Chemical equilibrium modeling of detonation
Fried, Laurence E.; Bastea, Sorin
2010-05-19
Energetic materials are unique for having a strong exothermic reactivity, which has made them desirable for both military and commercial applications. Energetic materials are commonly divided into high explosives, propellants, and pyrotechnics. We will focus on high explosive (HE) materials here, although there is a great deal of commonality between the classes of energetic materials. Furthermore the history of HE materials is long, their condensed-phase chemical properties are poorly understood.
Learning of Chemical Equilibrium through Modelling-Based Teaching
ERIC Educational Resources Information Center
Maia, Poliana Flavia; Justi, Rosaria
2009-01-01
This paper presents and discusses students' learning process of chemical equilibrium from a modelling-based approach developed from the use of the "Model of Modelling" diagram. The investigation was conducted in a regular classroom (students 14-15 years old) and aimed at discussing how modelling-based teaching can contribute to students learning…
ERIC Educational Resources Information Center
Chiu, Mei-Hung; Chou, Chin-Cheng; Liu, Chia-Ju
2002-01-01
Investigates students' mental models of chemical equilibrium using dynamic science assessments. Reports that students at various levels have misconceptions about chemical equilibrium. Involves 10th grade students (n=30) in the study doing a series of hands-on chemical experiments. Focuses on the process of constructing mental models, dynamic…
Computing Equilibrium Chemical Compositions
NASA Technical Reports Server (NTRS)
Mcbride, Bonnie J.; Gordon, Sanford
1995-01-01
Chemical Equilibrium With Transport Properties, 1993 (CET93) computer program provides data on chemical-equilibrium compositions. Aids calculation of thermodynamic properties of chemical systems. Information essential in design and analysis of such equipment as compressors, turbines, nozzles, engines, shock tubes, heat exchangers, and chemical-processing equipment. CET93/PC is version of CET93 specifically designed to run within 640K memory limit of MS-DOS operating system. CET93/PC written in FORTRAN.
NASA Astrophysics Data System (ADS)
Chiu, Mei-Hung; Chou, Chin-Cheng; Liu, Chia-Ju
2002-10-01
The purpose of this study was to investigate students' mental models of chemical equilibrium using dynamic science assessments. Research in chemical education has shown that students at various levels have misconceptions about chemical equilibrium. According to Chi's theory of conceptual change, the concept of chemical equilibrium has constraint-based features (e.g., random, simultaneous, uniform activities) that might prevent students from deeply understanding the nature of the concept of chemical equilibrium. In this study, we examined how students learned and constructed their mental models of chemical equilibrium in a cognitive apprenticeship context. Thirty 10th-grade students participated in the study: 10 in a control group and 20 in a treatment group. Both groups were presented with a series of hands-on chemical experiments. The students in the treatment group were instructed based on the main features of cognitive apprenticeship (CA), such as coaching, modeling, scaffolding, articulation, reflection, and exploration. However, the students in the control group (non-CA group) learned from the tutor without explicit CA support. The results revealed that the CA group significantly outperformed the non-CA group. The students in the CA group were capable of constructing the mental models of chemical equilibrium - including dynamic, random activities of molecules and interactions between molecules in the microworld - whereas the students in the non-CA group failed to construct similar correct mental models of chemical equilibrium. The study focuses on the process of constructing mental models, on dynamic changes, and on the actions of students (such as self-monitoring/self-correction) who are learning the concept of chemical equilibrium. Also, we discuss the implications for science education.
Yeh, G.T.; Iskra, G.A.; Szecsody, J.E.; Zachara, J.M.; Streile, G.P.
1995-01-01
This report presents the development of a mixed chemical Kinetic and Equilibrium MODel in which every chemical species can be treated either as a equilibrium-controlled or as a kinetically controlled reaction. The reaction processes include aqueous complexation, adsorption/desorption, ion exchange, precipitation/dissolution, oxidation/reduction, and acid/base reactions. Further development and modification of KEMOD can be made in: (1) inclusion of species switching solution algorithms, (2) incorporation of the effect of temperature and pressure on equilibrium and rate constants, and (3) extension to high ionic strength.
Exploring the Use of Multiple Analogical Models when Teaching and Learning Chemical Equilibrium
ERIC Educational Resources Information Center
Harrison, Allan G.; De Jong, Onno
2005-01-01
This study describes the multiple analogical models used to introduce and teach Grade 12 chemical equilibrium. We examine the teacher's reasons for using models, explain each model's development during the lessons, and analyze the understandings students derived from the models. A case study approach was used and the data were drawn from the…
NASA Astrophysics Data System (ADS)
Leal, Allan M. M.; Blunt, Martin J.; LaForce, Tara C.
2014-04-01
Chemical equilibrium calculations are essential for many environmental problems. It is also a fundamental tool for chemical kinetics and reactive transport modelling, since these applications may require hundreds to billions equilibrium calculations in a single simulation. Therefore, an equilibrium method for such critical applications must be very efficient, robust and accurate. In this work we demonstrate the potential effectiveness of a novel Gibbs energy minimisation algorithm for reactive transport simulations. The algorithm includes strategies to converge from poor initial guesses; capabilities to specify non-linear equilibrium constraints such as pH of an aqueous solution and activity or fugacity of a species; a rigorous phase stability test to determine the unstable phases; and a strategy to boost the convergence speed of the calculations to quadratic rates, requiring only few iterations to converge. We use this equilibrium method to solve geochemical problems relevant to carbon storage in saline aquifers, where aqueous, gaseous and minerals phases are present. The problems are formulated to mimic the ones found in kinetics and transport simulations, where a sequence of equilibrium calculations are performed, each one using the previous solution as the initial guess. The efficiency and convergence rates of the calculations are presented, which require an average of 1-2 iterations. These results indicate that critical applications such as chemical kinetics and reactive transport modelling can potentially benefit by using this multiphase equilibrium algorithm.
