 2), whereas stripping using 0.2M sodium hydroxide yielded the highest recovery of 98% within 60min. The distribution coefficient was independent of initial Cr(VI) concentration, and the linear distribution equilibrium isotherm could be modeled using Freundlich isotherm. The mass transfer kinetics of Cr(VI) was examined using pseudo-second-order and intraparticle diffusion models and a mass transfer mechanism was deduced. The distribution coefficient increased with temperature, which indicated endothermic nature of the reaction. Enthalpy and entropy change during Cr(VI) extraction were positive and varied in the range of 37-49kJ/mol and 114-155J/mol, respectively. The free energy change was negative, confirming the feasibility and spontaneity of the mass transfer process. Results obtained suggest that EIMs are efficient and sustainable for extraction of Cr(VI) from wastewater. Copyright © 2016 Elsevier B.V. All rights reserved.

Shape characteristics of equilibrium and non-equilibrium fractal clusters.

PubMed

Mansfield, Marc L; Douglas, Jack F

2013-07-28

It is often difficult in practice to discriminate between equilibrium and non-equilibrium nanoparticle or colloidal-particle clusters that form through aggregation in gas or solution phases. Scattering studies often permit the determination of an apparent fractal dimension, but both equilibrium and non-equilibrium clusters in three dimensions frequently have fractal dimensions near 2, so that it is often not possible to discriminate on the basis of this geometrical property. A survey of the anisotropy of a wide variety of polymeric structures (linear and ring random and self-avoiding random walks, percolation clusters, lattice animals, diffusion-limited aggregates, and Eden clusters) based on the principal components of both the radius of gyration and electric polarizability tensor indicates, perhaps counter-intuitively, that self-similar equilibrium clusters tend to be intrinsically anisotropic at all sizes, while non-equilibrium processes such as diffusion-limited aggregation or Eden growth tend to be isotropic in the large-mass limit, providing a potential means of discriminating these clusters experimentally if anisotropy could be determined along with the fractal dimension. Equilibrium polymer structures, such as flexible polymer chains, are normally self-similar due to the existence of only a single relevant length scale, and are thus anisotropic at all length scales, while non-equilibrium polymer structures that grow irreversibly in time eventually become isotropic if there is no difference in the average growth rates in different directions. There is apparently no proof of these general trends and little theoretical insight into what controls the universal anisotropy in equilibrium polymer structures of various kinds. This is an obvious topic of theoretical investigation, as well as a matter of practical interest. To address this general problem, we consider two experimentally accessible ratios, one between the hydrodynamic and gyration radii, the other between the viscosity and hydrodynamic radii, as potential measures of shape anisotropy. We also find a strong correlation between anisotropy and effective fractal dimension. These observations should provide new practical methods for quantifying the nature of particle clustering in diverse contexts.

Equiaxed and columnar dendrite growth simulation in Al-7Si- Mg ternary alloys using cellular automaton method

NASA Astrophysics Data System (ADS)

Chen, Rui; Xu, Qingyan; Liu, Baicheng

2015-06-01

In this paper, a modified cellular automaton (MCA) model allowing for the prediction of dendrite growth of Al-Si-Mg ternary alloys in two and three dimensions is presented. The growth kinetic of S/L interface is calculated based on the solute equilibrium approach. In order to describe the dendrite growth with arbitrarily crystallographic orientations, this model introduces a modified decentered octahedron algorithm for neighborhood tracking to eliminate the effect of mesh dependency on dendrite growth. The thermody namic and kinetic data needed for dendrite growth is obtained through coupling with Pandat software package in combination with thermodynamic/kinetic/equilibrium phase diagram calculation databases. The effect of interactions between various alloying elements on solute diffusion coefficient is considered in the model. This model has first been used to simulate Al-7Si (weight percent) binary dendrite growth followed by a validation using theoretical predictions. For ternary alloy, Al-7Si-0.5Mg dendrite simulation has been carried out and the effects of solute interactions on diffusion matrix as well as the differences of Si and Mg in solute distribution have been analyzed. For actual application, this model has been applied to simulate the equiaxed dendrite growth with various crystallographic orientations of Al-7Si-0.36Mg ternary alloy, and the predicted secondary dendrite arm spacing (SDAS) shows a reasonable agreement with the experimental ones. Furthermore, the columnar dendrite growth in directional solidification has also been simulated and the predicted primary dendrite arm spacing (PDAS) is in good agreement with experiments. The simulated results effectively demonstrate the abilities of the model in prediction of dendritic microstructure of Al-Si-Mg ternary alloy.

Transport of water and ions in partially water-saturated porous media. Part 2. Filtration effects

NASA Astrophysics Data System (ADS)

Revil, A.

2017-05-01

A new set of constitutive equations describing the transport of the ions and water through charged porous media and considering the effect of ion filtration is applied to the problem of reverse osmosis and diffusion of a salt. Starting with the constitutive equations derived in Paper 1, I first determine specific formula for the osmotic coefficient and effective diffusion coefficient of a binary symmetric 1:1 salt (such as KCl or NaCl) as a function of a dimensionless number Θ corresponding to the ratio between the cation exchange capacity (CEC) and the salinity. The modeling is first carried with the Donnan model used to describe the concentrations of the charge carriers in the pore water phase. Then a new model is developed in the thin double layer approximation to determine these concentrations. These models provide explicit relationships between the concentration of the ionic species in the pore space and those in a neutral reservoir in local equilibrium with the pore space and the CEC. The case of reverse osmosis and diffusion coefficient are analyzed in details for the case of saturated and partially saturated porous materials. Comparisons are done with experimental data from the literature obtained on bentonite. The model predicts correctly the influence of salinity (including membrane behavior at high salinities), porosity, cation type (K+ versus Na+), and water saturation on the osmotic coefficient. It also correctly predicts the dependence of the diffusion coefficient of the salt with the salinity.

Removal of three nitrophenols from aqueous solutions by adsorption onto char ash: equilibrium and kinetic modeling

NASA Astrophysics Data System (ADS)

Magdy, Yehia M.; Altaher, Hossam; ElQada, E.

2018-03-01

In this research, the removal of 2,4 dinitrophenol, 2 nitrophenol and 4 nitrophenol from aqueous solution using char ash from animal bones was investigated using batch technique. Three 2-parameter isotherms (Freundlich, Langmuir, and Temkin) were applied to analyze the experimental data. Both linear and nonlinear regression analyses were performed for these models to estimate the isotherm parameters. Three 3-parameter isotherms (Redlich-Peterson, Sips, Toth) were also tested. Moreover, the kinetic data were tested using pseudo-first order, pseudo-second order, Elovich, Intraparticle diffusion and Boyd methods. Langmuir adsorption isotherm provided the best fit for the experimental data indicating monolayer adsorption. The maximum adsorption capacity was 8.624, 7.55, 7.384 mg/g for 2 nitrophenol, 2,4 dinitrophenol, and 4 nitrophenol, respectively. The experimental data fitted well to pseudo-second order model suggested a chemical nature of the adsorption process. The R 2 values for this model were 0.973 up to 0.999. This result with supported by the Temkin model indicating heat of adsorption to be greater than 10 kJ/mol. The rate controlling step was intraparticle diffusion for 2 nitrophenol, and a combination of intraparticle diffusion and film diffusion for the other two phenols. The pH and temperature of solution were found to have a considerable effect, and the temperature indicated the exothermic nature of the adsorption process. The highest adsorption capacity was obtained at pH 9 and 25 °C.

Distance-dependent diffusion-controlled reaction of •NO and O2•- at chemical equilibrium with ONOO-.

PubMed

Botti, Horacio; Möller, Matías N; Steinmann, Daniel; Nauser, Thomas; Koppenol, Willem H; Denicola, Ana; Radi, Rafael

2010-12-16

The fast reaction of (•)NO and O(2)(•-) to give ONOO(-) has been extensively studied at irreversible conditions, but the reasons for the wide variations in observed forward rate constants (3.8 ≤ k(f) ≤ 20 × 10(9) M(-1) s(-1)) remain unexplained. We characterized the diffusion-dependent aqueous (pH > 12) chemical equilibrium of the form (•)NO + O(2)(•-) = ONOO(-) with respect to its dependence on temperature, viscosity, and [ONOO(-)](eq) by determining [ONOO(-)](eq) and [(•)NO](eq). The equilibrium forward reaction rate constant (k(f)(eq)) has negative activation energy, in contrast to that found under irreversible conditions. In contradiction to the law of mass action, we demonstrate that the equilibrium constant depends on ONOO(-) concentration. Therefore, a wide range of k(f)(eq) values could be derived (7.5-21 × 10(9) M(-1) s(-1)). Of general interest, the variations in k(f) can thus be explained by its dependence on the distance between ONOO(-) particles (sites of generation of (•)NO and O(2)(•-)).

Influence of chain topology on polymer crystallization: poly(ethylene oxide) (PEO) rings vs. linear chains.

PubMed

Zardalidis, George; Mars, Julian; Allgaier, Jürgen; Mezger, Markus; Richter, Dieter; Floudas, George

2016-10-04

The absence of entanglements, the more compact structure and the faster diffusion in melts of cyclic poly(ethylene oxide) (PEO) chains have consequences on their crystallization behavior at the lamellar and spherulitic length scales. Rings with molecular weight below the entanglement molecular weight (M < M e ), attain the equilibrium configuration composed from twice-folded chains with a lamellar periodicity that is half of the corresponding linear chains. Rings with M > M e undergo distinct step-like conformational changes to a crystalline lamellar with the equilibrium configuration. Rings melt from this configuration in the absence of crystal thickening in sharp contrast to linear chains. In general, rings more easily attain their extended equilibrium configuration due to strained segments and the absence of entanglements. In addition, rings have a higher equilibrium melting temperature. At the level of the spherulitic superstructure, growth rates are much faster for rings reflecting the faster diffusion and more compact structure. With respect to the segmental dynamics in their semi-crystalline state, ring PEOs with a steepness index of ∼34 form some of the "strongest" glasses.

Individual and competitive adsorption of phenol and nickel onto multiwalled carbon nanotubes

PubMed Central

Abdel-Ghani, Nour T.; El-Chaghaby, Ghadir A.; Helal, Farag S.

2014-01-01

Individual and competitive adsorption studies were carried out to investigate the removal of phenol and nickel ions by adsorption onto multiwalled carbon nanotubes (MWCNTs). The carbon nanotubes were characterized by different techniques such as X-ray diffraction, scanning electron microscopy, thermal analysis and Fourier transformation infrared spectroscopy. The different experimental conditions affecting the adsorption process were investigated. Kinetics and equilibrium models were tested for fitting the adsorption experimental data. The characterization experimental results proved that the studied adsorbent possess different surface functional groups as well as typical morphological features. The batch experiments revealed that 300 min of contact time was enough to achieve equilibrium for the adsorption of both phenol and nickel at an initial adsorbate concentration of 25 mg/l, an adsorbent dosage of 5 g/l, and a solution pH of 7. The adsorption of phenol and nickel by MWCNTs followed the pseudo-second order kinetic model and the intraparticle diffusion model was quite good in describing the adsorption mechanism. The Langmuir equilibrium model fitted well the experimental data indicating the homogeneity of the adsorbent surface sites. The maximum Langmuir adsorption capacities were found to be 32.23 and 6.09 mg/g, for phenol and Ni ions, respectively. The removal efficiency of MWCNTs for nickel ions or phenol in real wastewater samples at the optimum conditions reached up to 60% and 70%, respectively. PMID:26257938

Competing nucleation pathways in a mixture of oppositely charged colloids: out-of-equilibrium nucleation revisited.

PubMed

Peters, Baron

2009-12-28

Recent simulations of crystal nucleation from a compressed liquid of oppositely charged colloids show that the natural Brownian dynamics results in nuclei of a charge-disordered FCC (DFCC) solid whereas artificially accelerated dynamics with charge swap moves result in charge-ordered nuclei of a CsCl phase. These results were interpreted as a breakdown of the quasiequilibrium assumption for precritical nuclei. We use structure-specific nucleus size coordinates for the CsCl and DFCC structures and equilibrium based sampling methods to understand the dynamical effects on structure selectivity in this system. Nonequilibrium effects observed in previous simulations emerge from a diffusion tensor that dramatically changes when charge swap moves are used. Without the charge swap moves diffusion is strongly anisotropic with very slow motion along the charge-ordered CsCl axis and faster motion along the DFCC axis. Kramers-Langer-Berezhkovskii-Szabo theory predicts that under the realistic dynamics, the diffusion anisotropy shifts the current toward the DFCC axis. The diffusion tensor also varies with location on the free energy landscape. A numerical calculation of the current field with a diffusion tensor that depends on the location in the free energy landscape exacerbates the extent to which the current is skewed toward DFCC structures. Our analysis confirms that quasiequilibrium theories based on equilibrium properties can explain the nonequilibrium behavior of this system. Our analysis also shows that using a structure-specific nucleus size coordinate for each possible nucleation product can provide mechanistic insight on selectivity and competition between nucleation pathways.

Competing nucleation pathways in a mixture of oppositely charged colloids: Out-of-equilibrium nucleation revisited

NASA Astrophysics Data System (ADS)

Peters, Baron

2009-12-01

Recent simulations of crystal nucleation from a compressed liquid of oppositely charged colloids show that the natural Brownian dynamics results in nuclei of a charge-disordered FCC (DFCC) solid whereas artificially accelerated dynamics with charge swap moves result in charge-ordered nuclei of a CsCl phase. These results were interpreted as a breakdown of the quasiequilibrium assumption for precritical nuclei. We use structure-specific nucleus size coordinates for the CsCl and DFCC structures and equilibrium based sampling methods to understand the dynamical effects on structure selectivity in this system. Nonequilibrium effects observed in previous simulations emerge from a diffusion tensor that dramatically changes when charge swap moves are used. Without the charge swap moves diffusion is strongly anisotropic with very slow motion along the charge-ordered CsCl axis and faster motion along the DFCC axis. Kramers-Langer-Berezhkovskii-Szabo theory predicts that under the realistic dynamics, the diffusion anisotropy shifts the current toward the DFCC axis. The diffusion tensor also varies with location on the free energy landscape. A numerical calculation of the current field with a diffusion tensor that depends on the location in the free energy landscape exacerbates the extent to which the current is skewed toward DFCC structures. Our analysis confirms that quasiequilibrium theories based on equilibrium properties can explain the nonequilibrium behavior of this system. Our analysis also shows that using a structure-specific nucleus size coordinate for each possible nucleation product can provide mechanistic insight on selectivity and competition between nucleation pathways.

Spike solutions in Gierer#x2013;Meinhardt model with a time dependent anomaly exponent

NASA Astrophysics Data System (ADS)

Nec, Yana

2018-01-01

Experimental evidence of complex dispersion regimes in natural systems, where the growth of the mean square displacement in time cannot be characterised by a single power, has been accruing for the past two decades. In such processes the exponent γ(t) in ⟨r2⟩ ∼ tγ(t) at times might be approximated by a piecewise constant function, or it can be a continuous function. Variable order differential equations are an emerging mathematical tool with a strong potential to model these systems. However, variable order differential equations are not tractable by the classic differential equations theory. This contribution illustrates how a classic method can be adapted to gain insight into a system of this type. Herein a variable order Gierer-Meinhardt model is posed, a generic reaction- diffusion system of a chemical origin. With a fixed order this system possesses a solution in the form of a constellation of arbitrarily situated localised pulses, when the components' diffusivity ratio is asymptotically small. The pattern was shown to exist subject to multiple step-like transitions between normal diffusion and sub-diffusion, as well as between distinct sub-diffusive regimes. The analytical approximation obtained permits qualitative analysis of the impact thereof. Numerical solution for typical cross-over scenarios revealed such features as earlier equilibration and non-monotonic excursions before attainment of equilibrium. The method is general and allows for an approximate numerical solution with any reasonably behaved γ(t).

Trouble with diffusion: Reassessing hillslope erosion laws with a particle-based model

NASA Astrophysics Data System (ADS)

Tucker, Gregory E.; Bradley, D. Nathan

2010-03-01

Many geomorphic systems involve a broad distribution of grain motion length scales, ranging from a few particle diameters to the length of an entire hillslope or stream. Studies of analogous physical systems have revealed that such broad motion distributions can have a significant impact on macroscale dynamics and can violate the assumptions behind standard, local gradient flux laws. Here, a simple particle-based model of sediment transport on a hillslope is used to study the relationship between grain motion statistics and macroscopic landform evolution. Surface grains are dislodged by random disturbance events with probabilities and distances that depend on local microtopography. Despite its simplicity, the particle model reproduces a surprisingly broad range of slope forms, including asymmetric degrading scarps and cinder cone profiles. At low slope angles the dynamics are diffusion like, with a short-range, thin-tailed hop length distribution, a parabolic, convex upward equilibrium slope form, and a linear relationship between transport rate and gradient. As slope angle steepens, the characteristic grain motion length scale begins to approach the length of the slope, leading to planar equilibrium forms that show a strongly nonlinear correlation between transport rate and gradient. These high-probability, long-distance motions violate the locality assumption embedded in many common gradient-based geomorphic transport laws. The example of a degrading scarp illustrates the potential for grain motion dynamics to vary in space and time as topography evolves. This characteristic renders models based on independent, stationary statistics inapplicable. An accompanying analytical framework based on treating grain motion as a survival process is briefly outlined.

Trapped ion system for sympathetic cooling and non-equilibrium dynamics

NASA Astrophysics Data System (ADS)

Doret, Charlie; Jubin, Sierra; Stevenson, Sarah

2017-04-01

Atomic systems are superbly suited to the study of non-equilibrium dynamics. These systems' exquisite isolation from environmental perturbations leads to long relaxation times that enable exploration of far-from-equilibrium phenomena. We present progress towards trapping chains of multiple co-trapped calcium isotopes geared towards measuring thermal equilibration and sympathetic cooling rates. We also discuss plans for future experiments in non-equilibrium statistical mechanics, including exploration of the quantum-to-classical crossover between ballistic transport and diffusive, Fourier's Law conduction. This work is supported by Cottrell College Science Award from the Research Corporation for Science Advancement and by Williams College.

Oxygen potentials, oxygen diffusion coefficients and defect equilibria of nonstoichiometric (U,Pu)O2±x

NASA Astrophysics Data System (ADS)

Kato, Masato; Watanabe, Masashi; Matsumoto, Taku; Hirooka, Shun; Akashi, Masatoshi

2017-04-01

Oxygen potential of (U,Pu)O2±x was evaluated based on defect chemistry using an updated experimental data set. The relationship between oxygen partial pressure and deviation x in (U,Pu)O2±x was analyzed, and equilibrium constants of defect formation were determined as functions of Pu content and temperature. Brouwer's diagrams were constructed using the determined equilibrium constants, and a relational equation to determine O/M ratio was derived as functions of O/M ratio, Pu content and temperature. In addition, relationship between oxygen potential and oxygen diffusion coefficients were described.

Electrostatically confined nanoparticle interactions and dynamics.

PubMed

Eichmann, Shannon L; Anekal, Samartha G; Bevan, Michael A

2008-02-05

We report integrated evanescent wave and video microscopy measurements of three-dimensional trajectories of 50, 100, and 250 nm gold nanoparticles electrostatically confined between parallel planar glass surfaces separated by 350 and 600 nm silica colloid spacers. Equilibrium analyses of single and ensemble particle height distributions normal to the confining walls produce net electrostatic potentials in excellent agreement with theoretical predictions. Dynamic analyses indicate lateral particle diffusion coefficients approximately 30-50% smaller than expected from predictions including the effects of the equilibrium particle distribution within the gap and multibody hydrodynamic interactions with the confining walls. Consistent analyses of equilibrium and dynamic information in each measurement do not indicate any roles for particle heating or hydrodynamic slip at the particle or wall surfaces, which would both increase diffusivities. Instead, lower than expected diffusivities are speculated to arise from electroviscous effects enhanced by the relative extent (kappaa approximately 1-3) and overlap (kappah approximately 2-4) of electrostatic double layers on the particle and wall surfaces. These results demonstrate direct, quantitative measurements and a consistent interpretation of metal nanoparticle electrostatic interactions and dynamics in a confined geometry, which provides a basis for future similar measurements involving other colloidal forces and specific biomolecular interactions.

Rapid exploration of configuration space with diffusion-map-directed molecular dynamics.

PubMed

Zheng, Wenwei; Rohrdanz, Mary A; Clementi, Cecilia

2013-10-24

The gap between the time scale of interesting behavior in macromolecular systems and that which our computational resources can afford often limits molecular dynamics (MD) from understanding experimental results and predicting what is inaccessible in experiments. In this paper, we introduce a new sampling scheme, named diffusion-map-directed MD (DM-d-MD), to rapidly explore molecular configuration space. The method uses a diffusion map to guide MD on the fly. DM-d-MD can be combined with other methods to reconstruct the equilibrium free energy, and here, we used umbrella sampling as an example. We present results from two systems: alanine dipeptide and alanine-12. In both systems, we gain tremendous speedup with respect to standard MD both in exploring the configuration space and reconstructing the equilibrium distribution. In particular, we obtain 3 orders of magnitude of speedup over standard MD in the exploration of the configurational space of alanine-12 at 300 K with DM-d-MD. The method is reaction coordinate free and minimally dependent on a priori knowledge of the system. We expect wide applications of DM-d-MD to other macromolecular systems in which equilibrium sampling is not affordable by standard MD.

Fibonacci family of dynamical universality classes

PubMed Central

Popkov, Vladislav; Schadschneider, Andreas; Schmidt, Johannes; Schütz, Gunter M.