ORCHESTRA: an object-oriented framework for implementing chemical equilibrium models.
Meeussen, Johannes C L
2003-03-15
This work presents a new object-oriented structure for chemical equilibrium calculations that is used in the modeling framework ORCHESTRA (Objects Representing CHEmical Speciation and TRAnsport). In contrast to standard chemical equilibrium algorithms, such as MINEQL, MINTEQ2A, PHREEQC, and ECOSAT, model equations are not hard-coded in the source code, but instead all equations are defined in text format and read by the ORCHESTRA calculation kernel at run time. This makes model definitions easily accessible and extendible by users. Furthermore, it results in a very compact and efficient calculation kernel that is easy to use as a submodel within mass transport or kinetic models. Finally, the object-oriented structure of the chemical model definitions makes it possible to implement a new object-oriented framework for implementing chemical models. This framework consists of three basic object types, entities, reactions, and phases, that form the building blocks from which other chemical models are composed. The hierarchical approach ensures consistent and compact model definitions and is illustrated here by discussing the implementation of a number of commonly used chemical models such as aqueous complexation, activity correction, precipitation, surface complexation ion exchange, and several more sophisticated adsorption models including electrostatic interactions, NICA, and CD-MUSIC. The ORCHESTRA framework is electronically available from www.macaulay.ac.uk/ORCHESTRA. PMID:12680672
Exploring the use of multiple analogical models when teaching and learning chemical equilibrium
NASA Astrophysics Data System (ADS)
Harrison, Allan G.; de Jong, Onno
2005-12-01
This study describes the multiple analogical models used to introduce and teach Grade 12 chemical equilibrium. We examine the teacher's reasons for using models, explain each model's development during the lessons, and analyze the understandings students derived from the models. A case study approach was used and the data were drawn from the observation of three consecutive Grade 12 lessons on chemical equilibrium, pre- and post-lesson interviews, and delayed student interviews. The key analogical models used in teaching were: the school dance; the sugar in a teacup; the pot of curry; and the busy highway. The lesson and interview data were subject to multiple, independent analyses and yielded the following outcomes: The teacher planned to use the students' prior knowledge wherever possible and he responded to student questions with stories and extended and enriched analogies. He planned to discuss where each analogy broke down but did not. The students enjoyed the teaching but built variable mental models of equilibrium and some of their analogical mappings were unreliable. A female student disliked masculine analogies, other students tended to see elements of the multiple models in isolation, and some did not recognize all the analogical mappings embedded in the teaching plan. Most students learned that equilibrium reactions are dynamic, occur in closed systems, and the forward and reverse reactions are balanced. We recommend the use of multiple analogies like these and insist that teachers always show where the analogy breaks down and carefully negotiate the conceptual outcomes.
Chemical Principles Revisited: Chemical Equilibrium.
ERIC Educational Resources Information Center
Mickey, Charles D.
1980-01-01
Describes: (1) Law of Mass Action; (2) equilibrium constant and ideal behavior; (3) general form of the equilibrium constant; (4) forward and reverse reactions; (5) factors influencing equilibrium; (6) Le Chatelier's principle; (7) effects of temperature, changing concentration, and pressure on equilibrium; and (8) catalysts and equilibrium. (JN)
Molecular finite-size effects in stochastic models of equilibrium chemical systems.
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. PMID:26931675
Molecular finite-size effects in stochastic models of equilibrium chemical systems
NASA Astrophysics Data System (ADS)
Cianci, Claudia; Smith, Stephen; Grima, Ramon
2016-02-01
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.
General multi-group macroscopic modeling for thermo-chemical non-equilibrium gas mixtures.
Liu, Yen; Panesi, Marco; Sahai, Amal; Vinokur, Marcel
2015-04-01
This paper opens a new door to macroscopic modeling for thermal and chemical non-equilibrium. In a game-changing approach, we discard conventional theories and practices stemming from the separation of internal energy modes and the Landau-Teller relaxation equation. Instead, we solve the fundamental microscopic equations in their moment forms but seek only optimum representations for the microscopic state distribution function that provides converged and time accurate solutions for certain macroscopic quantities at all times. The modeling makes no ad hoc assumptions or simplifications at the microscopic level and includes all possible collisional and radiative processes; it therefore retains all non-equilibrium fluid physics. We formulate the thermal and chemical non-equilibrium macroscopic equations and rate coefficients in a coupled and unified fashion for gases undergoing completely general transitions. All collisional partners can have internal structures and can change their internal energy states after transitions. The model is based on the reconstruction of the state distribution function. The internal energy space is subdivided into multiple groups in order to better describe non-equilibrium state distributions. The logarithm of the distribution function in each group is expressed as a power series in internal energy based on the maximum entropy principle. The method of weighted residuals is applied to the microscopic equations to obtain macroscopic moment equations and rate coefficients succinctly to any order. The model's accuracy depends only on the assumed expression of the state distribution function and the number of groups used and can be self-checked for accuracy and convergence. We show that the macroscopic internal energy transfer, similar to mass and momentum transfers, occurs through nonlinear collisional processes and is not a simple relaxation process described by, e.g., the Landau-Teller equation. Unlike the classical vibrational energy
General multi-group macroscopic modeling for thermo-chemical non-equilibrium gas mixtures
NASA Astrophysics Data System (ADS)
Liu, Yen; Panesi, Marco; Sahai, Amal; Vinokur, Marcel
2015-04-01