2015-01-01

Universality is a well-established central concept of equilibrium physics. However, in systems far away from equilibrium, a deeper understanding of its underlying principles is still lacking. Up to now, a few classes have been identified. Besides the diffusive universality class with dynamical exponent z=2, another prominent example is the superdiffusive Kardar−Parisi−Zhang (KPZ) class with z=3/2. It appears, e.g., in low-dimensional dynamical phenomena far from thermal equilibrium that exhibit some conservation law. Here we show that both classes are only part of an infinite discrete family of nonequilibrium universality classes. Remarkably, their dynamical exponents zα are given by ratios of neighboring Fibonacci numbers, starting with either z1=3/2 (if a KPZ mode exist) or z1=2 (if a diffusive mode is present). If neither a diffusive nor a KPZ mode is present, all dynamical modes have the Golden Mean z=(1+5)/2 as dynamical exponent. The universal scaling functions of these Fibonacci modes are asymmetric Lévy distributions that are completely fixed by the macroscopic current density relation and compressibility matrix of the system and hence accessible to experimental measurement. PMID:26424449

Rapid Exploration of Configuration Space with Diffusion Map-directed-Molecular Dynamics

PubMed Central

Zheng, Wenwei; Rohrdanz, Mary A.; Clementi, Cecilia

2013-01-01

The gap between the timescale of interesting behavior in macromolecular systems and that which our computational resources can afford oftentimes limits Molecular Dynamics (MD) from understanding experimental results and predicting what is inaccessible in experiments. In this paper, we introduce a new sampling scheme, named Diffusion Map-directed-MD (DM-d-MD), to rapidly explore molecular configuration space. The method uses diffusion map to guide MD on the fly. DM-d-MD can be combined with other methods to reconstruct the equilibrium free energy, and here we used umbrella sampling as an example. We present results from two systems: alanine dipeptide and alanine-12. In both systems we gain tremendous speedup with respect to standard MD both in exploring the configuration space and reconstructing the equilibrium distribution. In particular, we obtain 3 orders of magnitude of speedup over standard MD in the exploration of the configurational space of alanine-12 at 300K with DM-d-MD. The method is reaction coordinate free and minimally dependent on a priori knowledge of the system. We expect wide applications of DM-d-MD to other macromolecular systems in which equilibrium sampling is not affordable by standard MD. PMID:23865517

Isolated effects of external bath osmolality, solute concentration, and electrical charge on solute transport across articular cartilage.

PubMed

Pouran, Behdad; Arbabi, Vahid; Zadpoor, Amir A; Weinans, Harrie

2016-12-01

The metabolic function of cartilage primarily depends on transport of solutes through diffusion mechanism. In the current study, we use contrast enhanced micro-computed tomography to determine equilibrium concentration of solutes through different cartilage zones and solute flux in the cartilage, using osteochondral plugs from equine femoral condyles. Diffusion experiments were performed with two solutes of different charge and approximately equal molecular weight, namely iodixanol (neutral) and ioxaglate (charge=-1) in order to isolate the effects of solute's charge on diffusion. Furthermore, solute concentrations as well as bath osmolality were changed to isolate the effects of steric hindrance on diffusion. Bath concentration and bath osmolality only had minor effects on the diffusion of the neutral solute through cartilage at the surface, middle and deep zones, indicating that the diffusion of the neutral solute was mainly Fickian. The negatively charged solute diffused considerably slower through cartilage than the neutral solute, indicating a large non-Fickian contribution in the diffusion of charged molecules. The numerical models determined maximum solute flux in the superficial zone up to a factor of 2.5 lower for the negatively charged solutes (charge=-1) as compared to the neutral solutes confirming the importance of charge-matrix interaction in diffusion of molecules across cartilage. Copyright © 2016 IPEM. Published by Elsevier Ltd. All rights reserved.

A parallel reaction-transport model applied to cement hydration and microstructure development

NASA Astrophysics Data System (ADS)

Bullard, Jeffrey W.; Enjolras, Edith; George, William L.; Satterfield, Steven G.; Terrill, Judith E.

2010-03-01

A recently described stochastic reaction-transport model on three-dimensional lattices is parallelized and is used to simulate the time-dependent structural and chemical evolution in multicomponent reactive systems. The model, called HydratiCA, uses probabilistic rules to simulate the kinetics of diffusion, homogeneous reactions and heterogeneous phenomena such as solid nucleation, growth and dissolution in complex three-dimensional systems. The algorithms require information only from each lattice site and its immediate neighbors, and this localization enables the parallelized model to exhibit near-linear scaling up to several hundred processors. Although applicable to a wide range of material systems, including sedimentary rock beds, reacting colloids and biochemical systems, validation is performed here on two minerals that are commonly found in Portland cement paste, calcium hydroxide and ettringite, by comparing their simulated dissolution or precipitation rates far from equilibrium to standard rate equations, and also by comparing simulated equilibrium states to thermodynamic calculations, as a function of temperature and pH. Finally, we demonstrate how HydratiCA can be used to investigate microstructure characteristics, such as spatial correlations between different condensed phases, in more complex microstructures.

Properties of interfaces and transport across them.

PubMed

Cabezas, H

2000-01-01

Much of the biological activity in cell cytoplasm occurs in compartments some of which may be formed, as suggested in this book, by phase separation, and many of the functions of such compartments depend on the transport or exchange of molecules across interfaces. Thus a fundamentally based discussion of the properties of phases, interfaces, and diffusive transport across interfaces has been given to further elucidate these phenomena. An operational criterion for the width of interfaces is given in terms of molecular and physical arguments, and the properties of molecules inside phases and interfaces are discussed in terms of molecular arguments. In general, the properties of the interface become important when the molecules diffusing across are smaller than the width of the interface. Equilibrium partitioning, Donnan phenomena, and electrochemical potentials at interfaces are also discussed in detail. The mathematical expressions for modeling transport across interfaces are discussed in detail. These describe a practical and detailed model for transport across interfaces. For molecules smaller than the width of the interface, this includes a detailed model for diffusion inside the interface. Last, the question of the time scale for phase formation and equilibration in biological systems is discussed.

"Squishy capacitor" model for electrical double layers and the stability of charged interfaces.

PubMed

Partenskii, Michael B; Jordan, Peter C

2009-07-01

Negative capacitance (NC), predicted by various electrical double layer (EDL) theories, is critically reviewed. Physically possible for individual components of the EDL, the compact or diffuse layer, it is strictly prohibited for the whole EDL or for an electrochemical cell with two electrodes. However, NC is allowed for the artificial conditions of sigma control, where an EDL is described by the equilibrium electric response of electrolyte to a field of fixed, and typically uniform, surface charge-density distributions, sigma. The contradiction is only apparent; in fact local sigma cannot be set independently, but is established by the equilibrium response to physically controllable variables, i.e., applied voltage phi (phi control) or total surface charge q (q control). NC predictions in studies based on sigma control signify potential instabilities and phase transitions for physically realizable conditions. Building on our previous study of phi control [M. B. Partenskii and P. C. Jordan, Phys. Rev. E 77, 061117 (2008)], here we analyze critical behavior under q control, clarifying the basic picture using an exactly solvable "squishy capacitor" toy model. We find that phi can change discontinuously in the presence of a lateral transition, specify stability conditions for an electrochemical cell, analyze the origin of the EDL's critical point in terms of compact and diffuse serial contributions, and discuss perspectives and challenges for theoretical studies not limited by sigma control.

Equilibrium and diffusion studies of metal-hydrogen systems

NASA Astrophysics Data System (ADS)

Maroevic, Petar

Several new methods and models have been developed pertaining to equilibrium properties of hydrogen in random binary substitutional alloys at room and lower temperatures, describing both statistics and kinetics of hydrogen in them. They represent a solution to the problem of the complete Fermi-Dirac description which is physically appropriate for these systems. Hydrogen diffusion which proceeds via lattice assisted quantum tunneling at room and lower temperatures requires a new and different description from the one based on the thermal hopping picture, which pertains only to relatively high temperatures. It is also shown that the analogs of the solution to the Fermi-Dirac problem of hydrogen can be successfully applied to the description of vacancies in a hydrogenated system, a phenomena known to occur due to high hydrogen-vacancy binding energies and the creation of hydrogen-vacancy clusters. The solution based on this model applies to much lower temperatures and higher concentrations than the tradition alone. This methodology has also been applied to the surface problem where very large vacancy and hydrogen concentrations occur. This is of special importance since mechanical properties are known to be greatly affected by the surface. As another consequence of hydrogen induced vacancies, hydrogen induced lattice migration (HILM) occurs. This has been demonstrated in our electrical resistivity study of palladium wires where recrystallization and annealing effects were observed upon hydrogen-heat-treatment (HHT).

Convective thinning of the lithosphere - A mechanism for the initiation of continental rifting

NASA Technical Reports Server (NTRS)

Spohn, T.; Schubert, G.

1982-01-01

A model of lithospheric thinning, in which heat is convected to the base and conducted within the lithosphere, is presented. An analytical equation for determinining the amount of thinning attainable on increasing the heat flux from the asthenosphere is derived, and a formula for lithosphere thickness approximations as a function of time is given. Initial and final equilibrium thicknesses, thermal diffusivity, transition temperature profile, and plume temperature profile are all factors considered for performing rate of thinning determinations. In addition, between initial and final equilibrium states, lithospheric thinning occurs at a rate which is inversely proportional to the square root of the time. Finally, uplift resulting from thermal expansion upon lithospheric thinning is on the order of 10 to the 2nd to 10 to the 3rd m.

Novel voltage signal at proximity-induced superconducting transition temperature in gold nanowires

NASA Astrophysics Data System (ADS)

Wang, Jian; Tang, JunXiong; Wang, ZiQiao; Sun, Yi; Sun, QingFeng; Chan, Moses H. W.

2018-08-01

We observed a novel voltage peak in the proximity-induced superconducting gold (Au) nanowire while cooling the sample through the superconducting transition temperature. The voltage peak turned dip during warming. The voltage peak or dip was found to originate respectively from the emergence or vanishing of the proximity-induced superconductivity in the Au nanowire. The amplitude of the voltage signal depends on the temperature scanning rate, and it cannot be detected when the temperature is changed slower than 0.03 K/min. This transient feature suggests the non-equilibrium property of the effect. Ginzburg-Landau model clarified the voltage peak by considering the emergence of Cooper pairs of relatively lower free energy in superconducting W contact and the non-equilibrium diffusion of Cooper pairs and quasiparticles.

Evaluating the multimedia fate of organic chemicals: A level III fugacity model

DOE Office of Scientific and Technical Information (OSTI.GOV)

Mackay, D.; Paterson, S.

A multimedia model is developed and applied to selected organic chemicals in evaluative and real regional environments. The model employs the fugacity concept and treats four bulk compartments: air, water, soil, and bottom sediment, which consist of subcompartments of varying proportions of air, water, and mineral and organic matter. Chemical equilibrium is assumed to apply within (but not between) each bulk compartment. Expressions are included for emissions, advective flows, degrading reactions, and interphase transport by diffusive and non-diffusive processes. Input to the model consists of a description of the environment, the physical-chemical and reaction properties of the chemical, and emissionmore » rates. For steady-state conditions the solution is a simple algebraic expression. The model is applied to six chemicals in the region of southern Ontario and the calculated fate and concentrations are compared with observations. The results suggest that the model may be used to determine the processes that control the environmental fate of chemicals in a region and provide approximate estimates of relative media concentrations.« less

Structural and water diffusion of poly(acryl amide)/poly(vinyl alcohol) blend films: Experiment and molecular dynamics simulations.

PubMed

Wang, Yanen; Wei, Qinghua; Wang, Shuzhi; Chai, Weihong; Zhang, Yingfeng

2017-01-01

To study the effects of composition ratios and temperature on the diffusion of water molecules in PVA/PAM blend films, five simulation models of PVA/PAM with ten water molecules at different composition ratios (4/0, 3/1, 2/2, 1/3, 0/4) were constructed and simulated by using a molecular dynamics (MD) simulation. The diffusion behavior of water molecules in blends were investigated from the aspects of the diffusion coefficient, free volume, pair correlation function (PCF) and trajectories of water molecules, respectively. And the hydrophilicity of blend composite was studied based on the contact angle and equilibrium water content (EWC) of the blend films. The simulation results show that the diffusion coefficient of water molecules and fractional free volume (FFV) of blend membranes increase with the addition of PAM, and a higher temperature can also improve the diffusion of water molecules. Additionally, the analysis of PCFs reveals the main reason why the diffusion coefficient of water in blend system increases with the addition of PAM. The measurement results of contact angle and EWC of blend films indicate that the hydrophilicity of blend films decreases with the addition of PAM, but the EWC of blends increases with the addition of PAM. Copyright © 2016 Elsevier Inc. All rights reserved.

A Physical Mechanism for the Asymmetry in Top-Down and Bottom-Up Diffusion.

NASA Astrophysics Data System (ADS)

Wyngaard, J. C.

1987-04-01

Recent large-eddy simulations of the vertical diffusion of a passive, conservative scalar through the convective boundary layer (CBL) show strikingly different eddy diffusivity profiles in the `top-down' and `bottom-up' cases. These results indicate that for a given turbulent velocity field and associated scalar flux, the mean change in scalar mixing ratio across the CBL is several times larger if the flux originates at the top of the boundary layer (i.e., in top-down diffusion) rather than at the bottom. The large-eddy simulation (LES) data show that this asymmetry is due to a breakdown of the eddy-diffusion concept.A simple updraft-downdraft model of the CBL reveals a physical mechanism that could cause this unexpected behavior. The large, positive skewness of the convectively driven vertical velocity gives an appreciably higher probability of downdrafts than updrafts; this excess probability of downdrafts, interacting with the time changes of the mean mixing ratio caused by the nonstationarity of the bottom-up and top-down diffusion processes, decreases the equilibrium value of mean mixing-ratio jump across the mixed layer in the bottom-up case and increases it in the top-down case. The resulting diffusion asymmetry agrees qualitatively with that found through LES.

Assessing the potential of quartz crystal microbalance to estimate water vapor transfer in micrometric size cellulose particles.

PubMed

Thoury-Monbrun, Valentin; Gaucel, Sébastien; Rouessac, Vincent; Guillard, Valérie; Angellier-Coussy, Hélène

2018-06-15

This study aims at assessing the use of a quartz crystal microbalance (QCM) coupled with an adsorption system to measure water vapor transfer properties in micrometric size cellulose particles. This apparatus allows measuring successfully water vapor sorption kinetics at successive relative humidity (RH) steps on a dispersion of individual micrometric size cellulose particles (1 μg) with a total acquisition duration of the order of one hour. Apparent diffusivity and water uptake at equilibrium were estimated at each step of RH by considering two different particle geometries in mass transfer modeling, i.e. sphere or finite cylinder, based on the results obtained from image analysis. Water vapor diffusivity values varied from 2.4 × 10 -14  m 2  s -1 to 4.2 × 10 -12  m 2  s -1 over the tested RH range (0-80%) whatever the model used. A finite cylinder or spherical geometry could be used equally for diffusivity identification for a particle size aspect ratio lower than 2. Copyright © 2018 Elsevier Ltd. All rights reserved.

Diffusion dynamics of the Li+ ion on a model surface of amorphous carbon: a direct molecular orbital dynamics study.

PubMed

Tachikawa, Hiroto; Shimizu, Akira

2005-07-14

Diffusion processes of the Li+ ion on a model surface of amorphous carbon (Li+C96H24 system) have been investigated by means of the direct molecular orbital (MO) dynamics method at the semiempirical AM1 level. The total energy and energy gradient on the full-dimensional AM1 potential energy surface were calculated at each time step in the dynamics calculation. The optimized structure, where Li+ is located in the center of the cluster, was used as the initial structure at time zero. The dynamics calculation was carried out in the temperature range 100-1000 K. The calculations showed that the Li+ ion vibrates around the equilibrium point below 200 K, while the Li+ ion moves on the surface above 250 K. At intermediate temperatures (300 K < T < 400 K), the ion moves on the surface and falls in the edge regions of the cluster. At higher temperatures (600 K < T), the Li+ ion transfers freely on the surface and edge regions. The diffusion pathway of the Li+ ion was discussed on the basis of theoretical results.

Active compound diffusivity of particle size reduced S. aromaticum and C. cassia fused starch edible films and the shelf life of mutton (Capra aegagrus hircus) meat.

PubMed

Chandra Mohan, C; Radha Krishnan, K; Babuskin, S; Sudharsan, K; Aafrin, Vajiha; Lalitha Priya, U; Mariyajenita, P; Harini, K; Madhushalini, D; Sukumar, M

2017-06-01

In the present study, mathematical models were used to examine the effect of active compound diffusion from edible film (supplemented with S. aromaticum and C. cassia) on the microbial, physical and chemical quality of mutton stored at 4 and 10°C. Cinnamaldehyde and eugenol release from edible film into liquid was found to be 80% and 75% of the equilibrium concentration. Active compound release into meat was 42-51% for cinnamaldehyde and 38-48% for eugenol, in storage temperatures of 4-15°C. Developed mathematical models showed the diffusivity of cinnamaldehyde (0.45×10 -15 ±0.04×10 -15 ) and eugenol (0.63×10 -10 ±0.01×10 -10 ) into meat, which was about 40% of that in liquid medium. On comparing physical, chemical and microbial results, shelf life of mutton meat was found to be increased by 1week at storage temperature of 10°C and 3weeks at storage temperature of 4°C. Copyright © 2017 Elsevier Ltd. All rights reserved.

Kinetics and equilibrium of solute diffusion into human hair.

PubMed

Wang, Liming; Chen, Longjian; Han, Lujia; Lian, Guoping

2012-12-01

The uptake kinetics of five molecules by hair has been measured and the effects of pH and physical chemical properties of molecules were investigated. A theoretical model is proposed to analyze the experimental data. The results indicate that the binding affinity of solute to hair, as characterized by hair-water partition coefficient, scales to the hydrophobicity of the solute and decreases dramatically as the pH increases to the dissociation constant. The effective diffusion coefficient of solute depended not only on the molecular size as most previous studies suggested, but also on the binding affinity as well as solute dissociation. It appears that the uptake of molecules by hair is due to both hydrophobic interaction and ionic charge interaction. Based on theoretical considerations of the cellular structure, composition and physical chemical properties of hair, quantitative-structure-property-relationships (QSPR) have been proposed to predict the hair-water partition coefficient (PC) and the effective diffusion coefficient (D (e)) of solute. The proposed QSPR models fit well with the experimental data. This paper could be taken as a reference for investigating the adsorption properties for polymeric materials, fibres, and biomaterials.

Adsorption equilibrium and kinetics of monomer-dimer monoclonal antibody mixtures on a cation exchange resin.

PubMed

Reck, Jason M; Pabst, Timothy M; Hunter, Alan K; Wang, Xiangyang; Carta, Giorgio

2015-07-10

Adsorption equilibrium and kinetics are determined for a monoclonal antibody (mAb) monomer and dimer species, individually and in mixtures, on a macroporous cation exchange resin both under the dilute limit of salt gradient elution chromatography and at high protein loads and low salt based on batch adsorption equilibrium and confocal laser scanning microscopy (CLSM) experiments. In the dilute limit and weak binding conditions, the dimer/monomer selectivity in 10mM phosphate at pH 7 varies between 8.7 and 2.3 decreasing with salt concentration in the range of 170-230mM NaCl. At high protein loads and strong binding conditions (0-60mM NaCl), the selectivity in the same buffer is near unity with no NaCl added, but increases gradually with salt concentration reaching high values between 2 and 15 with 60mM added NaCl. For these conditions, the two-component adsorption kinetics is controlled by pore diffusion and is predicted approximately by a dual shrinking core model using parameters based on single component equilibrium and kinetics measurements. Copyright © 2015 Elsevier B.V. All rights reserved.

Kinetic characteristics of Cu (II) adsorption on nano(poly)-cumulene

NASA Astrophysics Data System (ADS)

Babkin, Alexander; Neskoromnaya, Elena; Burakova, Irina; Kucherova, Ananstasia; Burakov, Alexander; Mkrtchyan, Elina

2017-11-01

The present paper considers the possibility of using a new type of nanocarbon materials for sorption - polycumulene modified with "Taunit-M" carbon nanotubes or graphene nanoplatelets. To evaluate the efficiency of these novel nanomodified materials as sorbents, the following studies were carried out: 1) determination of the optimum pH value to perform static batch sorption experiments, 2) identification of the onset of equilibrium for the adsorption of heavy metal ions (on the example of Cu(II) ions), and 3) elucidation of kinetic adsorption mechanisms. As a result of implementation of kinetic models such as external and internal diffusion, as well as pseudo-first- and pseudo-second-order and Elovich (to determine the contribution of chemisorption), rate constants for the Cu(II) adsorption were estimated. It was noted that the absorption process occurs in a mixed-diffusion mode with the influence of the limiting factor - "sorbate-sorbate" chemical interaction. The equilibrium time was found to be 45 min at the sorption capacity values of about 30.71 mg g-1 (in the case of the material containing carbon nanotubes) and about 24.7 mg g-1 (in the case of the material containing graphene nanoplatelets).

The influence of vibrational state-resolved transport coefficients on the wave propagation in diatomic gases

NASA Astrophysics Data System (ADS)

Kremer, Gilberto M.; Kunova, Olga V.; Kustova, Elena V.; Oblapenko, George P.

2018-01-01

A detailed kinetic-theory model for the vibrationally state-resolved transport coefficients is developed taking into account the dependence of the collision cross section on the size of vibrationally excited molecule. Algorithms for the calculation of shear and bulk viscosity, thermal conductivity, thermal diffusion and diffusion coefficients for vibrational states are proposed. The transport coefficients are evaluated for single-component diatomic gases N2, O2, NO, H2, Cl2 in the wide range of temperature, and the effects of molecular diameters and the number of accounted states are discussed. The developed model is applied to study wave propagation in diatomic gases. For the case of initial Boltzmann distribution, the influence of vibrational excitation on the phase velocity and attenuation coefficient is found to be weak. We expect more significant effect in the case of initial thermal non-equilibrium, for instance in gases with optically pumped selected vibrational states.

Water sorption equilibria and kinetics of henna leaves

NASA Astrophysics Data System (ADS)

Sghaier, Khamsa; Peczalski, Roman; Bagane, Mohamed

2018-05-01

In this work, firstly the sorption isotherms of henna leaves were determined using a dynamic vapor sorption ( DVS) device at 3 temperatures (30, 40, 50 °C). The equilibrium data were well fitted by the GAB model. Secondly, drying kinetics were measured using a pilot convective dryer for 3 air temperatures (same as above), 3 velocities (0.5, 1, 1.42 m/s) and 4 relative humidities (20, 30, 35, 40%). The drying kinetic coefficients were identified by fitting the DVS and pilot dryer data by Lewis semi-empirical model. In order to compare the obtained kinetic parameters with literature, the water diffusivities were also identified by fitting the data by the simplified solution of fickian diffusion equation. The identified kinetic coefficient was mainly dependent on air temperature and velocity what proved that it represented rather the external transfer and not the internal one.

Adsorptive Water Removal from Dichloromethane and Vapor-Phase Regeneration of a Molecular Sieve 3A Packed Bed

PubMed Central

2017-01-01

The drying of dichloromethane with a molecular sieve 3A packed bed process is modeled and experimentally verified. In the process, the dichloromethane is dried in the liquid phase and the adsorbent is regenerated by water desorption with dried dichloromethane product in the vapor phase. Adsorption equilibrium experiments show that dichloromethane does not compete with water adsorption, because of size exclusion; the pure water vapor isotherm from literature provides an accurate representation of the experiments. The breakthrough curves are adequately described by a mathematical model that includes external mass transfer, pore diffusion, and surface diffusion. During the desorption step, the main heat transfer mechanism is the condensation of the superheated dichloromethane vapor. The regeneration time is shortened significantly by external bed heating. Cyclic steady-state experiments demonstrate the feasibility of this novel, zero-emission drying process. PMID:28539701

The Secondary Organic Aerosol Processor (SOAP v1.0) model: a unified model with different ranges of complexity based on the molecular surrogate approach

NASA Astrophysics Data System (ADS)

Couvidat, F.; Sartelet, K.

2015-04-01

In this paper the Secondary Organic Aerosol Processor (SOAP v1.0) model is presented. This model determines the partitioning of organic compounds between the gas and particle phases. It is designed to be modular with different user options depending on the computation time and the complexity required by the user. This model is based on the molecular surrogate approach, in which each surrogate compound is associated with a molecular structure to estimate some properties and parameters (hygroscopicity, absorption into the aqueous phase of particles, activity coefficients and phase separation). Each surrogate can be hydrophilic (condenses only into the aqueous phase of particles), hydrophobic (condenses only into the organic phases of particles) or both (condenses into both the aqueous and the organic phases of particles). Activity coefficients are computed with the UNIFAC (UNIversal Functional group Activity Coefficient; Fredenslund et al., 1975) thermodynamic model for short-range interactions and with the Aerosol Inorganic-Organic Mixtures Functional groups Activity Coefficients (AIOMFAC) parameterization for medium- and long-range interactions between electrolytes and organic compounds. Phase separation is determined by Gibbs energy minimization. The user can choose between an equilibrium representation and a dynamic representation of organic aerosols (OAs). In the equilibrium representation, compounds in the particle phase are assumed to be at equilibrium with the gas phase. However, recent studies show that the organic aerosol is not at equilibrium with the gas phase because the organic phases could be semi-solid (very viscous liquid phase). The condensation-evaporation of organic compounds could then be limited by the diffusion in the organic phases due to the high viscosity. An implicit dynamic representation of secondary organic aerosols (SOAs) is available in SOAP with OAs divided into layers, the first layer being at the center of the particle (slowly reaches equilibrium) and the final layer being near the interface with the gas phase (quickly reaches equilibrium). Although this dynamic implicit representation is a simplified approach to model condensation-evaporation with a low number of layers and short CPU (central processing unit) time, it shows good agreements with an explicit representation of condensation-evaporation (no significant differences after a few hours of condensation).

M4FT-16LL080302052-Update to Thermodynamic Database Development and Sorption Database Integration

DOE Office of Scientific and Technical Information (OSTI.GOV)

Zavarin, Mavrik; Wolery, T. J.; Atkins-Duffin, C.

2016-08-16

This progress report (Level 4 Milestone Number M4FT-16LL080302052) summarizes research conducted at Lawrence Livermore National Laboratory (LLNL) within the Argillite Disposal R&D Work Package Number FT-16LL08030205. The focus of this research is the thermodynamic modeling of Engineered Barrier System (EBS) materials and properties and development of thermodynamic databases and models to evaluate the stability of EBS materials and their interactions with fluids at various physico-chemical conditions relevant to subsurface repository environments. The development and implementation of equilibrium thermodynamic models are intended to describe chemical and physical processes such as solubility, sorption, and diffusion.

Experimental determination and modelling of the swelling speed of a hydrogel polymer

NASA Astrophysics Data System (ADS)

Lenk, Sándor; Majoros, Tamás; Beleznai, Szabolcs; Ujhelyi, Ferenc; Péczeli, Imre; Karda, Zsolt; Barócsi, Attila

2018-03-01

When a hydrophilic intraocular lens material is immersed, its volume and mass start increase due to the diffusion of water (or isotonic saline solution) reaching a quasi-equilibrium in a time scale of several hours. Here, we present a combination of atomic force and confocal microscopy to measure the axial swelling speed of such polymers in distilled water. The measurements are used for the experimental verification of a simplistic finite element model developed for engineering applications in COMSOL environment. The model is calibrated with the temporal change of the sample mass. The swelling velocity is found to be inversely proportional to the square root of time.

Diffusion Dominant Solute Transport Modelling In Deep Repository Under The Effect of Emplacement Media Degradation - 13285

DOE Office of Scientific and Technical Information (OSTI.GOV)

Kwong, S.; Jivkov, A.P.

2013-07-01

Deep geologic disposal of high activity and long-lived radioactive waste is being actively considered and pursued in many countries, where low permeability geological formations are used to provide long term waste contaminant with minimum impact to the environment and risk to the biosphere. A multi-barrier approach that makes use of both engineered and natural barriers (i.e. geological formations) is often used to further enhance the containment performance of the repository. As the deep repository system subjects to a variety of thermo-hydro-chemo-mechanical (THCM) effects over its long 'operational' lifespan (e.g. 0.1 to 1.0 million years, the integrity of the barrier systemmore » will decrease over time (e.g. fracturing in rock or clay)). This is broadly referred as media degradation in the present study. This modelling study examines the effects of media degradation on diffusion dominant solute transport in fractured media that are typical of deep geological environment. In particular, reactive solute transport through fractured media is studied using a 2-D model, that considers advection and diffusion, to explore the coupled effects of kinetic and equilibrium chemical processes, while the effects of degradation is studied using a pore network model that considers the media diffusivity and network changes. Model results are presented to demonstrate the use of a 3D pore-network model, using a novel architecture, to calculate macroscopic properties of the medium such as diffusivity, subject to pore space changes as the media degrade. Results from a reactive transport model of a representative geological waste disposal package are also presented to demonstrate the effect of media property change on the solute migration behaviour, illustrating the complex interplay between kinetic biogeochemical processes and diffusion dominant transport. The initial modelling results demonstrate the feasibility of a coupled modelling approach (using pore-network model and reactive transport model) to examine the long term behaviour of deep geological repositories with media property change under complex geochemical conditions. (authors)« less

Application of zeolite-activated carbon macrocomposite for the adsorption of Acid Orange 7: isotherm, kinetic and thermodynamic studies.

PubMed

Lim, Chi Kim; Bay, Hui Han; Neoh, Chin Hong; Aris, Azmi; Abdul Majid, Zaiton; Ibrahim, Zaharah

2013-10-01

In this study, the adsorption behavior of azo dye Acid Orange 7 (AO7) from aqueous solution onto macrocomposite (MC) was investigated under various experimental conditions. The adsorbent, MC, which consists of a mixture of zeolite and activated carbon, was found to be effective in removing AO7. The MC were characterized by scanning electron microscopy (SEM), energy dispersive X-ray, point of zero charge, and Brunauer-Emmett-Teller surface area analysis. A series of experiments were performed via batch adsorption technique to examine the effect of the process variables, namely, contact time, initial dye concentration, and solution pH. The dye equilibrium adsorption was investigated, and the equilibrium data were fitted to Langmuir, Freundlich, and Tempkin isotherm models. The Langmuir isotherm model fits the equilibrium data better than the Freundlich isotherm model. For the kinetic study, pseudo-first-order, pseudo-second-order, and intraparticle diffusion model were used to fit the experimental data. The adsorption kinetic was found to be well described by the pseudo-second-order model. Thermodynamic analysis indicated that the adsorption process is a spontaneous and endothermic process. The SEM, Fourier transform infrared spectroscopy, ultraviolet-visible spectral and high performance liquid chromatography analysis were carried out before and after the adsorption process. For the phytotoxicity test, treated AO7 was found to be less toxic. Thus, the study indicated that MC has good potential use as an adsorbent for the removal of azo dye from aqueous solution.

Photochemistry of a Volcanically Driven Atmosphere on Io: Sulfur and Oxygen Species from a Pele-Type Eruption

NASA Astrophysics Data System (ADS)

Moses, Julianne I.; Zolotov, Mikhail Yu.; Fegley, Bruce

2002-03-01

To determine how active volcanism might affect the standard picture of sulfur dioxide photochemistry on Io, we have developed a one-dimensional atmospheric model in which a variety of sulfur-, oxygen-, sodium-, potassium-, and chlorine-bearing volatiles are volcanically outgassed at Io's surface and then evolve due to photolysis, chemical kinetics, and diffusion. Thermochemical equilibrium calculations in combination with recent observations of gases in the Pele plume are used to help constrain the composition and physical properties of the exsolved volcanic vapors. Both thermochemical equilibrium calculations (Zolotov and Fegley 1999, Icarus141, 40-52) and the Pele plume observations of Spencer et al. (2000; Science288, 1208-1210) suggest that S 2 may be a common gas emitted in volcanic eruptions on Io. If so, our photochemical models indicate that the composition of Io's atmosphere could differ significantly from the case of an atmosphere in equilibrium with SO 2 frost. The major differences as they relate to oxygen and sulfur species are an increased abundance of S, S 2, S 3, S 4, SO, and S 2O and a decreased abundance of O and O 2 in the Pele-type volcanic models as compared with frost sublimation models. The high observed SO/SO 2 ratio on Io might reflect the importance of a contribution from volcanic SO rather than indicate low eddy diffusion coefficients in Io's atmosphere or low SO "sticking" probabilities at Io's surface; in that case, the SO/SO 2 ratio could be temporally and/or spatially variable as volcanic activity fluctuates. Many of the interesting volcanic species (e.g., S 2, S 3, S 4, and S 2O) are short lived and will be rapidly destroyed once the volcanic plumes shut off; condensation of these species near the source vent is also likely. The diffuse red deposits associated with active volcanic centers on Io may be caused by S 4 radicals that are created and temporarily preserved when sulfur vapor (predominantly S 2) condenses around the volcanic vent. Condensation of SO across the surface and, in particular, in the polar regions might also affect the surface spectral properties. We predict that the S/O ratio in the torus and neutral clouds might be correlated with volcanic activity—during periods when volcanic outgassing of S 2 (or other molecular sulfur vapors) is prevalent, we would expect the escape of sulfur to be enhanced relative to that of oxygen, and the S/O ratio in the torus and neutral clouds could be correspondingly increased.

Predictions and Verification of an Isotope Marine Boundary Layer Model

NASA Astrophysics Data System (ADS)

Feng, X.; Posmentier, E. S.; Sonder, L. J.; Fan, N.

2017-12-01

A one-dimensional (1D), steady state isotope marine boundary layer (IMBL) model is constructed. The model includes meteorologically important features absent in Craig and Gordon type models, namely height-dependent diffusion/mixing and convergence of subsiding external air. Kinetic isotopic fractionation results from this height-dependent diffusion which starts as pure molecular diffusion at the air-water interface and increases linearly with height due to turbulent mixing. The convergence permits dry, isotopically depleted air subsiding adjacent to the model column to mix into ambient air. In δD-δ18O space, the model results fill a quadrilateral, of which three sides represent 1) vapor in equilibrium with various sea surface temperatures (SSTs) (high d18O boundary of quadrilateral); 2) mixture of vapor in equilibrium with seawater and vapor in the subsiding air (lower boundary depleted in both D and 18O); and 3) vapor that has experienced the maximum possible kinetic fractionation (high δD upper boundary). The results can be plotted in d-excess vs. δ18O space, indicating that these processes all cause variations in d-excess of MBL vapor. In particular, due to relatively high d-excess in the descending air, mixing of this air into the MBL causes an increase in d-excess, even without kinetic isotope fractionation. The model is tested by comparison with seven datasets of marine vapor isotopic ratios, with excellent correspondence; >95% of observational data fall within the quadrilateral area predicted by the model. The distribution of observations also highlights the significant influence of vapor from the nearby converging descending air on isotopic variations in the MBL. At least three factors may explain the <5% of observations that fall slightly outside of the predicted region in both δD-δ18O and d-excess - δ18O space: 1) variations in seawater isotopic ratios, 2) variations in isotopic composition of subsiding air, and 3) influence of sea spray. The model can be used for understanding the effects of boundary layer processes and meteorological conditions on isotopic composition of vapor within, and vapor fluxes through the MBL, and how changes in moisture source regions affect the isotopic composition of precipitation. The model can be applied to modern as well as paleo- climate conditions.

Treatment of wastewater containing toxic chromium using new activated carbon developed from date palm seed.

PubMed

El Nemr, Ahmed; Khaled, Azza; Abdelwahab, Ola; El-Sikaily, Amany

2008-03-21

The use of a new activated carbon developed from date palm seed wastes, generated in the jam industry, for removing toxic chromium from aqueous solution has been investigated. The activated carbon has been achieved from date palm seed by dehydrating methods using concentrated sulfuric acid. The batch experiments were conducted to determine the adsorption capacity of the biomass. The effect of initial metal concentration (25-125mgl(-1)), pH, contact time, and concentration of date palm seed carbon have been studied at room temperature. A strong dependence of the adsorption capacity on pH was observed, the capacity increase as pH value decrease and the optimum pH value is pH 1.0. Kinetics and adsorption equilibrium were studied at different sorbent doses. The adsorption process was fast and the equilibrium was reached within 180min. The maximum removal was 100% for 75mgl(-1) of Cr(+ concentration on 4gl(-1) carbon concentration and the maximum adsorption capacity was 120.48mgg(-1). The kinetic data were analyzed using various kinetic models - pseudo-first order equation, pseudo-second order equation, Elovich equation and intraparticle diffusion equation - and the equilibrium data were tested using several isotherm models, Langmuir, Freundlich, Koble-Corrigan, Redlich-Peterson, Tempkin, Dubinin-Radushkevich and Generalized isotherm equations. The Elovich equation and pseudo-second order equation provide the greatest accuracy for the kinetic data and Koble-Corrigan and Langmuir models the closest fit for the equilibrium data. Activation energy of sorption has also been evaluated as 0.115 and 0.229kJmol(-1).

A method for the direct numerical simulation of hypersonic boundary-layer instability with finite-rate chemistry

DOE Office of Scientific and Technical Information (OSTI.GOV)

Marxen, Olaf, E-mail: olaf.marxen@vki.ac.be; Aeronautics and Aerospace Department, von Karman Institute for Fluid Dynamics, Chaussée de Waterloo, 72, 1640 Rhode-St-Genèse; Magin, Thierry E.

2013-12-15

A new numerical method is presented here that allows to consider chemically reacting gases during the direct numerical simulation of a hypersonic fluid flow. The method comprises the direct coupling of a solver for the fluid mechanical model and a library providing the physio-chemical model. The numerical method for the fluid mechanical model integrates the compressible Navier–Stokes equations using an explicit time advancement scheme and high-order finite differences. This Navier–Stokes code can be applied to the investigation of laminar-turbulent transition and boundary-layer instability. The numerical method for the physio-chemical model provides thermodynamic and transport properties for different gases as wellmore » as chemical production rates, while here we exclusively consider a five species air mixture. The new method is verified for a number of test cases at Mach 10, including the one-dimensional high-temperature flow downstream of a normal shock, a hypersonic chemical reacting boundary layer in local thermodynamic equilibrium and a hypersonic reacting boundary layer with finite-rate chemistry. We are able to confirm that the diffusion flux plays an important role for a high-temperature boundary layer in local thermodynamic equilibrium. Moreover, we demonstrate that the flow for a case previously considered as a benchmark for the investigation of non-equilibrium chemistry can be regarded as frozen. Finally, the new method is applied to investigate the effect of finite-rate chemistry on boundary layer instability by considering the downstream evolution of a small-amplitude wave and comparing results with those obtained for a frozen gas as well as a gas in local thermodynamic equilibrium.« less

Experimental and theoretical studies of the effect of temperature on supercritical CO2 adsorption on illite

NASA Astrophysics Data System (ADS)

Joewondo, N.; Zhang, Y.; Prasad, M.

2016-12-01

Sequestration of carbon dioxide in shale has been a subject of interest as the result of the technological advancement in gas shale production. The process involves injection of CO2 to enhance methane recovery and storing CO2 in depleted shale reservoir at elevated pressures. To better understand both shale production and carbon storage one must study the physical phenomena acting at different scales that control the in situ fluid flow. Shale rocks are complex systems with heterogeneous structures and compositions. Pore structures of these systems are in nanometer scales and have significant gas storage capacity and surface area. Adsorption is prominent in nanometer sized pores due to the high attraction between gas molecules and the surface of the pores. Recent studies attempt to find correlation between storage capacity and the rock composition, particularly the clay content. This study, however, focuses on the study of supercritical adsorption of CO2 on pure clay sample. We have built an in-house manometric experimental setup that can be used to study both the equilibrium and kinetics of adsorption. The experiment is conducted at isothermal condition. The study of equilibrium of adsorption gives insight on the storage capacity of these systems, and the study of the kinetics of adsorption is essential in understanding the resistance to fluid transport. The diffusion coefficient, which can be estimated from the dynamic experimental results, is a parameter which quantify diffusion mobility, and is affected by many factors including pressure and temperature. The first part of this paper briefly discusses the study of both equilibrium and kinetics of the CO2 adsorption on illite. Both static and dynamic measurements on the system are compared to theoretical models available in the literature to estimate the storage capacity and the diffusion time constants. The main part of the paper discusses the effect of varying temperature on the static and dynamic experimental results.

Energy balance in the solar transition region. I - Hydrostatic thermal models with ambipolar diffusion

NASA Technical Reports Server (NTRS)

Fontenla, J. M.; Avrett, E. H.; Loeser, R.

1990-01-01

The energy balance in the lower transition region is analyzed by constructing theoretical models which satisfy the energy balance constraint. The energy balance is achieved by balancing the radiative losses and the energy flowing downward from the corona. This energy flow is mainly in two forms: conductive heat flow and hydrogen ionization energy flow due to ambipolar diffusion. Hydrostatic equilibrium is assumed, and, in a first calculation, local mechanical heating and Joule heating are ignored. In a second model, some mechanical heating compatible with chromospheric energy-balance calculations is introduced. The models are computed for a partial non-LTE approach in which radiation departs strongly from LTE but particles depart from Maxwellian distributions only to first order. The results, which apply to cases where the magnetic field is either absent, or uniform and vertical, are compared with the observed Lyman lines and continuum from the average quiet sun. The approximate agreement suggests that this type of model can roughly explain the observed intensities in a physically meaningful way, assuming only a few free parameters specified as chromospheric boundary conditions.

Electronic Noise and Fluctuations in Solids

NASA Astrophysics Data System (ADS)

Kogan, Sh.

2008-07-01

Preface; Part I. Introduction. Some Basic Concepts of the Theory of Random Processes: 1. Probability density functions. Moments. Stationary processes; 2. Correlation function; 3. Spectral density of noise; 4. Ergodicity and nonergodicity of random processes; 5. Random pulses and shot noise; 6. Markov processes. General theory; 7. Discrete Markov processes. Random telegraph noise; 8. Quasicontinuous (Diffusion-like) Markov processes; 9. Brownian motion; 10. Langevin approach to the kinetics of fluctuations; Part II. Fluctuation-Dissipation Relations in Equilibrium Systems: 11. Derivation of fluctuation-dissipation relations; 12. Equilibrium noise in quasistationary circuits. Nyquist theorem; 13. Fluctuations of electromagnetic fields in continuous media; Part III. Fluctuations in Nonequilibrium Gases: 14. Some basic concepts of hot-electrons' physics; 15. Simple model of current fluctuations in a semiconductor with hot electrons; 16. General kinetic theory of quasiclassical fluctuations in a gas of particles. The Boltzmann-Langevin equation; 17. Current fluctuations and noise temperature; 18. Current fluctuations and diffusion in a gas of hot electrons; 19. One-time correlation in nonequilibrium gases; 20. Intervalley noise in multivalley semiconductors; 21. Noise of hot electrons emitting optical phonons in the streaming regime; 22. Noise in a semiconductor with a postbreakdown stable current filament; Part IV. Generation-recombination noise: 23. G-R noise in uniform unipolar semiconductors; 24. Noise produced by recombination and diffusion; Part V. Noise in quantum ballistic systems: 25. Introduction; 26. Equilibrium noise and shot noise in quantum conductors; 27. Modulation noise in quantum point contacts; 28. Transition from a ballistic conductor to a macroscopic one; 29. Noise in tunnel junctions; Part VI. Resistance noise in metals: 30. Incoherent scattering of electrons by mobile defects; 31. Effect of mobile scattering centers on the electron interference pattern; 32. Fluctuations of the number of diffusing scattering centers; 33. Temperature fluctuations and the corresponding noise; Part VII. Noise in strongly disordered conductors: 34. Basic ideas of the percolation theory; 35. Resistance fluctuations in percolation systems. 36. Experiments; Part VIII. Low-frequency noise with an 1/f-type spectrum and random telegraph noise: 37. Introduction; 38. Some general properties of 1/f noise; 39. Basic models of 1/f noise; 40./f noise in metals; 41. Low-frequency noise in semiconductors; 42. Magnetic noise in spin glasses and some other magnetic systems; 43. Temperature fluctuations as a possible source of 1/f noise; 44. Random telegraph noise; 45. Fluctuations with 1/f spectrum in other systems; 46. General conclusions on 1/f noise; Part IX. Noise in Superconductors and Superconducting Structures: 47. Noise in Josephson junctions; 48. Noise in type II superconductors; References; Subject index.