This paper opens a new door to macroscopic modeling for thermal and chemical non-equilibrium. In a game-changing approach, we discard conventional theories and practices stemming from the separation of internal energy modes and the Landau-Teller relaxation equation. Instead, we solve the fundamental microscopic equations in their moment forms but seek only optimum representations for the microscopic state distribution function that provides converged and time accurate solutions for certain macroscopic quantities at all times. The modeling makes no ad hoc assumptions or simplifications at the microscopic level and includes all possible collisional and radiative processes; it therefore retains all non-equilibrium fluid physics. We formulate the thermal and chemical non-equilibrium macroscopic equations and rate coefficients in a coupled and unified fashion for gases undergoing completely general transitions. All collisional partners can have internal structures and can change their internal energy states after transitions. The model is based on the reconstruction of the state distribution function. The internal energy space is subdivided into multiple groups in order to better describe non-equilibrium state distributions. The logarithm of the distribution function in each group is expressed as a power series in internal energy based on the maximum entropy principle. The method of weighted residuals is applied to the microscopic equations to obtain macroscopic moment equations and rate coefficients succinctly to any order. The model's accuracy depends only on the assumed expression of the state distribution function and the number of groups used and can be self-checked for accuracy and convergence. We show that the macroscopic internal energy transfer, similar to mass and momentum transfers, occurs through nonlinear collisional processes and is not a simple relaxation process described by, e.g., the Landau-Teller equation. Unlike the classical vibrational energy
General multi-group macroscopic modeling for thermo-chemical non-equilibrium gas mixtures
Liu, Yen Vinokur, Marcel; Panesi, Marco; Sahai, Amal
2015-04-07
This paper opens a new door to macroscopic modeling for thermal and chemical non-equilibrium. In a game-changing approach, we discard conventional theories and practices stemming from the separation of internal energy modes and the Landau-Teller relaxation equation. Instead, we solve the fundamental microscopic equations in their moment forms but seek only optimum representations for the microscopic state distribution function that provides converged and time accurate solutions for certain macroscopic quantities at all times. The modeling makes no ad hoc assumptions or simplifications at the microscopic level and includes all possible collisional and radiative processes; it therefore retains all non-equilibrium fluid physics. We formulate the thermal and chemical non-equilibrium macroscopic equations and rate coefficients in a coupled and unified fashion for gases undergoing completely general transitions. All collisional partners can have internal structures and can change their internal energy states after transitions. The model is based on the reconstruction of the state distribution function. The internal energy space is subdivided into multiple groups in order to better describe non-equilibrium state distributions. The logarithm of the distribution function in each group is expressed as a power series in internal energy based on the maximum entropy principle. The method of weighted residuals is applied to the microscopic equations to obtain macroscopic moment equations and rate coefficients succinctly to any order. The model’s accuracy depends only on the assumed expression of the state distribution function and the number of groups used and can be self-checked for accuracy and convergence. We show that the macroscopic internal energy transfer, similar to mass and momentum transfers, occurs through nonlinear collisional processes and is not a simple relaxation process described by, e.g., the Landau-Teller equation. Unlike the classical vibrational energy
Chemical Equilibrium Modeling of Hanford Waste Tank Processing: Applications of Fundamental Science
Felmy, Andrew R.; Wang, Zheming; Dixon, David A.; Hess, Nancy J.
2004-05-01
The development of computational models based upon fundamental science is one means of quantitatively transferring the results of scientific investigations to practical application by engineers in laboratory and field situations. This manuscript describes one example of such efforts, specifically the development and application of chemical equilibrium models to different waste management issues at the U.S. Department of Energy (DOE) Hanford Site. The development of the chemical models is described with an emphasis on the fundamental science investigations that have been undertaken in model development followed by examples of different waste management applications. The waste management issues include the leaching of waste slurries to selective remove non-hazardous components and the separation of Sr90 and transuranics from the waste supernatants. The fundamental science contributions include: molecular simulations of the energetics of different molecular clusters to assist in determining the species present in solution, advanced synchrotron research to determine the chemical form of precipitates, and laser based spectroscopic studies of solutions and solids.
Chemical Equilibrium Detonation
NASA Astrophysics Data System (ADS)
Bastea, Sorin; Fried, Laurence E.
Energetic materials are unique for having a strong exothermic reactivity, which has made them desirable for both military and commercial applications. The fundamental principles outlined in this chapter pertain to the study of detonation in both gas-phase and condensed-phase energetic materials, but our main focus will be on the condensed ones, particularly on high explosives (HEs). They share many properties with other classes of condensed energetic compounds such as propellants and pyrotechnics, but a detailed understanding of detonation is especially important for numerous HE applications. The usage and study of HE materials goes back more than a century, but many questions remain to be answered, e.g., on their reaction pathways at high pressures and temperatures, chemical properties, etc.
NASA Technical Reports Server (NTRS)
Glass, Christopher E.
1990-01-01
The computer program EASI, an acronym for Equilibrium Air Shock Interference, was developed to calculate the inviscid flowfield, the maximum surface pressure, and the maximum heat flux produced by six shock wave interference patterns on a 2-D, cylindrical configuration. Thermodynamic properties of the inviscid flowfield are determined using either an 11-specie, 7-reaction equilibrium chemically reacting air model or a calorically perfect air model. The inviscid flowfield is solved using the integral form of the conservation equations. Surface heating calculations at the impingement point for the equilibrium chemically reacting air model use variable transport properties and specific heat. However, for the calorically perfect air model, heating rate calculations use a constant Prandtl number. Sample calculations of the six shock wave interference patterns, a listing of the computer program, and flowcharts of the programming logic are included.