Evidence for a Late Reducing Event in IAB-Silicate Inclusions

NASA Astrophysics Data System (ADS)

Seckendorff, V. V.; O'Neill, H. St. C.; Zipfel, J.; Palme, H.

1992-07-01

Coexisting orthopyroxene (opx) and olivine (ol) in silicate inclusions of IAB-iron meteorites have different Fe/(Fe+Mg) ratios. Ferrosilite (fs) contents of opx are higher than fayalite contents (fa) of ol (e.g., Bunch and Keil 1970). Non-ideal solid solution of fs in opx and/or fa in ol is generally assumed. We reinvestigated the equilibrium Fe-Mg distribution between coexisting ol+opx in the system MgO-FeO-SiO2 (von Seckendorff and O'Neill 1992). Reversal experiments at high- Mg compositions were performed from 900 to 1600 degrees C at 16 and 20 kbar using a barium borosilicate flux. The data could be fitted to a simple thermodynamic model with ol and opx treated as regular solutions and this model was found to describe satisfactorily the literature data extending down to 700 degrees C. For Fe/(Fe+Mg) between 0.05 to 0.15 we find KD^ol-opx close to one from 1600 to 700 degrees C, virtually independent of pressure and temperature. Fig. 1 shows experimental results at the Mg-rich end. Error bars mark 1-sigma standard deviations. Ol is in all cases more Fe-rich than coexisting opx, except for a single run at 1000 degrees C that probably did not reach equilibrium because of slow reaction kinetics. Two calculated distribution curves (1300, 700 degrees C at 16 kbar) lie close together indicating the absence of any significant temperature dependence of the exchange reaction at the Mg- rich end of the system. IAB-silicate inclusions plot outside the range of experimental data (Fig. 1). Although some previous models for Fe-Mg exchange between ol and opx (e.g., Sack 1980) extrapolate to KD<1 at temperatures near 500 degrees C, such models reproduce the experimental data (700 to 1600 degrees C) less well, than our updated model. In addition, temperatures at 500 degrees C are probably too low to allow Fe diffusion in opx. Two pyroxene equilibration temperatures of IAB-silicate inclusions are around 900-1000 degrees C suggesting a similar closure temperature for Fe diffusion in opx. Because of this and because of the essentially temperature-independent Fe-Mg distribution between ol and opx from 1600 to 700 degrees C, we conclude that the Fe-Mg distribution between ol and opx in IAB-silicate inclusion does not reflect thermodynamic equilibrium. As Fe-diffusion in ol is faster than in opx, redistribution of Fe in ol should have occurred at a temperature below the closure temperature for Fe-diffusion in opx. We suggest that FeO in ol was reduced to Fe metal by some species such as C, P, S, etc. A lower limit for the temperature of the reducing event is provided by Ca-zoning in ol, which develops below 650 degrees C (Kohler et al. 1991). Since strong FeO zoning in ol is absent, reduction of FeO in ol should have occurred above 650 degrees C, assuming similar diffusion coefficients for Ca and Fe in ol. References: Bunch T.E. and Keil K. (1970) Contrib. Mineral. Petrol. 25, 297-340. Kohler T., Palme H. and Brey G. (1991) N. Jb. Miner. Mh. 9, 423-431. Sack R.O. (1980) Contrib. Mineral. Petrol. 71, 257-269. v. Seckendorff V. and O'Neill H.St.C. (1992) Contr. Min. Petrol. (submitted).

SPECIES - EVALUATING THERMODYNAMIC PROPERTIES, TRANSPORT PROPERTIES & EQUILIBRIUM CONSTANTS OF AN 11-SPECIES AIR MODEL

NASA Technical Reports Server (NTRS)

Thompson, R. A.

1994-01-01

Accurate numerical prediction of high-temperature, chemically reacting flowfields requires a knowledge of the physical properties and reaction kinetics for the species involved in the reacting gas mixture. Assuming an 11-species air model at temperatures below 30,000 degrees Kelvin, SPECIES (Computer Codes for the Evaluation of Thermodynamic Properties, Transport Properties, and Equilibrium Constants of an 11-Species Air Model) computes values for the species thermodynamic and transport properties, diffusion coefficients and collision cross sections for any combination of the eleven species, and reaction rates for the twenty reactions normally occurring. The species represented in the model are diatomic nitrogen, diatomic oxygen, atomic nitrogen, atomic oxygen, nitric oxide, ionized nitric oxide, the free electron, ionized atomic nitrogen, ionized atomic oxygen, ionized diatomic nitrogen, and ionized diatomic oxygen. Sixteen subroutines compute the following properties for both a single species, interaction pair, or reaction, and an array of all species, pairs, or reactions: species specific heat and static enthalpy, species viscosity, species frozen thermal conductivity, diffusion coefficient, collision cross section (OMEGA 1,1), collision cross section (OMEGA 2,2), collision cross section ratio, and equilibrium constant. The program uses least squares polynomial curve-fits of the most accurate data believed available to provide the requested values more quickly than is possible with table look-up methods. The subroutines for computing transport coefficients and collision cross sections use additional code to correct for any electron pressure when working with ionic species. SPECIES was developed on a SUN 3/280 computer running the SunOS 3.5 operating system. It is written in standard FORTRAN 77 for use on any machine, and requires roughly 92K memory. The standard distribution medium for SPECIES is a 5.25 inch 360K MS-DOS format diskette. The contents of the diskettes are compressed using the PKWARE archiving tools. The utility to unarchive the files, PKUNZIP.EXE, is included. This program was last updated in 1991. SUN and SunOS are registered trademarks of Sun Microsystems, Inc.

Hopf Bifurcation Analysis of a Gene Regulatory Network Mediated by Small Noncoding RNA with Time Delays and Diffusion

NASA Astrophysics Data System (ADS)

Li, Chengxian; Liu, Haihong; Zhang, Tonghua; Yan, Fang

2017-12-01

In this paper, a gene regulatory network mediated by small noncoding RNA involving two time delays and diffusion under the Neumann boundary conditions is studied. Choosing the sum of delays as the bifurcation parameter, the stability of the positive equilibrium and the existence of spatially homogeneous and spatially inhomogeneous periodic solutions are investigated by analyzing the corresponding characteristic equation. It is shown that the sum of delays can induce Hopf bifurcation and the diffusion incorporated into the system can effect the amplitude of periodic solutions. Furthermore, the spatially homogeneous periodic solution always exists and the spatially inhomogeneous periodic solution will arise when the diffusion coefficients of protein and mRNA are suitably small. Particularly, the small RNA diffusion coefficient is more robust and its effect on model is much less than protein and mRNA. Finally, the explicit formulae for determining the direction of Hopf bifurcation and the stability of the bifurcating periodic solutions are derived by employing the normal form theory and center manifold theorem for partial functional differential equations. Finally, numerical simulations are carried out to illustrate our theoretical analysis.

Twin-domain size and bulk oxygen in-diffusion kinetics of YBa 2Cu 3O 6+x studied by neutron powder diffraction and gas volumetry

NASA Astrophysics Data System (ADS)

Poulsen, H. F.; Andersen, N. H.; Lebech, B.

1991-02-01

We report experimental results of twin-domain size and bulk oxygen in-diffusion kinetics of YBa 2Cu 3O 6+ x, which supplement a previous and simultaneous study of the structural phase diagram and oxygen equilibrium partial pressure. Analysis of neutron powder diffraction peak broadening show features which are identified to result from temperature independent twin-domain formation in to different orthorhombic phases with domain sizes and 250 and 350Å, respectively. The oxygen in-diffusion flow shows simple relaxation type behaviour J=J 0 exp( {-t}/{τ}) despite a rather broad particle size distribution. At higher temperatures, τ is activated with activation energies 0.55 and 0.25 eV in the tetragonal and orthorhombic phases, respectively. Comparison between twin-domain sizes and bulk oxygen in-diffusion time constants indicates that the twin-domain boundaries may contribute to the effective bulk oxygen in-diffusion. All our results may be interpreted in terms of the 2D ASYNNNI model description of the oxygen basal plane ordering, and they suggest that recent first principles interaction parameters should be modified.

Stability of nanoclusters in an oxide dispersion strengthened alloy under neutron irradiation

DOE PAGES

Liu, Xiang; Miao, Yinbin; Wu, Yaqiao; ...

2017-06-01

In this paper, we report atom probe tomography results of the nanoclusters in a neutron-irradiated oxide dispersion strengthened alloy. Following irradiation to 5 dpa at target temperatures of 300 °C and 450 °C, fewer large nanoclusters were found and the residual nanoclusters tend to reach an equilibrium Guinier radius of 1.8 nm. With increasing dose, evident decrease in peak oxygen and titanium (but not yttrium) concentrations in the nanoclusters was observed, which was explained by atomic weight, solubility, diffusivity, and chemical bonding arguments. Finally, the chemical modifications indicate the equilibrium size is indeed a balance of two competing processes: radiationmore » enhanced diffusion and collisional dissolution.« less

Importance sampling large deviations in nonequilibrium steady states. I.

PubMed

Ray, Ushnish; Chan, Garnet Kin-Lic; Limmer, David T

2018-03-28

Large deviation functions contain information on the stability and response of systems driven into nonequilibrium steady states and in such a way are similar to free energies for systems at equilibrium. As with equilibrium free energies, evaluating large deviation functions numerically for all but the simplest systems is difficult because by construction they depend on exponentially rare events. In this first paper of a series, we evaluate different trajectory-based sampling methods capable of computing large deviation functions of time integrated observables within nonequilibrium steady states. We illustrate some convergence criteria and best practices using a number of different models, including a biased Brownian walker, a driven lattice gas, and a model of self-assembly. We show how two popular methods for sampling trajectory ensembles, transition path sampling and diffusion Monte Carlo, suffer from exponentially diverging correlations in trajectory space as a function of the bias parameter when estimating large deviation functions. Improving the efficiencies of these algorithms requires introducing guiding functions for the trajectories.

Brownian motion in non-equilibrium systems and the Ornstein-Uhlenbeck stochastic process.

PubMed

Donado, F; Moctezuma, R E; López-Flores, L; Medina-Noyola, M; Arauz-Lara, J L

2017-10-03

The Ornstein-Uhlenbeck stochastic process is an exact mathematical model providing accurate representations of many real dynamic processes in systems in a stationary state. When applied to the description of random motion of particles such as that of Brownian particles, it provides exact predictions coinciding with those of the Langevin equation but not restricted to systems in thermal equilibrium but only conditioned to be stationary. Here, we investigate experimentally single particle motion in a two-dimensional granular system in a stationary state, consisting of 1 mm stainless balls on a plane circular surface. The motion of the particles is produced by an alternating magnetic field applied perpendicular to the surface of the container. The mean square displacement of the particles is measured for a range of low concentrations and it is found that following an appropriate scaling of length and time, the short-time experimental curves conform a master curve covering the range of particle motion from ballistic to diffusive in accordance with the description of the Ornstein-Uhlenbeck model.

Importance sampling large deviations in nonequilibrium steady states. I

NASA Astrophysics Data System (ADS)

Ray, Ushnish; Chan, Garnet Kin-Lic; Limmer, David T.

2018-03-01

Large deviation functions contain information on the stability and response of systems driven into nonequilibrium steady states and in such a way are similar to free energies for systems at equilibrium. As with equilibrium free energies, evaluating large deviation functions numerically for all but the simplest systems is difficult because by construction they depend on exponentially rare events. In this first paper of a series, we evaluate different trajectory-based sampling methods capable of computing large deviation functions of time integrated observables within nonequilibrium steady states. We illustrate some convergence criteria and best practices using a number of different models, including a biased Brownian walker, a driven lattice gas, and a model of self-assembly. We show how two popular methods for sampling trajectory ensembles, transition path sampling and diffusion Monte Carlo, suffer from exponentially diverging correlations in trajectory space as a function of the bias parameter when estimating large deviation functions. Improving the efficiencies of these algorithms requires introducing guiding functions for the trajectories.

Risk of population extinction from fixation of deleterious and reverse mutations.

PubMed

Lande, R

1998-01-01

A model is developed for alternate fixations of mildly deleterious and wild-type alleles arising by forward and reverse mutation in a finite population. For almost all parameter values, this gives an equilibrium load that agrees closely with the general expression derived from diffusion theory. Nearly neutral mutations with selection coefficient a few times larger than 1/(2N(e)) do the most damage by increasing the equilibrium load. The model of alternate fixations facilitates dynamical analysis of the expected load and the mean time to extinction in a population that has been suddenly reduced from a very large size to a small size. Reverse mutation can substantially improve population viability, increasing the mean time to extinction by an order of magnitude or more, but because many mutations are irreversible the effects may not be large. Populations with initially high mean fitness and small effective size, N(e) below a few hundred individuals, may be at serious risk of extinction from fixation of deleterious mutations within 10(3) to 10(4) generations.

Peach gum for efficient removal of methylene blue and methyl violet dyes from aqueous solution.

PubMed

Zhou, Li; Huang, Jiachang; He, Benzhao; Zhang, Faai; Li, Huabin

2014-01-30

This study investigated the potential use of natural peach gum (PG) as alternative adsorbent for the removal of dyes from aqueous solutions. The PG showed high adsorption capacities and selectivity for cationic dyes (e.g., methylene blue (MB) and methyl violet (MV)) in the pH range 6-10. 98% of MB and MV could be adsorbed within 5 min, and both of the adsorptions reached equilibrium within 30 min. The dye uptake process followed the pseudo-second-order kinetic model. The intraparticle diffusion was not the sole rate controlling step. Equilibrium adsorption isotherm data indicated a good fit to the Langmuir isotherm model. Regeneration study revealed that PG could be well regenerated in acid solution. The recovered PG still exhibited high adsorption capacity even after five cycles of desorption-adsorption. On the basis of its excellent adsorption performance and facile availability, PG can be employed as an efficient low cost adsorbent for environmental cleanup. Copyright © 2013 Elsevier Ltd. All rights reserved.

Photophysical behavior of polyatomic molecules

NASA Astrophysics Data System (ADS)

Ware, W. R.

1980-10-01

Part one of this report deals with attempts over the past several years to devise a more sophisticated theory of diffusion controlled reactions than that presented by Collins and Kimball. In particular, the investigators were interested in a more realistic formulation of the problem of high concentration quenching where quenches in the vicinity of the molecular to be quenched must be considered. It was desired however, to obtain a formalism which was tractable mathematically and which contained parameters which would be related to experiment. Part two deals with the photophysics of systems exhibiting molecular association both in the ground and excited states has been studied. The emphasis has been on kinetic models, the measurement of rate constants associated with these models, and the determination of activation parameters and equilibrium thermodynamic parameters associated with the exciplex formation and disappearance. Studies of solvent effects and steric effects on the behavior of exciplex systems have been carried out. The case of rapid equilibrium where the monomer and exciplex decay with the same rate constant has also been examined.

Uphill diffusion in multicomponent mixtures.

PubMed

Krishna, Rajamani

2015-05-21

Molecular diffusion is an omnipresent phenomena that is important in a wide variety of contexts in chemical, physical, and biological processes. In the majority of cases, the diffusion process can be adequately described by Fick's law that postulates a linear relationship between the flux of any species and its own concentration gradient. Most commonly, a component diffuses down the concentration gradient. The major objective of this review is to highlight a very wide variety of situations that cause the uphill transport of one constituent in the mixture. Uphill diffusion may occur in multicomponent mixtures in which the diffusion flux of any species is strongly coupled to that of its partner species. Such coupling effects often arise from strong thermodynamic non-idealities. For a quantitative description we need to use chemical potential gradients as driving forces. The transport of ionic species in aqueous solutions is coupled with its partner ions because of the electro-neutrality constraints; such constraints may accelerate or decelerate a specific ion. When uphill diffusion occurs, we observe transient overshoots during equilibration; the equilibration process follows serpentine trajectories in composition space. For mixtures of liquids, alloys, ceramics and glasses the serpentine trajectories could cause entry into meta-stable composition zones; such entry could result in phenomena such as spinodal decomposition, spontaneous emulsification, and the Ouzo effect. For distillation of multicomponent mixtures that form azeotropes, uphill diffusion may allow crossing of distillation boundaries that are normally forbidden. For mixture separations with microporous adsorbents, uphill diffusion can cause supra-equilibrium loadings to be achieved during transient uptake within crystals; this allows the possibility of over-riding adsorption equilibrium for achieving difficult separations.

Unity and diversity in mixing: Stretching, diffusion, breakup, and aggregation in chaotic flows

DOE Office of Scientific and Technical Information (OSTI.GOV)

Ottino, J.M.

1991-05-01

Experiments and theory have produced a reasonably good qualitative understanding of the evolution of chaotic mixing of passive tracers, especially in two-dimensional time-periodic flow fields. Such an understanding forms a fabric for the evolution of breakup, aggregation, and diffusion-controlled reactions in more complex flows. These systems can be viewed as a population of microstructures'' whose behavior is dictated by iterations of a chaotic flow; microstructures break, diffuse, and aggregate, causing the population to evolve in space and time. This paper presents simple physical models for such processes. Self-similarity is common to all the problems; examples arise in the context ofmore » the distribution of stretchings within chaotic flows, in the asymptotic evolution of diffusion-reaction processes at striation thickness scales, in the equilibrium distribution of drop sizes generated upon mixing of immiscible fluids, in the equations describing mean-field kinetics of coagulation, in the sequence of actions necessary for the destruction of islands in two-dimensional flow, and in the fractal structure of clusters produced upon aggregation in chaotic flows.« less

Use of carbonised beet pulp carbon for removal of Remazol Turquoise Blue-G 133 from aqueous solution.

PubMed

Dursun, Arzu Y; Tepe, Ozlem; Dursun, Gülbeyi

2013-01-01

Carbonised beet pulp (BPC) produced from agricultural solid waste by-product in sugar industry was used as adsorbent for the removal of Remazol Turquoise Blue-G 133 (RTB-G 133) dye in this study. The kinetics and equilibrium of sorption process were investigated with respect to pH, temperature and initial dye concentration. Adsorption studies with real textile wastewater were also performed. The results showed that adsorption was a strongly pH-dependent process, and optimum pH was determined as 1.0. The maximum dye adsorption capacity was obtained as 47.0 mg g(-1)at the temperature of 25 °C at this pH value. The Freundlich and Langmuir adsorption models were used for describing the adsorption equilibrium data of the dye, and isotherm constants were evaluated depending on sorption temperature. Equilibrium data of RTB-G 133 sorption fitted very well to the Freundlich isotherm. Mass transfer and kinetic models were applied to the experimental data to examine the mechanisms of adsorption and potential rate-controlling steps. It was found that both external mass transfer and intra-particle diffusion played an important role in the adsorption mechanisms of dye and adsorption kinetics followed the pseudo second-order type kinetic model. The thermodynamic analysis indicated that the sorption process was exothermic and spontaneous in nature.

Adsorption properties of kaolinite-based nanocomposites for Fe and Mn pollutants from aqueous solutions and raw ground water: kinetics and equilibrium studies.

PubMed

Shaban, Mohamed; Hassouna, Mohamed E M; Nasief, Fadya M; AbuKhadra, Mostafa R

2017-10-01

Raw kaolinite was used in the synthesis of metakaolinite/carbon nanotubes (K/CNTs) and kaolinite/starch (K/starch) nanocomposites. Raw kaolinite and the synthetic composites were characterized using XRD, SEM, and TEM techniques. The synthetic composites were used as adsorbents for Fe and Mn ions from aqueous solutions and natural underground water. The adsorption by the both composites is highly pH dependent and achieves high efficiency within the neutral pH range. The experimental adsorption data for the uptake of Fe and Mn ions by K/CNTs were found to be well represented by the pseudo-second-order kinetic model rather than the intra-particle diffusion model or Elovich model. For the adsorption using K/starch, the uptake results of Fe ions was well fitted by the second-order model, whereas the uptake of Mn ions fitted well to the Elovich model rather than pseudo-second-order and intra-particle diffusion models The equilibrium studies revealed the excellent fitting of the removal of Fe and Mn ions by K/CNTs and Fe using K/starch with the Langmuir isotherm model rather than with Freundlich and Temkin models. But the adsorption of Mn ions by K/starch is well fitted with Freundlich rather than Temkin and Langmuir isotherm models. The thermodynamic studies reflected the endothermic nature and the exothermic nature for the adsorption by K/CNTs and K/starch nanocomposites, respectively. Natural ground water contaminated by 0.4 mg/L Fe and 0.5 mg/L Mn was treated at the optimum conditions of pH 6 and 120 min contact time. Under these conditions, 92.5 and 72.5% Fe removal efficiencies were achieved using 20 mg of K/CNTs and K/starch nanocomposites, respectively. Also, K/CNTs nanocomposite shows higher efficiency in the removal of Mn ions as compared to K/starch nanocomposite.

Adsorption of Zinc(II) on diatomite and manganese-oxide-modified diatomite: a kinetic and equilibrium study.

PubMed

Caliskan, Necla; Kul, Ali Riza; Alkan, Salih; Sogut, Eda Gokirmak; Alacabey, Ihsan

2011-10-15

The removal of Zn(II) ions from aqueous solution was studied using natural and MnO(2) modified diatomite samples at different temperatures. The linear Langmuir, Freundlich and Dubinin-Radushkevich (D-R) adsorption equations were applied to describe the equilibrium isotherms. From the D-R model, the mean adsorption energy was calculated as >8 kJ mol(-1), indicating that the adsorption of Zn(II) onto diatomite and Mn-diatomite was physically carried out. In addition, the pseudo-first-order, pseudo-second-order and intraparticle diffusion models were used to determine the kinetic data. The experimental data were well fitted by the pseudo-second-order kinetic model. Thermodynamic parameters such as the enthalpy (ΔH(0)), Gibbs' free energy (ΔG(0)) and entropy (ΔS(0)) were calculated for natural and MnO(2) modified diatomite. These values showed that the adsorption of Zn(II) ions onto diatomite samples was controlled by a physical mechanism and occurred spontaneously. Copyright © 2011 Elsevier B.V. All rights reserved.

Self-Healing of Unentangled Polymer Networks with Reversible Bonds

PubMed Central

Stukalin, Evgeny B.; Cai, Li-Heng; Kumar, N. Arun; Leibler, Ludwik; Rubinstein, Michael

2013-01-01

Self-healing polymeric materials are systems that after damage can revert to their original state with full or partial recovery of mechanical strength. Using scaling theory we study a simple model of autonomic self-healing of unentangled polymer networks. In this model one of the two end monomers of each polymer chain is fixed in space mimicking dangling chains attachment to a polymer network, while the sticky monomer at the other end of each chain can form pairwise reversible bond with the sticky end of another chain. We study the reaction kinetics of reversible bonds in this simple model and analyze the different stages in the self-repair process. The formation of bridges and the recovery of the material strength across the fractured interface during the healing period occur appreciably faster after shorter waiting time, during which the fractured surfaces are kept apart. We observe the slowest formation of bridges for self-adhesion after bringing into contact two bare surfaces with equilibrium (very low) density of open stickers in comparison with self-healing. The primary role of anomalous diffusion in material self-repair for short waiting times is established, while at long waiting times the recovery of bonds across fractured interface is due to hopping diffusion of stickers between different bonded partners. Acceleration in bridge formation for self-healing compared to self-adhesion is due to excess non-equilibrium concentration of open stickers. Full recovery of reversible bonds across fractured interface (formation of bridges) occurs after appreciably longer time than the equilibration time of the concentration of reversible bonds in the bulk. PMID:24347684

Ni(II) removal from aqueous solutions using cone biomass of Thuja orientalis.

PubMed

Malkoc, Emine

2006-09-21

The biomass of terrestrial-plant materials has high removal capacities for a number of heavy metal ions. The Ni(II) biosorption capacity of the cone biomass of Thuja orientalis was studied in the batch mode. The biosorption equilibrium level was determined as a function of contact time, pH, temperature, agitation speed at several initial metal ion and adsorbent concentrations. The removal of Ni(II) from aqueous solutions increased with adsorbent concentration, temperature and agitation speed of the solution were increased. The biosorption process was very fast; 90% of biosorption occurred within 3 min and equilibrium was reached at around 7 min. It is found that the biosorption of Ni(II) on the cone biomass was correlated well (R2 > 0.99) with the Langmuir equation as compared to Freundlich, BET Temkin and D-R isotherm equation under the concentration range studied. According to Langmuir isotherm, the monolayer saturation capacity (Q(o)) is 12.42 mg g(-1). The pseudo-first-order, pseudo-second-order and intraparticle diffusion kinetic models were applied to test the experimental data for initial Ni(II) and cone biomass concentrations. The pseudo-second-order kinetic model provided the best correlation of the used experimental data compared to the pseudo-first-order and intraparticle diffusion kinetic models. The activation energy of biosorption (E(a)) was determined as 36.85 kJ mol(-1) using the Arrhenius equation. This study indicated that the cone biomass of T. orientalis can be used as an effective and environmentally friendly adsorbent for the treatment of Ni(II) containing aqueous solutions.

Evaporation and combustion of LOX under supercritical and subcritical conditions

NASA Technical Reports Server (NTRS)

Yang, A. S.; Hsieh, W. H.; Kuo, K. K.

1993-01-01

The objective is to study the evaporation and combustion of LOX under supercritical and subcritical conditions both experimentally and theoretically. In the evaporation studies, evaporation rate and surface temperature were measured when LOX vaporizing in helium environments at pressures ranging from 5 to 68 atm. A Varian 3700 gas chromatograph was employed to measure the oxygen concentration above the LOX surface. For the combustion tests, high-magnification video photography was used to record direct images of the flame shape of a LOX/H2/He laminar diffusion flame. The gas composition in the post-flame region is also being measured with the gas sampling and chromatography analysis. These data are being used to validate the theoretical model. A comprehensive theoretical model with the consideration of the solubility of ambient gases as well as variable thermophysical properties was formulated and solved numerically to study the gasification and burning of LOX at elevated pressures. The calculated flame shape agreed reasonably well with the edge of the observed luminous flame surface. The effect of gravity on the flame structure of laminar diffusion flames was found to be significant. In addition, the predicted results using the flame-sheet model were compared with those based upon full equilibrium calculations (which considered the formation of intermediate species) at supercritical pressures. Except at the flame front where temperature exceeded 2,800 K, the flame-sheet and equilibrium solutions in terms of temperature distributions were in very close agreement. The temperature deviation in the neighborhood of the flame front is caused by the effect of high-temperature dissociation.

Modeling of the anode of a liquid-feed DMFC: Inhomogeneous compression effects and two-phase transport phenomena

NASA Astrophysics Data System (ADS)

García-Salaberri, Pablo A.; Vera, Marcos; Iglesias, Immaculada

2014-01-01

An isothermal two-phase 2D/1D across-the-channel model for the anode of a liquid-feed Direct Methanol Fuel Cell (DMFC) is presented. The model takes into account the effects of the inhomogeneous assembly compression of the Gas Diffusion Layer (GDL), including the spatial variations of porosity, diffusivity, permeability, capillary pressure, and electrical conductivity. The effective anisotropic properties of the GDL are evaluated from empirical data reported in the literature corresponding to Toray carbon paper TGP-H series. Multiphase transport is modeled according to the classical theory of porous media (two-fluid model), considering the effect of non-equilibrium evaporation and condensation of methanol and water. The numerical results evidence that the hydrophobic Leverett J-function approach is physically inconsistent to describe capillary transport in the anode of a DMFC when assembly compression effects are considered. In contrast, more realistic results are obtained when GDL-specific capillary pressure curves reflecting the mixed-wettability characteristics of GDLs are taken into account. The gas coverage factor at the GDL/channel interface also exhibits a strong influence on the gas-void fraction distribution in the GDL, which in turn depends on the relative importance between the capillary resistance induced by the inhomogeneous compression, Rc(∝ ∂pc / ∂ ε) , and the capillary diffusivity, Dbarc(∝ ∂pc / ∂ s) .

Thermodynamics of the general diffusion process: Equilibrium supercurrent and nonequilibrium driven circulation with dissipation

NASA Astrophysics Data System (ADS)

Qian, H.

2015-07-01

Unbalanced probability circulation, which yields cyclic motions in phase space, is the defining characteristics of a stationary diffusion process without detailed balance. In over-damped soft matter systems, such behavior is a hallmark of the presence of a sustained external driving force accompanied with dissipations. In an under-damped and strongly correlated system, however, cyclic motions are often the consequences of a conservative dynamics. In the present paper, we give a novel interpretation of a class of diffusion processes with stationary circulation in terms of a Maxwell-Boltzmann equilibrium in which cyclic motions are on the level set of stationary probability density function thus non-dissipative, e.g., a supercurrent. This implies an orthogonality between stationary circulation J ss ( x) and the gradient of stationary probability density f ss ( x) > 0. A sufficient and necessary condition for the orthogonality is a decomposition of the drift b( x) = j( x) + D( x)∇φ( x) where ∇ṡ j( x) = 0 and j( x) ṡ∇φ( x) = 0. Stationary processes with such Maxwell-Boltzmann equilibrium has an underlying conservative dynamics , and a first integral ϕ( x) ≡ -ln f ss (x) = const, akin to a Hamiltonian system. At all time, an instantaneous free energy balance equation exists for a given diffusion system; and an extended energy conservation law among an entire family of diffusion processes with different parameter α can be established via a Helmholtz theorem. For the general diffusion process without the orthogonality, a nonequilibrium cycle emerges, which consists of external driven φ-ascending steps and spontaneous φ-descending movements, alternated with iso-φ motions. The theory presented here provides a rich mathematical narrative for complex mesoscopic dynamics, with contradistinction to an earlier one [H. Qian et al., J. Stat. Phys. 107, 1129 (2002)]. This article is supplemented with comments by H. Ouerdane and a final reply by the author.

Dusty Pair Plasma—Wave Propagation and Diffusive Transition of Oscillations

NASA Astrophysics Data System (ADS)

Atamaniuk, Barbara; Turski, Andrzej J.

2011-11-01

The crucial point of the paper is the relation between equilibrium distributions of plasma species and the type of propagation or diffusive transition of plasma response to a disturbance. The paper contains a unified treatment of disturbance propagation (transport) in the linearized Vlasov electron-positron and fullerene pair plasmas containing charged dust impurities, based on the space-time convolution integral equations. Electron-positron-dust/ion (e-p-d/i) plasmas are rather widespread in nature. Space-time responses of multi-component linearized Vlasov plasmas on the basis of multiple integral equations are invoked. An initial-value problem for Vlasov-Poisson/Ampère equations is reduced to the one multiple integral equation and the solution is expressed in terms of forcing function and its space-time convolution with the resolvent kernel. The forcing function is responsible for the initial disturbance and the resolvent is responsible for the equilibrium velocity distributions of plasma species. By use of resolvent equations, time-reversibility, space-reflexivity and the other symmetries are revealed. The symmetries carry on physical properties of Vlasov pair plasmas, e.g., conservation laws. Properly choosing equilibrium distributions for dusty pair plasmas, we can reduce the resolvent equation to: (i) the undamped dispersive wave equations, (ii) and diffusive transport equations of oscillations.

Elucidation of the naproxen sodium adsorption onto activated carbon prepared from waste apricot: kinetic, equilibrium and thermodynamic characterization.

PubMed

Onal, Y; Akmil-Başar, C; Sarici-Ozdemir, C

2007-09-30

In this study, activated carbon (WA11Zn5) was prepared from waste apricot, which is waste in apricot plants in Malatya, by chemical activation with ZnCl(2). BET surface area of activated carbon is determined as 1060 m(2)/g. The ability of WA11Zn5, to remove naproxen sodium from effluent solutions by adsorption has been studied. Equilibrium isotherms for the adsorption of naproxen sodium on activated carbon were measured experimentally. Results were analyzed by the Langmiur, Freundlich equation using linearized correlation coefficient at 298 K. The characteristic parameters for each isotherm have been determined. Langmiur equation is found to best represent the equilibrium data for naproxen sodium-WA11Zn5 systems. The monolayer adsorption capacity of WA11Zn5 for naproxen sodium was found to be 106.38 mg/g at 298 K. The process was favorable and spontaneous. The kinetics of adsorption of naproxen sodium have been discussed using three kinetic models, i.e., the pseudo first-order model, the pseudo second-order model, the intraparticle diffusion model. Kinetic parameters and correlation coefficients were determined. It was shown that the pseudo second-order kinetic equation could describe the adsorption kinetics for naproxen sodium onto WA11Zn5. The thermodynamic parameters, such as DeltaG degrees , DeltaS degrees and DeltaH degrees, were calculated. The thermodynamics of naproxen sodium-WA11Zn5 system indicates endothermic process.

Modeling of biomass to hydrogen via the supercritical water pyrolysis process

DOE Office of Scientific and Technical Information (OSTI.GOV)

Divilio, R.J.

1998-08-01

A heat transfer model has been developed to predict the temperature profile inside the University of Hawaii`s Supercritical Water Reactor. A series of heat transfer tests were conducted on the University of Hawaii`s apparatus to calibrate the model. Results of the model simulations are shown for several of the heat transfer tests. Tests with corn starch and wood pastes indicated that there are substantial differences between the thermal properties of the paste compared to pure water, particularly near the pseudo critical temperature. The assumption of constant thermal diffusivity in the temperature range of 250 to 450 C gave a reasonablemore » prediction of the reactor temperatures when paste is being fed. A literature review is presented for pyrolysis of biomass in water at elevated temperatures up to the supercritical range. Based on this review, a global reaction mechanism is proposed. Equilibrium calculations were performed on the test results from the University of Hawaii`s Supercritical Water Reactor when corn starch and corn starch and wood pastes were being fed. The calculations indicate that the data from the reactor falls both below and above the equilibrium hydrogen concentrations depending on test conditions. The data also indicates that faster heating rates may be beneficial to the hydrogen yield. Equilibrium calculations were also performed to examine the impact of wood concentration on the gas mixtures produced. This calculation showed that increasing wood concentrations favors the formation of methane at the expense of hydrogen.« less

The intrinsic periodic fluctuation of forest: a theoretical model based on diffusion equation

NASA Astrophysics Data System (ADS)

Zhou, J.; Lin, G., Sr.

2015-12-01

Most forest dynamic models predict the stable state of size structure as well as the total basal area and biomass in mature forest, the variation of forest stands are mainly driven by environmental factors after the equilibrium has been reached. However, although the predicted power-law size-frequency distribution does exist in analysis of many forest inventory data sets, the estimated distribution exponents are always shifting between -2 and -4, and has a positive correlation with the mean value of DBH. This regular pattern can not be explained by the effects of stochastic disturbances on forest stands. Here, we adopted the partial differential equation (PDE) approach to deduce the systematic behavior of an ideal forest, by solving the diffusion equation under the restricted condition of invariable resource occupation, a periodic solution was gotten to meet the variable performance of forest size structure while the former models with stable performance were just a special case of the periodic solution when the fluctuation frequency equals zero. In our results, the number of individuals in each size class was the function of individual growth rate(G), mortality(M), size(D) and time(T), by borrowing the conclusion of allometric theory on these parameters, the results perfectly reflected the observed "exponent-mean DBH" relationship and also gave a logically complete description to the time varying form of forest size-frequency distribution. Our model implies that the total biomass of a forest can never reach a stable equilibrium state even in the absence of disturbances and climate regime shift, we propose the idea of intrinsic fluctuation property of forest and hope to provide a new perspective on forest dynamics and carbon cycle research.

Modeling the propagation of mobile malware on complex networks

NASA Astrophysics Data System (ADS)

Liu, Wanping; Liu, Chao; Yang, Zheng; Liu, Xiaoyang; Zhang, Yihao; Wei, Zuxue

2016-08-01

In this paper, the spreading behavior of malware across mobile devices is addressed. By introducing complex networks to model mobile networks, which follows the power-law degree distribution, a novel epidemic model for mobile malware propagation is proposed. The spreading threshold that guarantees the dynamics of the model is calculated. Theoretically, the asymptotic stability of the malware-free equilibrium is confirmed when the threshold is below the unity, and the global stability is further proved under some sufficient conditions. The influences of different model parameters as well as the network topology on malware propagation are also analyzed. Our theoretical studies and numerical simulations show that networks with higher heterogeneity conduce to the diffusion of malware, and complex networks with lower power-law exponents benefit malware spreading.

Critical fluid thermal equilibration experiment (19-IML-1)

NASA Technical Reports Server (NTRS)

Wilkinson, R. Allen

1992-01-01

Gravity sometimes blocks all experimental techniques of making a desired measurement. Any pure fluid possesses a liquid-vapor critical point. It is defined by a temperature, pressure, and density state in thermodynamics. The critical issue that this experiment attempts to understand is the time it takes for a sample to reach temperature and density equilibrium as the critical point is approached; is it infinity due to mass and thermal diffusion, or do pressure waves speed up energy transport while mass is still under diffusion control. The objectives are to observe: (1) large phase domain homogenization without and with stirring; (2) time evolution of heat and mass after temperature step is applied to a one phase equilibrium sample; (3) phase evolution and configuration upon going two phase from a one phase equilibrium state; (4) effects of stirring on a low g two phase configuration; (5) two phase to one phase healing dynamics starting from a two phase low g configuration; and (6) effects of shuttle acceleration events on spatially and temporally varying compressible critical fluid dynamics.

Non-equilibrium forces drive the anomalous diffusion of telomeres in the nucleus of mammalian cells

NASA Astrophysics Data System (ADS)

Stadler, Lorenz; Weiss, Matthias

2017-11-01

Telomeres are vital nucleotide sequences at both ends of each chromosome, and their motion reports on the local dynamics of decondensed chromatin in the nucleus of interphase cells. Here, we show that the previously reported subdiffusive motion of telomeres is driven by non-equilibrium cytoskeletal forces. In particular, breaking down microtubules leads to a significantly reduced generalized diffusion coefficient of telomeres. This translates into a markedly reduced effective temperature in the stochastic forces that govern the telomeres’ random walk. Moreover, telomere motion in cells that lack microtubules is well described by the monomer dynamics of a Rouse polymer that is embeddded in a viscoelastic medium. In contrast, active cytoskeletal forces in untreated cells override the environment’s elastic contributions, resulting in the well-known scaling for conventional Rouse dynamics in viscous media. Our data highlight that even subdiffusive motion in cells in most cases may not be a simple thermal transport process but rather is driven by non-equilibrium events.

Diffuse interface method for a compressible binary fluid.

PubMed

Liu, Jiewei; Amberg, Gustav; Do-Quang, Minh

2016-01-01

Multicomponent, multiphase, compressible flows are very important in real life, as well as in scientific research, while their modeling is in an early stage. In this paper, we propose a diffuse interface model for compressible binary mixtures, based on the balance of mass, momentum, energy, and the second law of thermodynamics. We show both analytically and numerically that this model is able to describe the phase equilibrium for a real binary mixture (CO_{2} + ethanol is considered in this paper) very well by adjusting the parameter which measures the attraction force between molecules of the two components in the model. We also show that the calculated surface tension of the CO_{2} + ethanol mixture at different concentrations match measurements in the literature when the mixing capillary coefficient is taken to be the geometric mean of the capillary coefficient of each component. Three different cases of two droplets in a shear flow, with the same or different concentration, are simulated, showing that the higher concentration of CO_{2} the smaller the surface tension and the easier the drop deforms.

Convective diffusion in protein crystal growth

NASA Technical Reports Server (NTRS)

Baird, J. K.; Meehan, E. J., Jr.; Xidis, A. L.; Howard, S. B.

1986-01-01

A protein crystal modeled as a flat plate suspended in the parent solution, with the normal to the largest face perpendicular to gravity and the protein concentration in the solution adjacent to the plate taken to be the equilibrium solubility, is studied. The Navier-Stokes equation and the equation for convective diffusion in the boundary layer next to the plate are solved to calculate the flow velocity and the protein mass flux. The local rate of growth of the plate is shown to vary significantly with depth due to the convection. For an aqueous solution of lysozyme at a concentration of 40 mg/ml, the boundary layer at the top of a 1-mm-high crystal has a thickness of 80 microns at 1 g, and 2570 microns at 10 to the -6th g.

Computational and theoretical modeling of pH and flow effects on the early-stage non-equilibrium self-assembly of optoelectronic peptides

NASA Astrophysics Data System (ADS)

Mansbach, Rachael; Ferguson, Andrew

Self-assembling π-conjugated peptides are attractive candidates for the fabrication of bioelectronic materials possessing optoelectronic properties due to electron delocalization over the conjugated peptide groups. We present a computational and theoretical study of an experimentally-realized optoelectronic peptide that displays triggerable assembly in low pH to resolve the microscopic effects of flow and pH on the non-equilibrium morphology and kinetics of assembly. Using a combination of molecular dynamics simulations and hydrodynamic modeling, we quantify the time and length scales at which convective flows employed in directed assembly compete with microscopic diffusion to influence assembly. We also show that there is a critical pH below which aggregation proceeds irreversibly, and quantify the relationship between pH, charge density, and aggregate size. Our work provides new fundamental understanding of pH and flow of non-equilibrium π-conjugated peptide assembly, and lays the groundwork for the rational manipulation of environmental conditions and peptide chemistry to control assembly and the attendant emergent optoelectronic properties. This work was supported by the U.S. Department of Energy, Office of Science, Basic Energy Sciences, under Award # DE-SC0011847, and by the Computational Science and Engineering Fellowship from the University of Illinois at Urbana-Champaign.

Fundamental mass transfer modeling of emission of volatile organic compounds from building materials

NASA Astrophysics Data System (ADS)

Bodalal, Awad Saad

In this study, a mass transfer theory based model is presented for characterizing the VOC emissions from building materials. A 3-D diffusion model is developed to describe the emissions of volatile organic compounds (VOCs) from individual sources. Then the formulation is extended to include the emissions from composite sources (system comprising an assemblage of individual sources). The key parameters for the model (The diffusion coefficient of the VOC in the source material D, and the equilibrium partition coefficient k e) were determined independently (model parameters are determined without the use of chamber emission data). This procedure eliminated to a large extent the need for emission testing using environmental chambers, which is costly, time consuming, and may be subject to confounding sink effects. An experimental method is developed and implemented to measure directly the internal diffusion (D) and partition coefficients ( ke). The use of the method is illustrated for three types of VOC's: (i) Aliphatic Hydrocarbons, (ii) Aromatic Hydrocarbons and ( iii) Aldehydes, through typical dry building materials (carpet, plywood, particleboard, vinyl floor tile, gypsum board, sub-floor tile and OSB). Then correlations for predicting D and ke based solely on commonly available properties such as molecular weight and vapour pressure were proposed for each product and type of VOC. These correlations can be used to estimate the D and ke when direct measurement data are not available, and thus facilitate the prediction of VOC emissions from the building materials using mass transfer theory. The VOC emissions from a sub-floor material (made of the recycled automobile tires), and a particleboard are measured and predicted. Finally, a mathematical model to predict the diffusion coefficient through complex sources (floor adhesive) as a function of time was developed. Then this model (for diffusion coefficient in complex sources) was used to predict the emission rate from material system (namely, substrate//glue//vinyl tile).

Dynamical inversion of the energy landscape promotes non-equilibrium self-assembly of binary mixtures

DOE PAGES

Pestana, Luis Ruiz; Minnetian, Natalie; Lammers, Laura Nielsen; ...