NASA Astrophysics Data System (ADS)
Shi, Bowen; Raby, Stuart
2015-10-01
We provide a systematic treatment of chemical equilibrium in the presence of a specific type of time dependent background. The type of time dependent background we consider appears, for example, in recently proposed axion/Majoron leptogenesis models [A. Kusenko, K. Schmitz, and T. T. Yanagida, Phys. Rev. Lett. 115, 011302 (2015) and M. Ibe and K. Kaneta, Phys. Rev. D 92, 035019 (2015)]. In describing the chemical equilibrium we use quantities which are invariant under redefinition of fermion phases (we refer to this redefinition as a change of basis for short In this paper, change of basis does not mean change of Lorentz frame. All calculations in this paper are performed in the center-of-momentum frame of the thermal plasma, i.e. the Lorentz frame in which the average momentum of particles is zero.), and therefore it is a basis invariant treatment. The change of the anomaly terms due to the change of the path integral measure [K. Fujikawa, Phys. Rev. Lett. 42, 1195 (1979) and K. Fujikawa, Phys. Rev. D 29, 285 (1984)] under a basis change is taken into account. We find it is useful to go back and forth between different bases, and there are insights which can be more easily obtained in one basis rather than another. A toy model is provided to illustrate the ideas. For the axion leptogenesis model [A. Kusenko, K. Schmitz, and T. T. Yanagida, Phys. Rev. Lett. 115, 011302 (2015)], our result suggests that at T >1013 GeV , when sphaleron processes decouple and ΓB +L≪H <ΓL (where H is the Hubble parameter at temperature T and ΓL is the Δ L =2 lepton number violating interaction rate), the amount of B -L created is controlled by the smallness of the sphaleron interaction rate, ΓB +L. Therefore it is not as efficient as described. In addition, we notice an interesting modification of gauge boson dispersion relations at subleading order.
NASA Technical Reports Server (NTRS)
Grodzka, P.; Facemire, B.
1977-01-01
Three investigations conducted aboard Skylab IV and Apollo-Soyuz involved phenomena that are of interest to the biochemistry community. The formaldehyde clock reaction and the equilibrium shift reaction experiments conducted aboard Apollo Soyuz demonstrate the effect of low-g foams or air/liquid dispersions on reaction rate and chemical equilibrium. The electrodeposition reaction experiment conducted aboard Skylab IV demonstrate the effect of a low-g environment on an electrochemical displacement reaction. The implications of the three space experiments for various applications are considered.
Zhang, Fan; Yeh, Gour-Tsyh; Parker, Jack C; Brooks, Scott C; Pace, Molly; Kim, Young Jin; Jardine, Philip M; Watson, David B
2007-01-01
This paper presents a reaction-based water quality transport model in subsurface flow systems. Transport of chemical species with a variety of chemical and physical processes is mathematically described by M partial differential equations (PDEs). Decomposition via Gauss-Jordan column reduction of the reaction network transforms M species reactive transport equations into two sets of equations: a set of thermodynamic equilibrium equations representing NE equilibrium reactions and a set of reactive transport equations of M-NE kinetic-variables involving no equilibrium reactions (a kinetic-variable is a linear combination of species). The elimination of equilibrium reactions from reactive transport equations allows robust and efficient numerical integration. The model solves the PDEs of kinetic-variables rather than individual chemical species, which reduces the number of reactive transport equations and simplifies the reaction terms in the equations. A variety of numerical methods are investigated for solving the coupled transport and reaction equations. Simulation comparisons with exact solutions were performed to verify numerical accuracy and assess the effectiveness of various numerical strategies to deal with different application circumstances. Two validation examples involving simulations of uranium transport in soil columns are presented to evaluate the ability of the model to simulate reactive transport with complex reaction networks involving both kinetic and equilibrium reactions.
NASA Astrophysics Data System (ADS)
Saaltink, Maarten W.; Vilarrasa, Victor; De Gaspari, Francesca; Silva, Orlando; Carrera, Jesús; Rötting, Tobias S.
2013-12-01
CO2 injection and storage in deep saline aquifers involves many coupled processes, including multiphase flow, heat and mass transport, rock deformation and mineral precipitation and dissolution. Coupling is especially critical in carbonate aquifers, where minerals will tend to dissolve in response to the dissolution of CO2 into the brine. The resulting neutralization will drive further dissolution of both CO2 and calcite. This suggests that large cavities may be formed and that proper simulation may require full coupling of reactive transport and multiphase flow. We show that solving the latter may suffice whenever two requirements are met: (1) all reactions can be assumed to occur in equilibrium and (2) the chemical system can be calculated as a function of the state variables of the multiphase flow model (i.e., liquid and gas pressure, and temperature). We redefine the components of multiphase flow codes (traditionally, water and CO2), so that they are conservative for all reactions of the chemical system. This requires modifying the traditional constitutive relationships of the multiphase flow codes, but yields the concentrations of all species and all reaction rates by simply performing speciation and mass balance calculations at the end of each time step. We applied this method to the H2O-CO2-Na-Cl-CaCO3 system, so as to model CO2 injection into a carbonate aquifer containing brine. Results were very similar to those obtained with traditional formulations, which implies that full coupling of reactive transport and multi-phase flow is not really needed for this kind of systems, but the resulting simplifications may make it advisable even for cases where the above requirements are not met. Regarding the behavior of carbonate rocks, we find that porosity development near the injection well is small because of the low solubility of calcite. Moreover, dissolution concentrates at the front of the advancing CO2 plume because the brine below the plume tends to reach
Microscopic Simulation and Macroscopic Modeling for Thermal and Chemical Non-Equilibrium
NASA Technical Reports Server (NTRS)
Liu, Yen; Panesi, Marco; Vinokur, Marcel; Clarke, Peter
2013-01-01
This paper deals with the accurate microscopic simulation and macroscopic modeling of extreme non-equilibrium phenomena, such as encountered during hypersonic entry into a planetary atmosphere. The state-to-state microscopic equations involving internal excitation, de-excitation, dissociation, and recombination of nitrogen molecules due to collisions with nitrogen atoms are solved time-accurately. Strategies to increase the numerical efficiency are discussed. The problem is then modeled using a few macroscopic variables. The model is based on reconstructions of the state distribution function using the maximum entropy principle. The internal energy space is subdivided into multiple groups in order to better describe the non-equilibrium gases. The method of weighted residuals is applied to the microscopic equations to obtain macroscopic moment equations and rate coefficients. The modeling is completely physics-based, and its accuracy depends only on the assumed expression of the state distribution function and the number of groups used. The model makes no assumption at the microscopic level, and all possible collisional and radiative processes are allowed. The model is applicable to both atoms and molecules and their ions. Several limiting cases are presented to show that the model recovers the classical twotemperature models if all states are in one group and the model reduces to the microscopic equations if each group contains only one state. Numerical examples and model validations are carried out for both the uniform and linear distributions. Results show that the original over nine thousand microscopic equations can be reduced to 2 macroscopic equations using 1 to 5 groups with excellent agreement. The computer time is decreased from 18 hours to less than 1 second.
NASA Technical Reports Server (NTRS)
Snyder, Gregory A.; Taylor, Lawrence A.; Neal, Clive R.
1992-01-01
A chemical model for simulating the sources of the lunar mare basalts was developed by considering a modified mafic cumulate source formed during the combined equilibrium and fractional crystallization of a lunar magma ocean (LMO). The parameters which influence the initial LMO and its subsequent crystallization are examined, and both trace and major elements are modeled. It is shown that major elements tightly constrain the composition of mare basalt sources and the pathways to their creation. The ability of this LMO model to generate viable mare basalt source regions was tested through a case study involving the high-Ti basalts.
Chemical Principles Revisited: Using the Equilibrium Concept.
ERIC Educational Resources Information Center
Mickey, Charles D., Ed.
1981-01-01
Discusses the concept of equilibrium in chemical systems, particularly in relation to predicting the position of equilibrium, predicting spontaneity of a reaction, quantitative applications of the equilibrium constant, heterogeneous equilibrium, determination of the solubility product constant, common-ion effect, and dissolution of precipitates.…
NASA Astrophysics Data System (ADS)
Dudal, Yves; Gérard, Frédéric
2004-08-01
Soil organic matter consists of a highly complex and diversified blend of organic molecules, ranging from low molecular weight organic acids (LMWOAs), sugars, amines, alcohols, etc., to high apparent molecular weight fulvic and humic acids. The presence of a wide range of functional groups on these molecules makes them very reactive and influential in soil chemistry, in regards to acid-base chemistry, metal complexation, precipitation and dissolution of minerals and microbial reactions. Out of these functional groups, the carboxylic and phenolic ones are the most abundant and most influential in regards to metal complexation. Therefore, chemical equilibrium models have progressively dealt with organic matter in their calculations. This paper presents a review of six chemical equilibrium models, namely N ICA-Donnan, E Q3/6, G EOCHEM, M INTEQA2, P HREEQC and W HAM, in light of the account they make of natural organic matter (NOM) with the objective of helping potential users in choosing a modelling approach. The account has taken various faces, mainly by adding specific molecules within the existing model databases (E Q3/6, G EOCHEM, and P HREEQC) or by using either a discrete (W HAM) or a continuous (N ICA-Donnan and M INTEQA2) distribution of the deprotonated carboxylic and phenolic groups. The different ways in which soil organic matter has been integrated into these models are discussed in regards to the model-experiment comparisons that were found in the literature, concerning applications to either laboratory or natural systems. Much of the attention has been focused on the two most advanced models, W HAM and N ICA-Donnan, which are able to reasonably describe most of the experimental results. Nevertheless, a better knowledge of the humic substances metal-binding properties is needed to better constrain model inputs with site-specific parameter values. This represents the main axis of research that needs to be carried out to improve the models. In addition to
NASA Astrophysics Data System (ADS)
Zhu, Xun
2003-07-01
The classic two-level or equivalent two-level model that includes only the statistical equilibrium of radiative and thermal processes of excitation and quenching between two vibrational energy levels is extended by adding chemical production to the rate equations. The modifications to the non-local thermodynamic equilibrium source function and cooling rate are parameterized by ϕc, which characterizes the ratio of chemical production to collisional quenching. For applications of broadband emission of O3 at 9.6 μm, the non-LTE effect of chemical production on the cooling rate and limb emission is proportional to the ratio of O to O3. For a typical [O]/[O3], the maximum enhancements of limb radiance and cooling rate are about 15% 30% and 0.03 0.05 K day-1, respectively, both occurring near the mesopause regions. This suggests that the broadband limb radiance above ˜80 km is sensitive to O3 density but not sensitive to the direct cooling rate along the line-of-sight, which makes O3 retrieval feasible but the direct cooling rate retrieval difficult by using the O3 9.6 μm band limb emission.
Exploring Chemical Equilibrium in Hot Jovians
NASA Astrophysics Data System (ADS)
Blumenthal, Sarah; Harrington, Joseph; Mandell, Avi; Hébrard, Eric; Venot, Olivia; Cubillos, Patricio; Blecic, Jasmina; Challener, Ryan
2016-01-01
It has been established that equilibrium chemistry is usually achieved deep in the atmosphere of hot Jovians where timescales are short (Line and Yung 2013). Thus, equilibrium chemistry has been used as a starting point (setting initial conditions) for evaluating disequilibrium processes. We explore parameters of setting these initial conditions including departures from solar metallicity, the number of species allowed in a system, the types of species allowed in a system, and different thermodynamic libraries in an attempt to create a standard for evaluating equilibrium chemistry. NASA's open source code Chemical Equilibrium and Applications (CEA) is used to calculate model planet abundances by varying the metallicity, in the pressure regime 0.1 to 1 bar. These results are compared to a variety of exoplanets(Teq between 600 and 2100K) qualitatively by color maps of the dayside with different temperature redistributions. Additionally, CEA (with an up-dated thermodynamic library) is compared with the thermochemical model presented in Venotet al. (2012) for HD 209458b and HD 189733b. This same analysis is then applied to the cooler planet HD 97658b. Spectra are generated and we compare both models' outputs using the open source codetransit (https://github.com/exosports/transit) using the opacities of 15 molecules. We make the updated CEA thermodyanamic library and supporting Python scripts to do the CEA analyses available open source. Thiswork was supported by NASA Planetary Atmospheres grant NNX12AI69G.