2018-01-02

When driven out of equilibrium, many diverse systems can form complex spatial and dynamical patterns, even in the absence of attractive interactions. Using kinetic Monte Carlo simulations, we investigate the phase behavior of a binary system of particles of dissimilar size confined between semiflexible planar surfaces, in which the nanoconfinement introduces a non-local coupling between particles, which we model as an activation energy barrier to diffusion that decreases with the local fraction of the larger particle. The system autonomously reaches a cyclical non-equilibrium state characterized by the formation and dissolution of metastable micelle-like clusters with the small particles in themore » core and the large ones in the surrounding corona. The power spectrum of the fluctuations in the aggregation number exhibits 1/f noise reminiscent of self-organized critical systems. Finally, we suggest that the dynamical metastability of the micellar structures arises from an inversion of the energy landscape, in which the relaxation dynamics of one of the species induces a metastable phase for the other species.« less

Dilatometric investigation of α(orthorhombic)→β(tetragonal) transformation in U-15 wt.% Cr alloy

NASA Astrophysics Data System (ADS)

Rameshkumar, Santhosh; Raju, Subramanian; Saibaba, Saroja

2018-04-01

The α→β transformation characteristics in U-15wt.% Cr alloy have been investigated by dilatometry at slow heating rates (3-10 K min-1). The starting microstructure of U-15Cr alloy consists of a mixture of metastable βm-U(body centred tetroganal), α-U(orthorhombic) and elemental Cr(bcc) phases. Upon heating, the metastable βmU phase has progressively transformed to equilibrium α-U structure; before, finally undergoing equilibrium α→β transformation with further increase in temperature. The measured α→β transformation temperature, when extrapolated to 0 K min-1 heating rate has been found to be higher than the currently accepted equilibrium phase diagram estimate. This is due to the kinetic difficulty associated with Cr-diffusion in U-15Cr alloy. The kinetics of α→β transformation upon continuous heating has been modeled in terms of a suitable framework for diffusional transformations, and the effective activation energy for overall transformation has been estimated to be in the range 160-180 kJ mol-1.

Analytical modeling of the temporal evolution of hot spot temperatures in silicon solar cells

NASA Astrophysics Data System (ADS)

Wasmer, Sven; Rajsrima, Narong; Geisemeyer, Ino; Fertig, Fabian; Greulich, Johannes Michael; Rein, Stefan

2018-03-01

We present an approach to predict the equilibrium temperature of hot spots in crystalline silicon solar cells based on the analysis of their temporal evolution right after turning on a reverse bias. For this end, we derive an analytical expression for the time-dependent heat diffusion of a breakdown channel that is assumed to be cylindrical. We validate this by means of thermography imaging of hot spots right after turning on a reverse bias. The expression allows to be used to extract hot spot powers and radii from short-term measurements, targeting application in inline solar cell characterization. The extracted hot spot powers are validated at the hands of long-term dark lock-in thermography imaging. Using a look-up table of expected equilibrium temperatures determined by numerical and analytical simulations, we utilize the determined hot spot properties to predict the equilibrium temperatures of about 100 industrial aluminum back-surface field solar cells and achieve a high correlation coefficient of 0.86 and a mean absolute error of only 3.3 K.

Dynamical inversion of the energy landscape promotes non-equilibrium self-assembly of binary mixtures

DOE Office of Scientific and Technical Information (OSTI.GOV)

Pestana, Luis Ruiz; Minnetian, Natalie; Lammers, Laura Nielsen

When driven out of equilibrium, many diverse systems can form complex spatial and dynamical patterns, even in the absence of attractive interactions. Using kinetic Monte Carlo simulations, we investigate the phase behavior of a binary system of particles of dissimilar size confined between semiflexible planar surfaces, in which the nanoconfinement introduces a non-local coupling between particles, which we model as an activation energy barrier to diffusion that decreases with the local fraction of the larger particle. The system autonomously reaches a cyclical non-equilibrium state characterized by the formation and dissolution of metastable micelle-like clusters with the small particles in themore » core and the large ones in the surrounding corona. The power spectrum of the fluctuations in the aggregation number exhibits 1/f noise reminiscent of self-organized critical systems. Finally, we suggest that the dynamical metastability of the micellar structures arises from an inversion of the energy landscape, in which the relaxation dynamics of one of the species induces a metastable phase for the other species.« less

Mechanisms of boron diffusion in silicon and germanium

NASA Astrophysics Data System (ADS)

Mirabella, S.; De Salvador, D.; Napolitani, E.; Bruno, E.; Priolo, F.

2013-01-01

B migration in Si and Ge matrices raised a vast attention because of its influence on the production of confined, highly p-doped regions, as required by the miniaturization trend. In this scenario, the diffusion of B atoms can take place under severe conditions, often concomitant, such as very large concentration gradients, non-equilibrium point defect density, amorphous-crystalline transition, extrinsic doping level, co-doping, B clusters formation and dissolution, ultra-short high-temperature annealing. In this paper, we review a large amount of experimental work and present our current understanding of the B diffusion mechanism, disentangling concomitant effects and describing the underlying physics. Whatever the matrix, B migration in amorphous (α-) or crystalline (c-) Si, or c-Ge is revealed to be an indirect process, activated by point defects of the hosting medium. In α-Si in the 450-650 °C range, B diffusivity is 5 orders of magnitude higher than in c-Si, with a transient longer than the typical amorphous relaxation time. A quick B precipitation is also evidenced for concentrations larger than 2 × 1020 B/cm3. B migration in α-Si occurs with the creation of a metastable mobile B, jumping between adjacent sites, stimulated by dangling bonds of α-Si whose density is enhanced by B itself (larger B density causes higher B diffusivity). Similar activation energies for migration of B atoms (3.0 eV) and of dangling bonds (2.6 eV) have been extracted. In c-Si, B diffusion is largely affected by the Fermi level position, occurring through the interaction between the negatively charged substitutional B and a self-interstitial (I) in the neutral or doubly positively charged state, if under intrinsic or extrinsic (p-type doping) conditions, respectively. After charge exchanges, the migrating, uncharged BI pair is formed. Under high n-type doping conditions, B diffusion occurs also through the negatively charged BI pair, even if the migration is depressed by Coulomb pairing with n-type dopants. The interplay between B clustering and migration is also modeled, since B diffusion is greatly affected by precipitation. Small (below 1 nm) and relatively large (5-10 nm in size) BI clusters have been identified with different energy barriers for thermal dissolution (3.6 or 4.8 eV, respectively). In c-Ge, B motion is by far less evident than in c-Si, even if the migration mechanism is revealed to be similarly assisted by Is. If Is density is increased well above the equilibrium (as during ion irradiation), B diffusion occurs up to quite large extents and also at relatively low temperatures, disclosing the underlying mechanism. The lower B diffusivity and the larger activation barrier (4.65 eV, rather than 3.45 eV in c-Si) can be explained by the intrinsic shortage of Is in Ge and by their large formation energy. B diffusion can be strongly enhanced with a proper point defect engineering, as achieved with embedded GeO2 nanoclusters, causing at 650 °C a large Is supersaturation. These aspects of B diffusion are presented and discussed, modeling the key role of point defects in the two different matrices.

Transfer Kinetics at the Aqueous/Non-Aqueous Phase Liquid Interface. A Statistical Mechanic Approach

NASA Astrophysics Data System (ADS)

Doss, S. K.; Ezzedine, S.; Ezzedine, S.; Ziagos, J. P.; Hoffman, F.; Gelinas, R. J.

2001-05-01

Many modeling efforts in the literature use a first-order, linear-driving-force model to represent the chemical dissolution process at the non-aqueous/aqueous phase liquid (NAPL/APL) interface. In other words, NAPL to APL phase flux is assumed to be equal to the difference between the solubility limit and the "bulk aqueous solution" concentrations times a mass transfer coefficient. Under such assumptions, a few questions are raised: where, in relation to a region of pure NAPL, does the "bulk aqueous solution" regime begin and how does it behave? The answers are assumed to be associated with an arbitrary, predetermined boundary layer, which separates the NAPL from the surrounding solution. The mass transfer rate is considered to be, primarily, limited by diffusion of the component through the boundary layer. In fact, compositional models of interphase mass transfer usually assume that a local equilibrium is reached between phases. Representing mass flux as a rate-limiting process is equivalent to assuming diffusion through a stationary boundary layer with an instantaneous local equilibrium and linear concentration profile. Some environmental researchers have enjoyed success explaining their data using chemical engineering-based correlations. Correlations are strongly dependent on the experimental conditions employed. A universally applicable theory for NAPL dissolution in natural systems does not exist. These correlations are usually expressed in terms of the modified Sherwood number as a function of Reynolds, Peclet, and Schmidt numbers. The Sherwood number may be interpreted as the ratio between the grain size and the thickness of the Nernst stagnant film. In the present study, we show that transfer kinetics at the NAPL/APL interface under equilibrium conditions disagree with approaches based on the Nernst stagnant film concept. It is unclear whether local equilibrium assumptions used in current models are suitable for all situations.A statistical mechanic framework has been chosen to study the transfer kinetic processes at the microscale level. The rationale for our approach is based on both the activation energy of transfer of an ion and its velocity across the NAPL/APL interface. There are four major energies controlling the interfacial NAPL dissolution kinetics: (de)solvation energy, interfacial tension energy, electrostatic energy, and thermal fluctuation energy. Transfer of an ion across the NAPL/APL interface is accelerated by the viscous forces which can be described using the averaged Langevin master equation. The resulting energies and viscous forces were combined using the Boltzmann probability distribution. Asymptotic time limits of the resulting kinetics lead to instantaneous local equilibrium conditions that contradict the Nernst equilibrium equation. The NAPL/APL interface is not an ideal one: it does not conserve energy and heat. In our case the interface is treated as a thin film or slush zone that alters the thermodynamic variables. Such added zone, between the two phases, is itself a phase, and, therefore, the equilibrium does not occur between two phases but rather three. All these findings led us to develop a new non-linearly coupled flow and transport system of equations which is able to account for specific chemical dissolution processes and precludes the need for empirical mass-transfer parameters. Work performed under the auspices of the U.S. Department of Energy by Lawrence Livermore National Laboratory under Contract W-7405-Eng-48.

Diffusion Behavior of Mn and Si Between Liquid Oxide Inclusions and Solid Iron-Based Alloy at 1473 K

NASA Astrophysics Data System (ADS)

Kim, Sun-Joong; Tago, Hanae; Kim, Kyung-Ho; Kitamura, Shin-ya; Shibata, Hiroyuki

2018-06-01

In order to clarify the changes in the composition of oxide inclusions in steel, the effect of the metal and oxide composition on the reaction between solid Fe-based alloys and liquid multi-component oxides was investigated using the diffusion couple method at 1473 K. The measured concentration gradients of Mn and Si in the metal indicated that Mn diffused into the metal from the oxide, while the diffusion of Si occurred in the opposite direction. In addition, the MnO content in the oxide decreased with heat treatment time, while the SiO2 content increased. The compositional changes in both phases indicated that the Mn content in the metal near the interface increased with heat treatment with decreasing MnO content in the oxide. Assuming local equilibrium at the interface, the calculated [Mn]2/[Si] ratio at the interface in equilibrium with the oxide increased with increases in the MnO/SiO2 ratio in the oxide. The difference in the [Mn]2/[Si] ratios between the interface and the metal matrix increased, which caused the diffusion of Mn and Si between the multi-component oxide and metal. By measuring the diffusion lengths of Mn and Si in the metal, the chemical diffusion coefficients of Mn and Si were obtained to calculate the composition changes in Mn and Si in the metal. The calculated changes in Mn and Si in the metal agreed with the experimental results.

Incomplete Loading of Sodium Lauryl Sulfate and Fasted State Simulated Intestinal Fluid Micelles Within the Diffusion Layers of Dispersed Drug Particles During Dissolution.

PubMed

Galipeau, Kendra; Socki, Michael; Socia, Adam; Harmon, Paul A

2018-01-01

Poorly water soluble drug candidates have been common in developmental pipelines over the last several decades. This has fueled considerable research around understanding how bile salt and model micelles can improve drug particle dissolution rates and human drug exposure levels. However, in the pharmaceutical context only a single mechanism of how micelles load solute has been assumed, that being the direct loading mechanism put forth by Cussler and coworkers (Am Inst Chem Eng J. 1976;22(6):1006-1012) 40 years ago. In this model, micelles load at the particle surface and will be loaded to their equilibrium loading values. More recently, Kumar and Gandhi and coworkers (Langmuir. 2003;19:4014-4026) developed a comprehensive theory of micelle solubilization which also features an indirect loading mechanism which they argue should operate in ionic surfactant systems. In this mechanism, micelles cannot directly load at the solute particle surface and thus may not reach equilibrium loading values within the particle diffusion layer. In this work, we endeavor to understand if the indirect micelle loading mechanism represents a plausible description in the pharmaceutical context. The overall data in SLS and FaSSIF systems obtained here, as well as several other previously published datasets, can be described by the indirect micelle loading mechanism. Implications for pharmaceutical development of poorly soluble compounds are discussed. Copyright © 2018. Published by Elsevier Inc.

Modeling electronegative plasma discharge

DOE Office of Scientific and Technical Information (OSTI.GOV)

Lichtenberg, A.J.; Lieberman, M.A.

Macroscopic analytic models for a three-component electronegative gas discharge are developed. Assuming the negative ions to be in Boltzmann equilibrium, a positive ion ambipolar diffusion equation is derived. The discharge consists of an electronegative core and electropositive edges. The electron density in the core is nearly uniform, allowing a parabolic approximation to the plasma profile to be employed. The resulting equilibrium equations are solved analytically and matched to a constant mobility transport model of an electropositive edge plasma. The solutions are compared to a simulation of a parallel-plane r.f. driven oxygen plasma for p = 50 mTorr and n{sub eo}=more » 2.4 x 10{sup 15} m{sup -3}. The ratio {alpha}{sub o} of central negative ion density to electron density, and the electron temperature T{sub e}, found in the simulation, are in reasonable agreement with the values calculated from the model. The model is extended to: (1) low pressures, where a variable mobility model is used in the electropositive edge region; and (2) high {alpha}{sub o} in which the edge region disappears. The inclusion of a second positive ion species, which can be very important in describing electronegative discharges used for materials processing, is a possible extension of the model.« less

Global exponential stability of BAM neural networks with time-varying delays and diffusion terms

NASA Astrophysics Data System (ADS)

Wan, Li; Zhou, Qinghua

2007-11-01

The stability property of bidirectional associate memory (BAM) neural networks with time-varying delays and diffusion terms are considered. By using the method of variation parameter and inequality technique, the delay-independent sufficient conditions to guarantee the uniqueness and global exponential stability of the equilibrium solution of such networks are established.

Simulation of adsorbed hydrogen on tungsten surface

NASA Astrophysics Data System (ADS)

Degtyarenko, N. N.; Pisarev, A. A.

2017-12-01

Calculations of the energy of the H-W system were performed using DFT method based on plane waves. Adsorption energies, equilibrium states, vibration spectra, saddle points, activation energies of jumps, and diffusion paths have been analyzed for H atom on W(100) and W(110). Diffusion coefficient for H on W(110) agrees very well with experimental data.

Steam stripping of the unsaturated zone of contaminated sub-soils: The effect of diffusion/dispersion in the start-up phase

NASA Astrophysics Data System (ADS)

Brouwers, H. J. H.; Gilding, B. H.

2006-02-01

The unsteady process of steam stripping of the unsaturated zone of soils contaminated with volatile organic compounds (VOCs) is addressed. A model is presented. It accounts for the effects of water and contaminants remaining in vapour phase, as well as diffusion and dispersion of contaminants in this phase. The model has two components. The first is a one-dimensional description of the propagation of a steam front in the start-up phase. This is based on Darcy's law and conservation laws of mass and energy. The second component describes the transport of volatile contaminants. Taking the view that non-equilibrium between liquid and vapour phases exists, it accounts for evaporation, transport, and condensation at the front. This leads to a moving-boundary problem. The moving-boundary problem is brought into a fixed domain by a suitable transformation of the governing partial differential equations, and solved numerically. For a broad range of the governing dimensionless numbers, such as the Henry, Merkel and Péclet numbers, computational results are discussed. A mathematical asymptotic analysis supports this discussion. The range of parameter values for which the model is valid is investigated. Diffusion and dispersion are shown to be of qualitative importance, but to have little quantitative effect in the start-up phase.

The complex fluid dynamics of simple diffusion

NASA Astrophysics Data System (ADS)

Vold, Erik

2017-11-01

Diffusion as the mass transport process responsible for mixing fluids at the atomic level is often underestimated in its complexity. An initial discontinuity between two species of different atomic masses exhibits a mass density discontinuity under isothermal pressure equilibrium implying equal species molar densities. The self-consistent kinetic transport processes across such an interface leads to a zero sum of mass flux relative to the center of mass and so diffusion alone cannot relax an initially stationary mass discontinuity nor broaden the density profile at the interface. The diffusive mixing leads to a molar imbalance which drives a center of mass velocity which moves the heavier species toward the lighter species leading to the interfacial density relaxation. Simultaneously, the species non-zero molar flux modifies the pressure profile in a transient wave and in a local perturbation. The resulting center of mass velocity has two components; one, associated with the divergence of the flow, persists in the diffusive mixing region throughout the diffusive mixing process, and two, travelling waves at the front of the pressure perturbations propagate away from the mixing region. The momentum in these waves is necessary to maintain momentum conservation in the center of mass frame. Thus, in a number of ways, the diffusive mixing provides feedback into the small scale advective motions. Numerical methods which diffuse all species assuming P-T equilibrium may not recover the subtle dynamics of mass transport at an interface. Work performed by the LANS, LLC, under USDOE Contract No. DE-AC52-06NA25396, funded by the (ASC) Program.

Magma Dynamics at Mid-Ocean Ridges by Noble Gas Kinetic Fractionation: Assessment of Magmatic Ascent Rates and Mantle Composition

NASA Astrophysics Data System (ADS)

Paonita, A.; Martelli, M.

2007-12-01

Topical scientific literature on magma degassing at mid-ocean ridges more and more focuses on exsolution processes occurring under conditions that are far from thermodynamic equilibrium between bubbles and silicate melt. Indeed, the dynamics of magma ascent and decompression can be faster than that of CO2 diffusion into bubbles, in which case the diffusivity ratios among volatiles are the main control of the composition of the exsolving gas phase. We have developed a model of bubble growth in silicate melts that calculates the extent of both CO2 supersaturation and kinetic fractionation among noble gases in vesicles in relation to the decompressive rate of basaltic melts. The model predicts that, due to comparable Ar and CO2 diffusivity, magma degassing at low pressure fractionates both He/Ar and He/CO2 ratios by a similar extent, while the slower CO2 diffusion at high pressure causes early kinetic effects on Ar/CO2 ratio and dramatically changes the degassing paths. By using this tool, we have reviewed the global He-Ar-CO2 dataset of fluid inclusions in mid-ocean-ridge glasses. We display that non-equilibrium fractionations among He, Ar and CO2, driven by their different diffusivities in silicate melts, are common in most of the natural conditions of magma decompression and their signature strongly depends on pressure of degassing. The different geochemical signatures among suites of data coming from different ridge segments mainly depend on the depth of the magma chamber where the melt was stored. Moreover, variations inside a single suite emerge due to the interplay between variable ascent speed of magma and cooling rate of the emplaced lava. As a result, two data groups coming from the Pito Seamount suite (Easter Microplate East ridge), showing different degree of CO2 supersaturation and He/Ar fractionation, provide ascent rates which differ by ten folds or even more. The large variations in both the He/CO2 and Ar/CO2 ratios at almost constant He/Ar, displayed in products coming from the Mid-Atlantic Ridge 24°N segment and the Rodriguez Triple Junction, require magma storage and degassing processes occurring at high-pressure conditions. In contrast, the simultaneous increase in both He/CO2 and He/Ar of the East Pacific Rise and South-East Indian Ridge data sets suggests the dominance of low-pressure fractionation, implying that the shallow magma chambers are at a lower depth than those of the Mid-Atlantic Ridge 24°N and Rodriguez Triple Junction. Our conclusions support the presence of a relationship between spreading rate and depth of high-temperature zones below ridges, and are consistent with the depth of magma chambers as suggested from seismic studies. Finally, the non-equilibrium degassing model provides striking constraints on the compositions of noble gases and carbon in mantle-derived magmas. Our results dispense in fact with the supposed need for He-Ar-CO2 heterogeneities in the upper mantle, because the degassing of a single, popping-rock-like primary magma is able to explain all the available data.

Modeling diffusion control on organic matter decomposition in unsaturated soil pore space

NASA Astrophysics Data System (ADS)

Vogel, Laure; Pot, Valérie; Garnier, Patricia; Vieublé-Gonod, Laure; Nunan, Naoise; Raynaud, Xavier; Chenu, Claire

2014-05-01

Soil Organic Matter decomposition is affected by soil structure and water content, but field and laboratory studies about this issue conclude to highly variable outcomes. Variability could be explained by the discrepancy between the scale at which key processes occur and the measurements scale. We think that physical and biological interactions driving carbon transformation dynamics can be best understood at the pore scale. Because of the spatial disconnection between carbon sources and decomposers, the latter rely on nutrient transport unless they can actively move. In hydrostatic case, diffusion in soil pore space is thus thought to regulate biological activity. In unsaturated conditions, the heterogeneous distribution of water modifies diffusion pathways and rates, thus affects diffusion control on decomposition. Innovative imaging and modeling tools offer new means to address these effects. We have developed a new model based on the association between a 3D Lattice-Boltzmann Model and an adimensional decomposition module. We designed scenarios to study the impact of physical (geometry, saturation, decomposers position) and biological properties on decomposition. The model was applied on porous media with various morphologies. We selected three cubic images of 100 voxels side from µCT-scanned images of an undisturbed soil sample at 68µm resolution. We used LBM to perform phase separation and obtained water phase distributions at equilibrium for different saturation indices. We then simulated the diffusion of a simple soluble substrate (glucose) and its consumption by bacteria. The same mass of glucose was added as a pulse at the beginning of all simulations. Bacteria were placed in few voxels either regularly spaced or concentrated close to or far from the glucose source. We modulated physiological features of decomposers in order to weight them against abiotic conditions. We could evidence several effects creating unequal substrate access conditions for decomposers, hence inducing contrasted decomposition kinetics: position of bacteria relative to the substrate diffusion pathways, diffusion rate and hydraulic connectivity between bacteria and substrate source, local substrate enrichment due to restricted mass transfer. Physiological characteristics had a strong impact on decomposition only when glucose diffused easily but not when diffusion limitation prevailed. This suggests that carbon dynamics should not be considered to derive from decomposers' physiology alone but rather from the interactions of biological and physical processes at the microscale.