Quantum chemical modeling of humic acid/air equilibrium partitioning of organic vapors.
Niederer, Christian; Goss, Kai-Uwe
2007-05-15
Classical approaches for predicting soil organic matter partition coefficients of organic compounds require a calibration with experimental partition data and, for good accuracy, experimental compound descriptors. In this study we evaluate the quantum chemical model COSMO-RS in its COSMOtherm implementation for the prediction of about 200 experimental Leonardite humic acid/air partition coefficients without calibration or experimental compound descriptors, but simply based on molecular structures. For this purpose a Leonardite Humic Acid model monomer limited to 31 carbon atoms was derived from 13C NMR analysis, elemental analysis, and acidic function analysis provided in the literature. Altogether the COSMOtherm calculations showed a good performance and we conclude that it may become a very promising tool for the prediction of sorption in soil organic matter for compounds for which the molecular structure is the only reliable information available. COSMOtherm can be expected to be very robust with respectto new and complex compound structures because its calculations are based on a fundamental assessment of the underlying intermolecular forces. In contrast, other empirical models that are also based on the molecular structure of the sorbate have an application domain that is limited by their calibration data set that is often unknown to the user. PMID:17547191
Chemical Equilibrium And Transport (CET)
NASA Technical Reports Server (NTRS)
Mcbride, B. J.
1991-01-01
Powerful, machine-independent program calculates theoretical thermodynamic properties of chemical systems. Aids in design of compressors, turbines, engines, heat exchangers, and chemical processing equipment.
Computing Properties Of Chemical Mixtures At Equilibrium
NASA Technical Reports Server (NTRS)
Mcbride, B. J.; Gordon, S.
1995-01-01
Scientists and engineers need data on chemical equilibrium compositions to calculate theoretical thermodynamic properties of chemical systems. Information essential in design and analysis of such equipment as compressors, turbines, nozzles, engines, shock tubes, heat exchangers, and chemical-processing equipment. CET93 is general program that calculates chemical equilibrium compositions and properties of mixtures for any chemical system for which thermodynamic data are available. Includes thermodynamic data for more than 1,300 gaseous and condensed species and thermal-transport data for 151 gases. Written in FORTRAN 77.
Chemical equilibrium and reaction modeling of arsenic and selenium in soils
Technology Transfer Automated Retrieval System (TEKTRAN)
The chemical processes and soil factors that affect the concentrations of As and Se in soil solution were discussed. Both elements occur in two redox states differing in toxicity and reactivity. Methylation and volatilization reactions occur in soils and can act as detoxification pathways. Precip...
An Elementary Discussion of Chemical Equilibrium.
ERIC Educational Resources Information Center
David, Carl W.
1988-01-01
This discussion uses a more difficult reaction as the prototype to derive the standard equation for chemical equilibrium. It can be used by students who can understand and use partial derivatives. (CW)
Spreadsheet Templates for Chemical Equilibrium Calculations.
ERIC Educational Resources Information Center
Joshi, Bhairav D.
1993-01-01
Describes two general spreadsheet templates to carry out all types of one-equation chemical equilibrium calculations encountered by students in undergraduate chemistry courses. Algorithms, templates, macros, and representative examples are presented to illustrate the approach. (PR)
Exploring Chemical and Thermal Non-equilibrium in Nitrogen Arcs
NASA Astrophysics Data System (ADS)
Ghorui, S.; Das, A. K.
2012-12-01
Plasma torches operating with nitrogen are of special importance as they can operate with usual tungsten based refractory electrodes and offer radical rich non-oxidizing high temperature environment for plasma chemistry. Strong gradients in temperature as well as species densities and huge convective fluxes lead to varying degrees of chemical non-equilibrium in associated regions. An axi-symmetric two-temperature chemical non-equilibrium model of a nitrogen plasma torch has been developed to understand the effects of thermal and chemical non-equilibrium in arcs. A 2-D finite volume CFD code in association with a non-equilibrium property routine enabled extraction of steady state self-consistent distributions of various plasma quantities inside the torch under various thermal and chemical non-equilibrium conditions. Chemical non-equilibrium has been incorporated through computation of diffusive and convective fluxes in each finite volume cell in every iteration and associating corresponding thermodynamic and transport properties through the scheme of 'chemical non-equilibrium parameter' introduced by Ghorui et. al. Recombination coefficient data from Nahar et. al. and radiation data from Krey and Morris have been used in the simulation. Results are presented for distributions of temperature, pressure, velocity, current density, electric potential, species densities and chemical non-equilibrium effects. Obtained results are compared with similar results under LTE.
Binding of Iron(III) to Organic Soils: Exafs Spectroscopy And Chemical Equilibrium Modeling
Gustafsson, J.P.; Persson, I.; Kleja, D.B.; Schaik, J.W.J.van
2007-07-09
The complexation of iron(III) to soil organic matter is important for the binding of trace metals in natural environments because of competition effects. In this study, we used extended X-ray absorption fine structure (EXAFS) spectroscopy to characterize the binding mode for iron(III) in two soil samples from organic mor layers, one of which was also treated with iron(III). In most cases the EXAFS spectra had three significant contributions, inner-core Fe-O/N interactions at about 2.02(2) angstroms, Fe-C interactions in the second scattering shell at 3.00(4) angstroms, and a mean Fe-Fe distance at 3.37(3) angstroms. One untreated sample showed features typical for iron (hydr)oxides; however, after treatment of iron(III) the EXAFS spectrum was dominated by organically complexed iron. The presence of a Fe-Fe distance in all samples showed that the major part of the organically complexed iron was hydrolyzed, most likely in a mixture of complexes with an inner core of (O{sub 5}Fe){sub 2}O and (O{sub 5}Fe){sub 3}O. These results were used to constrain a model for metal-humic complexation, the Stockholm Humic Model (SHM). The model was able to describe iron(III) binding very well at low pH considering only one dimeric iron(III)-humic complex. The competition effect on trace metals was also well described.
ERIC Educational Resources Information Center
Wood, Dean Arthur
A special purpose digital computer which utilizes the Monte Carlo integration method of obtaining simulations of chemical processes was developed and constructed. The computer, designated as the Monte Carlo Integration Computer (MCIC), was designed as an instructional model for the illustration of kinetic and equilibrium processes, and was…
NASA Astrophysics Data System (ADS)
Sun, Hao; Tanaka, Yasunori; Tomita, Kentaro; Wu, Yi; Rong, Mingzhe; Uesugi, Yoshihiko; Ishijima, Tatsuo
2016-02-01
A non-chemically equilibrium (non-CE) model was established to investigate the N2 arc plasma in the decaying phase during the arc interruption, and was validated by comparison with the experimental results based on laser Thomson scattering. Unlike the conventional model assuming the local thermodynamic equilibrium (LTE), in this non-CE model, the magneto-hydro-dynamics (MHD) method was coupled with the reaction kinetics to obtain the time-dependent species compositions and properties. The current calculation took into account five species in hot gas and 22 chemical reactions in total. The time-dependent species compositions of hot N2 were derived from the mass conservation equation for each species, considering the effect of the convection, diffusion and the chemical reaction. The influence of the non-CE compositions on the arc decaying behavior was realized by updating the thermodynamic and transport properties at each iterative step. The results indicate that the non-CE model can result in the departure of the arc decaying behavior from the LTE model, because it alters the time evolution of the species composition and consequently changes the thermodynamic and transport properties. At the edge of the arc, the time evolutions of the species are dominant by both the diffusion and the chemical reactions while at the center of the arc they are mainly influenced by the chemical reactions. Generally, the non-CE effect can lead to the delay of all the particles’ variations, particularly the electron decay, so that the arc interruption performance will be reduced compared with that in the LTE model.
Algorithm For Hypersonic Flow In Chemical Equilibrium
NASA Technical Reports Server (NTRS)
Palmer, Grant
1989-01-01
Implicit, finite-difference, shock-capturing algorithm calculates inviscid, hypersonic flows in chemical equilibrium. Implicit formulation chosen because overcomes limitation on mathematical stability encountered in explicit formulations. For dynamical portion of problem, Euler equations written in conservation-law form in Cartesian coordinate system for two-dimensional or axisymmetric flow. For chemical portion of problem, equilibrium state of gas at each point in computational grid determined by minimizing local Gibbs free energy, subject to local conservation of molecules, atoms, ions, and total enthalpy. Major advantage: resulting algorithm naturally stable and captures strong shocks without help of artificial-dissipation terms to damp out spurious numerical oscillations.
Calculating Shocks In Flows At Chemical Equilibrium
NASA Technical Reports Server (NTRS)
Eberhardt, Scott; Palmer, Grant
1988-01-01
Boundary conditions prove critical. Conference paper describes algorithm for calculation of shocks in hypersonic flows of gases at chemical equilibrium. Although algorithm represents intermediate stage in development of reliable, accurate computer code for two-dimensional flow, research leading up to it contributes to understanding of what is needed to complete task.
Teaching Chemical Equilibrium with the Jigsaw Technique
ERIC Educational Resources Information Center
Doymus, Kemal
2008-01-01
This study investigates the effect of cooperative learning (jigsaw) versus individual learning methods on students' understanding of chemical equilibrium in a first-year general chemistry course. This study was carried out in two different classes in the department of primary science education during the 2005-2006 academic year. One of the classes…
NASA Astrophysics Data System (ADS)
Bajwa, Kanwardeep S.; Aneja, Viney P.; Pal Arya, S.
Ammonia has recently gained importance for its increasing atmospheric concentrations and its role in the formation of aerosols. The anaerobic lagoon and spray method, commonly used for waste storage and disposal in confined animal feeding operations (CAFO), is a significant source of ammonia emissions. An accurate emission model for ammonia from aqueous surfaces can help in the development of emission factors. Data collected from field measurements made at hog waste lagoons in south eastern North Carolina, using the flow through dynamic chamber technique, were used to evaluate the Coupled mass transfer and Chemical reactions model and Equilibrium model developed by Aneja et al. [2001a. Measurement and modeling of ammonia emissions at waste treatment lagoon-Atmospheric Interface. Water, Air and Soil pollution: Focus 1, 177-188]. Sensitivity analysis shows that ammonia flux increases exponentially with lagoon temperature and pH, but a linear increase was observed with an increase in total ammoniacal nitrogen (TAN). Ammonia flux also shows a nonlinear increase with increasing wind speed. Observed ammonia fluxes were generally lower in the cold season than in the warm season when lagoon temperatures are higher. About 41% of the equilibrium model predictions and 43% of the Coupled model predictions are found to be within a factor of two of the observed fluxes. Several model performance statistics were used to evaluate the performance of the two models against the observed flux data. These indicate that the simpler Equilibrium model does as well as the Coupled model. The possible effects of the "artificial" environment within the chamber, which is different from that in the ambient atmospheric conditions above the open lagoon surface, on the measured fluxes are also recognized.