Current understanding of point defects and diffusion processes in silicon

NASA Technical Reports Server (NTRS)

Tan, T. Y.; Goesele, U.

1985-01-01

The effects of oxidation of Si which established that vacancies (V) and Si self interstitials (I) coexist in Si at high temperatures under thermal equilibrium and oxidizing conditions are discussed. Some essential points associated with Au diffusion in Si are then discussed. Analysis of Au diffusion results allowed a determination of the I component and an estimate of the V component of the Si self diffusion coefficient. A discussion of theories on high concentration P diffusion into Si is then presented. Although presently there still is no theory that is completely satisfactory, significant progresses are recently made in treating some essential aspects of this subject.

Maximum entropy production principle for geostrophic turbulence

NASA Astrophysics Data System (ADS)

Sommeria, J.; Bouchet, F.; Chavanis, P. H.

2003-04-01

In 2D turbulence, complex stirring leads to the formation of steady organized states, once fine scale fluctuations have been filtered out. This self-organization can be explained in terms of statistical equilibrium for vorticity, as the most likely outcome of vorticity parcel rearrangements with the constraints of the conservation laws. A mixing entropy describing the vorticity rearrangements is introduced. Extension to the shallow water system has been proposed by Chavanis P.H. and Sommeria J. (2002), Phys. Rev. E. Generalization to multi-layer geostrophic flows is formally straightforward. Outside equilibrium, eddy fluxes should drive the system toward equilibrium, in the spirit of non equilibrium linear thermodynamics. This can been formalized in terms of a principle of maximum entropy production (MEP), as shown by Robert and Sommeria (1991), Phys. Rev. Lett. 69. Then a parameterization of eddy fluxes is obtained, involving an eddy diffusivity plus a drift term acting at larger scale. These two terms balance each other at equilibrium, resulting in a non trivial steady flow, which is the mean state of the statistical equilibrium. Applications of this eddy parametrization will be presented, in the context of oceanic circulation and Jupiter's Great Red Spot. Quantitative tests will be discussed, obtained by comparisons with direct numerical simulations. Kinetic models, inspired from plasma physics, provide a more precise description of the relaxation toward equilibrium, as shown by Chavanis P.H. 2000 ``Quasilinear theory of the 2D Euler equation'', Phys. Rev. Lett. 84. This approach provides relaxation equations with a form similar to the MEP, but not identical. In conclusion, the MEP provides the right trends of the system but its precise justification remains elusive.

The allele-frequency spectrum in a decoupled Moran model with mutation, drift, and directional selection, assuming small mutation rates.

PubMed

Vogl, Claus; Clemente, Florian

2012-05-01

We analyze a decoupled Moran model with haploid population size N, a biallelic locus under mutation and drift with scaled forward and backward mutation rates θ(1)=μ(1)N and θ(0)=μ(0)N, and directional selection with scaled strength γ=sN. With small scaled mutation rates θ(0) and θ(1), which is appropriate for single nucleotide polymorphism data in highly recombining regions, we derive a simple approximate equilibrium distribution for polymorphic alleles with a constant of proportionality. We also put forth an even simpler model, where all mutations originate from monomorphic states. Using this model we derive the sojourn times, conditional on the ancestral and fixed allele, and under equilibrium the distributions of fixed and polymorphic alleles and fixation rates. Furthermore, we also derive the distribution of small samples in the diffusion limit and provide convenient recurrence relations for calculating this distribution. This enables us to give formulas analogous to the Ewens-Watterson estimator of θ for biased mutation rates and selection. We apply this theory to a polymorphism dataset of fourfold degenerate sites in Drosophila melanogaster. Copyright © 2012 Elsevier Inc. All rights reserved.

Kinetic and equilibrium characteristics of sorption of saponin of Quillaja Saponaria Molina on chitosan

NASA Astrophysics Data System (ADS)

Mironenko, N. V.; Smuseva, S. O.; Brezhneva, T. A.; Selemenev, V. F.

2016-12-01

The equilibrium and kinetic curves of the sorption of saponin of Quillaja saponaria molina on chitosan were analyzed. The inner diffusion was found to be limiting, and its coefficients were calculated. It was found that the form of the curves of the sorption isotherms of saponin is determined by the competing processes of association in solution and absorption by chitosan.

Truncation effect on Taylor-Aris dispersion in lattice Boltzmann schemes: Accuracy towards stability

NASA Astrophysics Data System (ADS)

Ginzburg, Irina; Roux, Laetitia

2015-10-01

The Taylor dispersion in parabolic velocity field provides a well-known benchmark for advection-diffusion (ADE) schemes and serves as a first step towards accurate modeling of the high-order non-Gaussian effects in heterogeneous flow. While applying the Lattice Boltzmann ADE two-relaxation-times (TRT) scheme for a transport with given Péclet number (Pe) one should select six free-tunable parameters, namely, (i) molecular-diffusion-scale, equilibrium parameter; (ii) three families of equilibrium weights, assigned to the terms of mass, velocity and numerical-diffusion-correction, and (iii) two relaxation rates. We analytically and numerically investigate the respective roles of all these degrees of freedom in the accuracy and stability in the evolution of a Gaussian plume. For this purpose, the third- and fourth-order transient multi-dimensional analysis of the recurrence equations of the TRT ADE scheme is extended for a spatially-variable velocity field. The key point is in the coupling of the truncation and Taylor dispersion analysis which allows us to identify the second-order numerical correction δkT to Taylor dispersivity coefficient kT. The procedure is exemplified for a straight Poiseuille flow where δkT is given in a closed analytical form in equilibrium and relaxation parameter spaces. The predicted longitudinal dispersivity is in excellent agreement with the numerical experiments over a wide parameter range. In relatively small Pe-range, the relative dispersion error increases with Péclet number. This deficiency reduces in the intermediate and high Pe-range where it becomes Pe-independent and velocity-amplitude independent. Eliminating δkT by a proper parameter choice and employing specular reflection for zero flux condition on solid boundaries, the d2Q9 TRT ADE scheme may reproduce the Taylor-Aris result quasi-exactly, from very coarse to fine grids, and from very small to arbitrarily high Péclet numbers. Since free-tunable product of two eigenfunctions also controls stability of the model, the validity of the analytically established von Neumann stability diagram is examined in Poiseuille profile. The simplest coordinate-stencil subclass, which is the d2Q5 TRT bounce-back scheme, demonstrates the best performance and achieves the maximum accuracy for most stable relaxation parameters.

Comparison of transport properties models for numerical simulations of Mars entry vehicles

NASA Astrophysics Data System (ADS)

Hao, Jiaao; Wang, Jingying; Gao, Zhenxun; Jiang, Chongwen; Lee, Chunhian

2017-01-01

Effects of two different models for transport properties, including the approximate model and the collision integral model, on hypersonic flow simulations of Mars entry vehicles are numerically investigated. A least square fitting is firstly performed using the best-available data of collision integrals for Martian atmosphere species within the temperature range of 300-20,000 K. Then, the performance of these two transport properties models are compared for an equilibrium Martian atmosphere gas mixture at 10 kPa and temperatures ranging from 1000 to 10,000 K. Finally, four flight conditions chosen from the trajectory of the Mars Pathfinder entry vehicle are numerically simulated. It is indicated that the approximate model is capable of accurately providing the distributions of species mass fractions and temperatures in the flowfield. Both models give similar translational-rotational and vibrational heat fluxes. However, the chemical diffusion heat fluxes predicted by the approximate model are significantly larger than the results computed by the collision integral model, particularly in the vicinity of the forebody stagnation point, whose maximum relative error of 15% for the super-catalytic case. The diffusion model employed in the approximate model is responsible to the discrepancy. In addition, the wake structure is largely unaffected by the transport properties models.

Optimization of the combined ultrasonic assisted/adsorption method for the removal of malachite green by gold nanoparticles loaded on activated carbon: Experimental design

NASA Astrophysics Data System (ADS)

Roosta, M.; Ghaedi, M.; Shokri, N.; Daneshfar, A.; Sahraei, R.; Asghari, A.

2014-01-01

The present study was aimed to experimental design optimization applied to removal of malachite green (MG) from aqueous solution by ultrasound-assisted removal onto the gold nanoparticles loaded on activated carbon (Au-NP-AC). This nanomaterial was characterized using different techniques such as FESEM, TEM, BET, and UV-vis measurements. The effects of variables such as pH, initial dye concentration, adsorbent dosage (g), temperature and sonication time on MG removal were studied using central composite design (CCD) and the optimum experimental conditions were found with desirability function (DF) combined response surface methodology (RSM). Fitting the experimental equilibrium data to various isotherm models such as Langmuir, Freundlich, Tempkin and Dubinin-Radushkevich models show the suitability and applicability of the Langmuir model. Kinetic models such as pseudo -first order, pseudo-second order, Elovich and intraparticle diffusion models applicability was tested for experimental data and the second-order equation and intraparticle diffusion models control the kinetic of the adsorption process. The small amount of proposed adsorbent (0.015 g) is applicable for successful removal of MG (RE > 99%) in short time (4.4 min) with high adsorption capacity (140-172 mg g-1).

Clines in quantitative traits: The role of migration patterns and selection scenarios

PubMed Central

Geroldinger, Ludwig; Bürger, Reinhard

2015-01-01

The existence, uniqueness, and shape of clines in a quantitative trait under selection toward a spatially varying optimum is studied. The focus is on deterministic diploid two-locus n-deme models subject to various migration patterns and selection scenarios. Migration patterns may exhibit isolation by distance, as in the stepping-stone model, or random dispersal, as in the island model. The phenotypic optimum may change abruptly in a single environmental step, more gradually, or not at all. Symmetry assumptions are imposed on phenotypic optima and migration rates. We study clines in the mean, variance, and linkage disequilibrium (LD). Clines result from polymorphic equilibria. The possible equilibrium configurations are determined as functions of the migration rate. Whereas for weak migration, many polymorphic equilibria may be simultaneously stable, their number decreases with increasing migration rate. Also for intermediate migration rates polymorphic equilibria are in general not unique, however, for loci of equal effects the corresponding clines in the mean, variance, and LD are unique. For sufficiently strong migration, no polymorphism is maintained. Both migration pattern and selection scenario exert strong influence on the existence and shape of clines. The results for discrete demes are compared with those from models in which space varies continuously and dispersal is modeled by diffusion. Comparisons with previous studies, which investigated clines under neutrality or under linkage equilibrium, are performed. If there is no long-distance migration, the environment does not change abruptly, and linkage is not very tight, populations are almost everywhere close to linkage equilibrium. PMID:25446959

Kinetic sorption of contaminants of emerging concern by a palygorskite-montmorillonite filter medium.

PubMed

Berhane, Tedros M; Levy, Jonathan; Krekeler, Mark P S; Danielson, Neil D

2017-06-01

Kinetic sorption of bisphenol A (BPA), carbamazepine (CMZ) and ciprofloxacin (CIP) by three palygorskite-montmorillonite (Pal-Mt) granule sizes was studied. For BPA, CMZ and CIP, apparent sorption equilibrium was reached within about 3, 5 and 16 h, respectively. The highest and the lowest sorption capacities were by the small and the large granule sizes, respectively. Experimental results were compared to various sorption kinetics models to gain insights regarding the sorption processes and achieve a predictive capacity. The pseudo-second order (PSO) and the Elovich models performed the best while the pseudo-first order (PFO) model was only adequate for CMZ. The intraparticle-diffusion (IPD) model showed a two-step linear plot of BPA, CMZ and CIP sorption versus square root of time that was indicative of surface-sorption followed by IPD as a rate-limiting process before equilibrium was reached. Using the pseudo-first order (PFO) and the pseudo-second order (PSO) rate constants combined with previously-established Langmuir equilibrium sorption models, the kinetic sorption (k a ) and desorption (k d ) Langmuir kinetic rate constants were theoretically calculated for BPA and CIP. Kinetic sorption was then simulated using these theoretically calculated k a and k d values, and the simulations were compared to the observed behavior. The simulations fit the observed sorbed concentrations better during the early part of the experiments; the observed sorption during later times occurred more slowly than expected, supporting the hypothesis that IPD becomes a rate-limiting process during the course of the experiment. Copyright © 2017 Elsevier Ltd. All rights reserved.

Configurational Entropy Approach to the Kinetics of Glasses

PubMed Central

Di Marzio, Edmund A.; Yang, Arthur J. M.

1997-01-01

A kinetic theory of glasses is developed using equilibrium theory as a foundation. After establishing basic criteria for glass formation and the capability of the equilibrium entropy theory to describe the equilibrium aspects of glass formation, a minimal model for the glass kinetics is proposed. Our kinetic model is based on a trapping description of particle motion in which escapes from deep wells provide the rate-determining steps for motion. The formula derived for the zero frequency viscosity η (0,T) is log η (0,T) = B − AF(T)kT where F is the free energy and T the temperature. Contrast this to the Vogel-Fulcher law log η (0,T) = B + A/(T − Tc). A notable feature of our description is that even though the location of the equilibrium second-order transition in temperature-pressure space is given by the break in the entropy or volume curves the viscosity and its derivative are continuous through the transition. The new expression for η (0,T) has no singularity at a critical temperature Tc as in the Vogel-Fulcher law and the behavior reduces to the Arrhenius form in the glass region. Our formula for η (0,T) is discussed in the context of the concepts of strong and fragile glasses, and the experimentally observed connection of specific heat to relaxation response in a homologous series of polydimethylsiloxane is explained. The frequency and temperature dependencies of the complex viscosity η (ω< T), the diffusion coefficient D(ω< T), and the dielectric response ε (ω< T) are also obtained for our kinetic model and found to be consistent with stretched exponential behavior. PMID:27805133

Non-equilibrium time evolution of higher order cumulants of conserved charges and event-by-event analysis

NASA Astrophysics Data System (ADS)

Kitazawa, Masakiyo; Asakawa, Masayuki; Ono, Hirosato

2014-01-01

We investigate the time evolution of higher order cumulants of conserved charges in a volume with the diffusion master equation. Applying the result to the diffusion of non-Gaussian fluctuations in the hadronic stage of relativistic heavy ion collisions, we show that the fourth-order cumulant of net-electric charge at LHC energy is suppressed compared with the recently observed second-order cumulant at ALICE, if the higher order cumulants at hadronization are suppressed compared with their values in the hadron phase in equilibrium. The significance of the experimental information on the rapidity window dependence of various cumulants in investigating the history of the dynamical evolution of the hot medium created in relativistic heavy ion collisions is emphasized.

Populational equilibrium through exosome-mediated Wnt signaling in tumor progression of diffuse large B-cell lymphoma.

PubMed

Koch, Raphael; Demant, Martin; Aung, Thiha; Diering, Nina; Cicholas, Anna; Chapuy, Bjoern; Wenzel, Dirk; Lahmann, Marlen; Güntsch, Annemarie; Kiecke, Christina; Becker, Sabrina; Hupfeld, Timo; Venkataramani, Vivek; Ziepert, Marita; Opitz, Lennart; Klapper, Wolfram; Trümper, Lorenz; Wulf, Gerald G

2014-04-03

Tumors are composed of phenotypically heterogeneous cell populations. The nongenomic mechanisms underlying transitions and interactions between cell populations are largely unknown. Here, we show that diffuse large B-cell lymphomas possess a self-organized infrastructure comprising side population (SP) and non-SP cells, where transitions between clonogenic states are modulated by exosome-mediated Wnt signaling. DNA methylation modulated SP-non-SP transitions and was correlated with the reciprocal expressions of Wnt signaling pathway agonist Wnt3a in SP cells and the antagonist secreted frizzled-related protein 4 in non-SP cells. Lymphoma SP cells exhibited autonomous clonogenicity and exported Wnt3a via exosomes to neighboring cells, thus modulating population equilibrium in the tumor.

Equilibrium, kinetic, and reactive transport models for plutonium

NASA Astrophysics Data System (ADS)

Schwantes, Jon Michael

Equilibrium, kinetic, and reactive transport models for plutonium (Pu) have been developed to help meet environmental concerns posed by past war-related and present and future peacetime nuclear technologies. A thorough review of the literature identified several hurdles that needed to be overcome in order to develop capable predictive tools for Pu. These hurdles include: (1) missing or ill-defined chemical equilibrium and kinetic constants for environmentally important Pu species; (2) no adequate conceptual model describing the formation of Pu oxy/hydroxide colloids and solids; and (3) an inability of two-phase reactive transport models to adequately simulate Pu behavior in the presence of colloids. A computer program called INVRS K was developed that integrates the geochemical modeling software of PHREEQC with a nonlinear regression routine. This program provides a tool for estimating equilibrium and kinetic constants from experimental data. INVRS K was used to regress on binding constants for Pu sorbing onto various mineral and humic surfaces. These constants enhance the thermodynamic database for Pu and improve the capability of current predictive tools. Time and temperature studies of the Pu intrinsic colloid were also conducted and results of these studies were presented here. Formation constants for the fresh and aged Pu intrinsic colloid were regressed upon using INVRS K. From these results, it was possible to develop a cohesive diagenetic model that describes the formation of Pu oxy/hydroxide colloids and solids. This model provides for the first time a means of deciphering historically unexplained observations with respect to the Pu intrinsic colloid, as well as a basis for simulating the behavior within systems containing these solids. Discussion of the development and application of reactive transport models is also presented and includes: (1) the general application of a 1-D in flow, three-phase (i.e., dissolved, solid, and colloidal), reactive transport model; (2) a simulation of the effects of dissolution of PuO2 solid and radiolysis on the behavior of Pu diffusing out of a confined pore space; and (3) application of a steady-state three phase reactive transport model to groundwater at the Nevada Test Site.

The non-equilibrium allele frequency spectrum in a Poisson random field framework.

PubMed

Kaj, Ingemar; Mugal, Carina F

2016-10-01

In population genetic studies, the allele frequency spectrum (AFS) efficiently summarizes genome-wide polymorphism data and shapes a variety of allele frequency-based summary statistics. While existing theory typically features equilibrium conditions, emerging methodology requires an analytical understanding of the build-up of the allele frequencies over time. In this work, we use the framework of Poisson random fields to derive new representations of the non-equilibrium AFS for the case of a Wright-Fisher population model with selection. In our approach, the AFS is a scaling-limit of the expectation of a Poisson stochastic integral and the representation of the non-equilibrium AFS arises in terms of a fixation time probability distribution. The known duality between the Wright-Fisher diffusion process and a birth and death process generalizing Kingman's coalescent yields an additional representation. The results carry over to the setting of a random sample drawn from the population and provide the non-equilibrium behavior of sample statistics. Our findings are consistent with and extend a previous approach where the non-equilibrium AFS solves a partial differential forward equation with a non-traditional boundary condition. Moreover, we provide a bridge to previous coalescent-based work, and hence tie several frameworks together. Since frequency-based summary statistics are widely used in population genetics, for example, to identify candidate loci of adaptive evolution, to infer the demographic history of a population, or to improve our understanding of the underlying mechanics of speciation events, the presented results are potentially useful for a broad range of topics. Copyright © 2016 Elsevier Inc. All rights reserved.

The influence of vertical sorbed phase transport on the fate of organic chemicals in surface soils.

PubMed

McLachlan, Michael S; Czub, Gertje; Wania, Frank

2002-11-15

Gaseous exchange between surface soil and the atmosphere is an important process in the environmental fate of many chemicals. It was hypothesized that this process is influenced by vertical transport of chemicals sorbed to soil particles. Vertical sorbed phase transport in surface soils occurs by many processes such as bioturbation, cryoturbation, and erosion into cracks formed by soil drying. The solution of the advection/diffusion equation proposed by Jury et al. to describe organic chemical fate in a uniformly contaminated surface soil was modified to include vertical sorbed phase transport This process was modeled using a sorbed phase diffusion coefficient, the value of which was derived from soil carbon mass balances in the literature. The effective diffusivity of the chemical in a typical soil was greater in the modified model than in the model without sorbed phase transport for compounds with log K(OW) > 2 and log K(OA) > 6. Within this chemical partitioning space, the rate of volatilization from the surface soil was larger in the modified model than in the original model by up to a factor of 65. The volatilization rate was insensitive to the value of the sorbed phase diffusion coefficient throughout much of this chemical partitioning space, indicating that the surface soil layer was essentially well-mixed and that the mass transfer coefficient was determined by diffusion through the atmospheric boundary layer only. When this process was included in a non-steady-state regional multimedia chemical fate model running with a generic emissions scenario to air, the predicted soil concentrations increased by upto a factor of 25,whilethe air concentrations decreased by as much as a factor of approximately 3. Vertical sorbed phase transport in the soil thus has a major impact on predicted air and soil concentrations, the state of equilibrium, and the direction and magnitude of the chemical flux between air and soil. It is a key process influencing the environmental fate of persistent organic pollutants (POPs).

Invariant characteristics of self-organization modes in Belousov reaction modeling

NASA Astrophysics Data System (ADS)

Glyzin, S. D.; Goryunov, V. E.; Kolesov, A. Yu

2018-01-01

We consider the problem of mathematical modeling of oxidation-reduction oscillatory chemical reactions based on the mechanism of Belousov reaction. The process of the main components interaction in such reaction can be interpreted by a phenomenologically similar to it “predator-prey” model. Thereby, we consider a parabolic boundary value problem consisting of three Volterra-type equations, which is a mathematical model of this reaction. We carry out a local study of the neighborhood of the system’s non-trivial equilibrium state and construct the normal form of the considering system. Finally, we do a numerical analysis of the coexisting chaotic oscillatory modes of the boundary value problem in a flat area, which have different nature and occur as the diffusion coefficient decreases.

Sorption reaction mechanism of some hazardous radionuclides from mixed waste by impregnated crown ether onto polymeric resin.

PubMed

Shehata, F A; Attallah, M F; Borai, E H; Hilal, M A; Abo-Aly, M M

2010-02-01

A novel impregnated polymeric resin was practically tested as adsorbent material for removal of some hazardous radionuclides from radioactive liquid waste. The applicability for the treatment of low-level liquid radioactive waste was investigated. The material was prepared by loading 4,4'(5')di-t-butylbenzo 18 crown 6 (DtBB18C6) onto poly(acrylamide-acrylic acid-acrylonitril)-N, N'-methylenediacrylamide (P(AM-AA-AN)-DAM). The removal of (134)Cs, (60)Co, (65)Zn , and ((152+154))Eu onto P(AM-AA-AN)-DAM/DtBB18C6 was investigated using a batch equilibrium technique with respect to the pH, contact time, and temperature. Kinetic models are used to determine the rate of sorption and to investigate the mechanism of sorption process. Five kinetics models, pseudo-first-order, pseudo-second-order, intra-particle diffusion, homogeneous particle diffusion (HPDM), and Elovich models, were used to investigate the sorption process. The obtained results of kinetic models predicted that, pseudo-second-order is applicable; the sorption is controlled by particle diffusion mechanism and the process is chemisorption. The obtained values of thermodynamics parameters, DeltaH degrees , DeltaS degrees , and DeltaG degrees indicated that the endothermic nature, increased randomness at the solid/solution interface and the spontaneous nature of the sorption processes. Copyright (c) 2009 Elsevier Ltd. All rights reserved.

Diffusion and sorption of organic micropollutants in biofilms with varying thicknesses.

PubMed

Torresi, Elena; Polesel, Fabio; Bester, Kai; Christensson, Magnus; Smets, Barth F; Trapp, Stefan; Andersen, Henrik R; Plósz, Benedek Gy

2017-10-15

Solid-liquid partitioning is one of the main fate processes determining the removal of micropollutants in wastewater. Little is known on the sorption of micropollutants in biofilms, where molecular diffusion may significantly influence partitioning kinetics. In this study, the diffusion and the sorption of 23 micropollutants were investigated in novel moving bed biofilm reactor (MBBR) carriers with controlled biofilm thickness (50, 200 and 500 μm) using targeted batch experiments (initial concentration = 1 μg L -1 , for X-ray contrast media 15 μg L -1 ) and mathematical modelling. We assessed the influence of biofilm thickness and density on the dimensionless effective diffusivity coefficient f (equal to the biofilm-to-aqueous diffusivity ratio) and the distribution coefficient K d,eq (L g -1 ). Sorption was significant only for eight positively charged micropollutants (atenolol, metoprolol, propranolol, citalopram, venlafaxine, erythromycin, clarithromycin and roxithromycin), revealing the importance of electrostatic interactions with solids. Sorption equilibria were likely not reached within the duration of batch experiments (4 h), particularly for the thickest biofilm, requiring the calculation of the distribution coefficient K d,eq based on the approximation of the asymptotic equilibrium concentration (t > 4 h). K d,eq values increased with increasing biofilm thickness for all sorptive micropollutants (except atenolol), possibly due to higher porosity and accessible surface area in the thickest biofilm. Positive correlations between K d,eq and micropollutant properties (polarity and molecular size descriptors) were identified but not for all biofilm thicknesses, thus confirming the challenge of improving predictive sorption models for positively charged compounds. A diffusion-sorption model was developed and calibrated against experimental data, and estimated f values also increased with increasing biofilm thickness. This indicates that diffusion in thin biofilms may be strongly limited (f ≪ 0.1) by the high biomass density (reduced porosity). Copyright © 2017 Elsevier Ltd. All rights reserved.

Venus climate stability and volcanic resurfacing rates

NASA Technical Reports Server (NTRS)

Bullock, M. A.; Grinspoon, D. H.; Pollack, J. B.

1994-01-01

The climate of Venus is to a large degree controlled by the radiative properties of its massive atmosphere. In addition, outgassing due to volcanic activity, exospheric escape processes, and surface/atmosphere interactions may all be important in moderating the abundances of atmospheric CO2 and other volatiles. We have developed an evolutionary climate model for Venus using a systems approach that emphasizes feedbacks between elements in the climate system. Modules for atmospheric radiative transfer, surface/atmosphere interactions, tropospheric chemistry, and exospheric escape processes have so far been developed. Climate feedback loops result from interconnections between modules, in the form of the environmental parameters pressure, temperature, and atmospheric mixing ratios. The radiative transfer module has been implemented by using Rosseland mean opacities in a one dimensional grey radiative-convective model. The model has been solved for the static (time independent) case to determine climate equilibrium points. The dynamics of the model have also been explored by employing reaction/diffusion kinetics for possible surface atmosphere heterogeneous reactions over geologic timescales. It was found that under current conditions, the model predicts that the climate of Venus is at or near an unstable equilibrium point. The effects of constant rate volcanism and corresponding exsolution of volatiles on the stability of the climate model were also explored.

Characterizing super-spreading in microblog: An epidemic-based information propagation model

NASA Astrophysics Data System (ADS)

Liu, Yu; Wang, Bai; Wu, Bin; Shang, Suiming; Zhang, Yunlei; Shi, Chuan

2016-12-01

As the microblogging services are becoming more prosperous in everyday life for users on Online Social Networks (OSNs), it is more favorable for hot topics and breaking news to gain more attraction very soon than ever before, which are so-called "super-spreading events". In the information diffusion process of these super-spreading events, messages are passed on from one user to another and numerous individuals are influenced by a relatively small portion of users, a.k.a. super-spreaders. Acquiring an awareness of super-spreading phenomena and an understanding of patterns of wide-ranged information propagations benefits several social media data mining tasks, such as hot topic detection, predictions of information propagation, harmful information monitoring and intervention. Taking into account that super-spreading in both information diffusion and spread of a contagious disease are analogous, in this study, we build a parameterized model, the SAIR model, based on well-known epidemic models to characterize super-spreading phenomenon in tweet information propagation accompanied with super-spreaders. For the purpose of modeling information diffusion, empirical observations on a real-world Weibo dataset are statistically carried out. Both the steady-state analysis on the equilibrium and the validation on real-world Weibo dataset of the proposed model are conducted. The case study that validates the proposed model shows that the SAIR model is much more promising than the conventional SIR model in characterizing a super-spreading event of information propagation. In addition, numerical simulations are carried out and discussed to discover how sensitively the parameters affect the information propagation process.

Diffusion-driven fluid dynamics in ideal gases and plasmas

NASA Astrophysics Data System (ADS)

Vold, E. L.; Yin, L.; Taitano, W.; Molvig, K.; Albright, B. J.

2018-06-01

The classical transport theory based on Chapman-Enskog methods provides self-consistent approximations for the kinetic flux of mass, heat, and momentum in a fluid limit characterized with a small Knudsen number. The species mass fluxes relative to the center of mass, or "diffusive fluxes," are expressed as functions of known gradient quantities with kinetic coefficients evaluated using similar analyses for mixtures of gases or plasma components. The sum over species of the diffusive mass fluxes is constrained to be zero in the Lagrange frame, and thus results in a non-zero molar flux leading to a pressure perturbation. At an interface between two species initially in pressure equilibrium, the pressure perturbation driven by the diffusive molar flux induces a center of mass velocity directed from the species of greater atomic mass towards the lighter atomic mass species. As the ratio of the species particle masses increases, this center of mass velocity carries an increasingly greater portion of the mass across the interface and for a particle mass ratio greater than about two, the center of mass velocity carries more mass than the gradient driven diffusion flux. Early time transients across an interface between two species in a 1D plasma regime and initially in equilibrium are compared using three methods; a fluid code with closure in a classical transport approximation, a particle in cell simulation, and an implicit Fokker-Planck solver for the particle distribution functions. The early time transient phenomenology is shown to be similar in each of the computational simulation methods, including a pressure perturbation associated with the stationary "induced" component of the center of mass velocity which decays to pressure equilibrium during diffusion. At early times, the diffusive process generates pressure and velocity waves which propagate outward from the interface and are required to maintain momentum conservation. The energy in the outgoing waves dissipates as heat in viscous regions, and it is hypothesized that these diffusion driven waves may sustain fluctuations in less viscid finite domains after reflections from the boundaries. These fluid dynamic phenomena are similar in gases or plasmas and occur in flow transients with a moderate Knudsen number. The analysis and simulation results show how the kinetic flux, represented in the fluid transport closure, directly modifies the mass averaged flow described with the Euler equations.

Transscleral diffusion of ethacrynic acid and sodium fluorescein

PubMed Central

Lin, Cheng-Wen; Wang, Yong; Challa, Pratap; Epstein, David L.

2007-01-01

Purpose One of the current limitations in developing novel glaucoma drugs that target the trabecular meshwork (TM) is the induced corneal toxicity from eyedrop formulations. To avoid the corneal toxicity, an alternative approach would be to deliver TM drugs through the sclera. To this end, we quantified ex vivo diffusion coefficient of a potential TM drug, ethacrynic acid (ECA), and investigated mechanisms of ECA transport in the sclera. Methods An Ussing-type diffusion apparatus was built to measure the apparent diffusion coefficient of ECA in fresh porcine sclera at 4 °C. To understand mechanisms of ECA transport, we quantified the transscleral transport of a fluorescent tracer, sodium fluorescein (NaF), that has a similar molecular weight but is more hydrophilic compared to ECA. Furthermore, we developed a mathematical model to simulate the transport processes and used it to analyze the experimental data. The model was also used to investigate the dependence of diffusion coefficients on volume fraction of viable cells and the binding of NaF and ECA to scleral tissues. Results The diffusion coefficients of ECA and NaF in the sclera were 48.5±15.1x10-7 cm2/s (n=9) and 5.23±1.93x10-7 cm2/s (n=8), respectively. Both diffusion coefficients were insensitive to cell shrinkage caused by ECA during the diffusion experiments and cell damage caused by the storage of tissues ex vivo before the experiments. Binding of ECA to scleral tissues could not be detected. The apparent maximum binding capacity and the apparent equilibrium dissociation constant for NaF were 80±5 mM and 2.5±0.5 mM (n=3), respectively. Conclusions These data demonstrated that ECA diffusion was minimally hindered by structures in the sclera, presumably due to the lack of cells and binding sites for ECA in the sclera. PMID:17356511

Reactive transport of metal contaminants in alluvium - Model comparison and column simulation

USGS Publications Warehouse

Brown, J.G.; Bassett, R.L.; Glynn, P.D.

2000-01-01

A comparative assessment of two reactive-transport models, PHREEQC and HYDROGEOCHEM (HGC), was done to determine the suitability of each for simulating the movement of acidic contamination in alluvium. For simulations that accounted for aqueous complexation, precipitation and dissolution, the breakthrough and rinseout curves generated by each model were similar. The differences in simulated equilibrium concentrations between models were minor and were related to (1) different units in model output, (2) different activity coefficients, and (3) ionic-strength calculations. When adsorption processes were added to the models, the rinseout pH simulated by PHREEQC using the diffuse double-layer adsorption model rose to a pH of 6 after pore volume 15, about 1 pore volume later than the pH simulated by HGC using the constant-capacitance model. In PHREEQC simulation of a laboratory column experiment, the inability of the model to match measured outflow concentrations of selected constituents was related to the evident lack of local geochemical equilibrium in the column. The difference in timing and size of measured and simulated breakthrough of selected constituents indicated that the redox and adsorption reactions in the column occurred slowly when compared with the modeled reactions. MINTEQA2 and PHREEQC simulations of the column experiment indicated that the number of surface sites that took part in adsorption reactions was less than that estimated from the measured concentration of Fe hydroxide in the alluvium.

Enhanced reaction kinetics in biological cells

NASA Astrophysics Data System (ADS)

Loverdo, C.; Bénichou, O.; Moreau, M.; Voituriez, R.

2008-02-01

The cell cytoskeleton is a striking example of an `active' medium driven out-of-equilibrium by ATP hydrolysis. Such activity has been shown to have a spectacular impact on the mechanical and rheological properties of the cellular medium, as well as on its transport properties: a generic tracer particle freely diffuses as in a standard equilibrium medium, but also intermittently binds with random interaction times to motor proteins, which perform active ballistic excursions along cytoskeletal filaments. Here, we propose an analytical model of transport-limited reactions in active media, and show quantitatively how active transport can enhance reactivity for large enough tracers such as vesicles. We derive analytically the average interaction time with motor proteins that optimizes the reaction rate, and reveal remarkable universal features of the optimal configuration. We discuss why active transport may be beneficial in various biological examples: cell cytoskeleton, membranes and lamellipodia, and tubular structures such as axons.

Non-equilibrium radiation from viscous chemically reacting two-phase exhaust plumes

NASA Technical Reports Server (NTRS)

Penny, M. M.; Smith, S. D.; Mikatarian, R. R.; Ring, L. R.; Anderson, P. G.

1976-01-01

A knowledge of the structure of the rocket exhaust plumes is necessary to solve problems involving plume signatures, base heating, plume/surface interactions, etc. An algorithm is presented which treats the viscous flow of multiphase chemically reacting fluids in a two-dimensional or axisymmetric supersonic flow field. The gas-particle flow solution is fully coupled with the chemical kinetics calculated using an implicit scheme to calculate chemical production rates. Viscous effects include chemical species diffusion with the viscosity coefficient calculated using a two-equation turbulent kinetic energy model.

Simulations of reactive transport and precipitation with smoothed particle hydrodynamics

NASA Astrophysics Data System (ADS)

Tartakovsky, Alexandre M.; Meakin, Paul; Scheibe, Timothy D.; Eichler West, Rogene M.

2007-03-01

A numerical model based on smoothed particle hydrodynamics (SPH) was developed for reactive transport and mineral precipitation in fractured and porous materials. Because of its Lagrangian particle nature, SPH has several advantages for modeling Navier-Stokes flow and reactive transport including: (1) in a Lagrangian framework there is no non-linear term in the momentum conservation equation, so that accurate solutions can be obtained for momentum dominated flows and; (2) complicated physical and chemical processes such as surface growth due to precipitation/dissolution and chemical reactions are easy to implement. In addition, SPH simulations explicitly conserve mass and linear momentum. The SPH solution of the diffusion equation with fixed and moving reactive solid-fluid boundaries was compared with analytical solutions, Lattice Boltzmann [Q. Kang, D. Zhang, P. Lichtner, I. Tsimpanogiannis, Lattice Boltzmann model for crystal growth from supersaturated solution, Geophysical Research Letters, 31 (2004) L21604] simulations and diffusion limited aggregation (DLA) [P. Meakin, Fractals, scaling and far from equilibrium. Cambridge University Press, Cambridge, UK, 1998] model simulations. To illustrate the capabilities of the model, coupled three-dimensional flow, reactive transport and precipitation in a fracture aperture with a complex geometry were simulated.

Phase-field modeling of void anisotropic growth behavior in irradiated zirconium

DOE Office of Scientific and Technical Information (OSTI.GOV)

Han, G. M.; Wang, H.; Lin, De-Ye

2017-06-01

A three-dimensional (3D) phase field model was developed to study the effects of surface energy and diffusivity anisotropy on void growth behavior in irradiated Zr. The gamma surface energy function, which is used in the phase field model, was developed with the surface energy anisotropy calculated from the molecular dynamics (MD) simulations. It is assumed that vacancies have much larger mobility in c-axis than a- and b- axes while interstitials have much larger mobility in basal plane then that in c-axis. With the model, the equilibrium void morphology and the effect of defect concentrations and defect mobility anisotropy on voidmore » growth behavior were simulated. The simulations demonstrated that 1) The developed phase-field model can correctly reproduce the faceted void morphology predicted by the Wullf construction. 2) With isotropic diffusivity the void prefers to grow on the basal plane. 3) When the vacancy has large mobility along c-axis and interstitial has a large mobility on the basal plane of hexagonal closed packed (hcp) Zr alloys a platelet void grows in c-direction and shrinks on the basal plane, which is in agreement with the experimental observation of void growth behavior in irradiated Zr.« less

Protein diffusiophoresis and salt osmotic diffusion in aqueous solutions.

PubMed

Annunziata, Onofrio; Buzatu, Daniela; Albright, John G

2012-10-25

Diffusion of a solute can be induced by the concentration gradient of another solute in solution. This transport mechanism is known as cross-diffusion. We have investigated cross-diffusion in a ternary protein-salt-water system. Specifically, we measured the two cross-diffusion coefficients for the lysozyme-NaCl-water system at 25 °C and pH 4.5 as a function of protein and salt concentrations by Rayleigh interferometry. One cross-diffusion coefficient characterizes salt osmotic diffusion induced by a protein concentration gradient, and is related to protein-salt thermodynamic interactions as described by the theories of Donnan membrane equilibrium and protein preferential hydration. The other cross-diffusion coefficient characterizes protein diffusiophoresis induced by a salt concentration gradient, and is described as the difference between a preferential-interaction coefficient and a transport parameter. We first relate our experimental results to the protein net charge and the thermodynamic excess of water near the protein surface. We then extract the Stefan-Maxwell diffusion coefficient describing protein-salt interactions in water. We find that the value of this coefficient is negative, contrary to the friction interpretation of Stefan-Maxwell equations. This result is explained by considering protein hydration. Finally, protein diffusiophoresis is quantitatively examined by considering electrophoretic and hydration effects on protein migration and utilized to accurately estimate lysozyme electrophoretic mobility. To our knowledge, this is the first time that protein diffusiophoresis has been experimentally characterized and a protein-salt Stefan-Maxwell diffusion coefficient reported. This work represents a significant contribution for understanding and modeling the effect of concentration gradients in protein-salt aqueous systems relevant to diffusion-based mass-transfer technologies and transport in living systems.

Transport and concentration controls for chloride, strontium, potassium and lead in Uvas Creek, a small cobble-bed stream in Santa Clara County, California, U.S.A. 2. Mathematical modeling

USGS Publications Warehouse

Jackman, A.P.; Walters, R.A.; Kennedy, V.C.

1984-01-01

Three models describing solute transport of conservative ion species and another describing transport of species which adsorb linearly and reversibly on bed sediments are developed and tested. The conservative models are based on three different conceptual models of the transient storage of solute in the bed. One model assumes the bed to be a well-mixed zone with flux of solute into the bed proportional to the difference between stream concentration and bed concentration. The second model assumes solute in the bed is transported by a vertical diffusion process described by Fick's law. The third model assumes that convection occurs in a selected portion of the bed while the mechanism of the first model functions everywhere. The model for adsorbing species assumes that the bed consists of particles of uniform size with the rate of uptake controlled by an intraparticle diffusion process. All models are tested using data collected before, during and after a 24-hr. pulse injection of chloride, strontium, potassium and lead ions into Uvas Creek near Morgan Hill, California, U.S.A. All three conservative models accurately predict chloride ion concentrations in the stream. The model employing the diffusion mechanism for bed transport predicts better than the others. The adsorption model predicts both strontium and potassium ion concentrations well during the injection of the pulse but somewhat overestimates the observed concentrations after the injection ceases. The overestimation may be due to the convection of solute deep into the bed where it is retained longer than the 3-week post-injection observation period. The model, when calibrated for strontium, predicts potassium equally well when the adsorption equilibrium constant for strontium is replaced by that for potassium. ?? 1984.

Critical conditions for the buoyancy-driven detachment of a wall-bound pendant drop

NASA Astrophysics Data System (ADS)

Lamorgese, A.; Mauri, R.

2016-03-01

We investigate numerically the critical conditions for detachment of an isolated, wall-bound emulsion droplet acted upon by surface tension and wall-normal buoyancy forces alone. To that end, we present a simple extension of a diffuse-interface model for partially miscible binary mixtures that was previously employed for simulating several two-phase flow phenomena far and near the critical point [A. G. Lamorgese et al. "Phase-field approach to multiphase flow modeling," Milan J. Math. 79(2), 597-642 (2011)] to allow for static contact angles other than 90°. We use the same formulation of the Cahn boundary condition as first proposed by Jacqmin ["Contact-line dynamics of a diffuse fluid interface," J. Fluid Mech. 402, 57-88 (2000)], which accommodates a cubic (Hermite) interpolation of surface tensions between the wall and each phase at equilibrium. We show that this model can be successfully employed for simulating three-phase contact line problems in stable emulsions with nearly immiscible components. We also show a numerical determination of critical Bond numbers as a function of static contact angle by phase-field simulation.

Molybdate transport in a chemically complex aquifer: Field measurements compared with solute-transport model predictions

USGS Publications Warehouse

Stollenwerk, Kenneth G.

1998-01-01

A natural-gradient tracer test was conducted in an unconfined sand and gravel aquifer on Cape Cod, Massachusetts. Molybdate was included in the injectate to study the effects of variable groundwater chemistry on its aqueous distribution and to evaluate the reliability of laboratory experiments for identifying and quantifying reactions that control the transport of reactive solutes in groundwater. Transport of molybdate in this aquifer was controlled by adsorption. The amount adsorbed varied with aqueous chemistry that changed with depth as freshwater recharge mixed with a plume of sewage-contaminated groundwater. Molybdate adsorption was strongest near the water table where pH (5.7) and the concentration of the competing solutes phosphate (2.3 micromolar) and sulfate (86 micromolar) were low. Adsorption of molybdate decreased with depth as pH increased to 6.5, phosphate increased to 40 micromolar, and sulfate increased to 340 micromolar. A one-site diffuse-layer surface-complexation model and a two-site diffuse-layer surface-complexation model were used to simulate adsorption. Reactions and equilibrium constants for both models were determined in laboratory experiments and used in the reactive-transport model PHAST to simulate the two-dimensional transport of molybdate during the tracer test. No geochemical parameters were adjusted in the simulation to improve the fit between model and field data. Both models simulated the travel distance of the molybdate cloud to within 10% during the 2-year tracer test; however, the two-site diffuse-layer model more accurately simulated the molybdate concentration distribution within the cloud.