Mac Low, Mordecai-Mark; Glover, Simon C. O. E-mail: glover@uni-heidelberg.de
2012-02-20
Observations of spiral galaxies show a strong linear correlation between the ratio of molecular to atomic hydrogen surface density R{sub 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 H{sub 2} from cold atomic gas. The formation timescale for H{sub 2} is sufficiently long that equilibrium is not reached within the 20-30 Myr lifetimes of molecular clouds. The equilibrium balance between radiative dissociation and H{sub 2} formation on dust grains fails to predict the time-dependent molecular fractions we find. A simple, time-dependent model of H{sub 2} 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 H{sub 2}. The observed correlation of R{sub 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{sub mol} with density. If we examine the value of R{sub 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.
The Conceptual Change Approach to Teaching Chemical Equilibrium
ERIC Educational Resources Information Center
Canpolat, Nurtac; Pinarbasi, Tacettin; Bayrakceken, Samih; Geban, Omer
2006-01-01
This study investigates the effect of a conceptual change approach over traditional instruction on students' understanding of chemical equilibrium concepts (e.g. dynamic nature of equilibrium, definition of equilibrium constant, heterogeneous equilibrium, qualitative interpreting of equilibrium constant, changing the reaction conditions). This…
Thermo-chemical dynamics and chemical quasi-equilibrium of plasmas in thermal non-equilibrium
Massot, Marc; Graille, Benjamin; Magin, Thierry E.
2011-05-20
We examine both processes of ionization by electron and heavy-particle impact in spatially uniform plasmas at rest in the absence of external forces. A singular perturbation analysis is used to study the following physical scenario, in which thermal relaxation becomes much slower than chemical reactions. First, electron-impact ionization is investigated. The dynamics of the system rapidly becomes close to a slow dynamics manifold that allows for defining a unique chemical quasi-equilibrium for two-temperature plasmas and proving that the second law of thermodynamics is satisfied. Then, all ionization reactions are taken into account simultaneously, leading to a surprising conclusion: the inner layer for short time scale (or time boundary layer) directly leads to thermal equilibrium. Global thermo-chemical equilibrium is reached within a short time scale, involving only chemical reactions, even if thermal relaxation through elastic collisions is assumed to be slow.
Helical axis stellarator equilibrium model
Koniges, A.E.; Johnson, J.L.
1985-02-01
An asymptotic model is developed to study MHD equilibria in toroidal systems with a helical magnetic axis. Using a characteristic coordinate system based on the vacuum field lines, the equilibrium problem is reduced to a two-dimensional generalized partial differential equation of the Grad-Shafranov type. A stellarator-expansion free-boundary equilibrium code is modified to solve the helical-axis equations. The expansion model is used to predict the equilibrium properties of Asperators NP-3 and NP-4. Numerically determined flux surfaces, magnetic well, transform, and shear are presented. The equilibria show a toroidal Shafranov shift.
Investigating High School Students' Understanding of Chemical Equilibrium Concepts
ERIC Educational Resources Information Center
Karpudewan, Mageswary; Treagust, David F.; Mocerino, Mauro; Won, Mihye; Chandrasegaran, A. L.
2015-01-01
This study investigated the year 12 students' (N = 56) understanding of chemical equilibrium concepts after instruction using two conceptual tests, the "Chemical Equilibrium Conceptual Test 1" ("CECT-1") consisting of nine two-tier multiple-choice items and the "Chemical Equilibrium Conceptual Test 2"…
Felmy, Andrew R.; Mason, Marvin; Qafoku, Odeta; Xia, Yuanxian; Wang, Zheming; MacLean, Graham
2003-03-27
Developing accurate thermodynamic models for predicting the chemistry of the high-level waste tanks at Hanford is an extremely daunting challenge in electrolyte and radionuclide chemistry. These challenges stem from the extremely high ionic strength of the tank waste supernatants, presence of chelating agents in selected tanks, wide temperature range in processing conditions and the presence of important actinide species in multiple oxidation states. This presentation summarizes progress made to date in developing accurate models for these tank waste solutions, how these data are being used at Hanford and the important challenges that remain. New thermodynamic measurements on Sr and actinide complexation with specific chelating agents (EDTA, HEDTA and gluconate) will also be presented.
Chemical heterogeneities in the mantle: The equilibrium thermodynamic approach
NASA Astrophysics Data System (ADS)
Tirone, M.; Buhre, S.; Schmück, H.; Faak, K.
2016-02-01
This study attempts to answer a simple and yet fundamental question in relation to our understanding of the chemical evolution of deep Earth and planetary interiors. Given two initially separate assemblages (lithologies) in chemical equilibrium can we predict the chemical and mineralogical compositions of the two assemblages when they are put together to form a new equilibrated system? Perhaps a common perception is that given sufficient time, the two assemblages will homogenize chemically and mineralogically, however from a chemical thermodynamic point of view, this is not the case. Certain petrological differences in terms of bulk composition, mineralogy and mineral abundance remain unless other processes, like melting or mechanical mixing come into play. While there is not a standard procedure to address this problem, in this study it is shown that by applying chemical thermodynamic principles and some reasonable assumptions, it is possible to determine the equilibrium composition of each of the two assemblages. Some examples that consider typical mantle rocks, peridotite, lherzolite, dunite and eclogite described by simplified chemical systems are used to illustrate the general approach. A preliminary application to evaluate the effect of melting a heterogeneous mantle in complete chemical equilibrium using a thermodynamic formulation coupled with a two-phase geodynamic model shows that major element composition of the melt product generated by different peridotites is very similar. This may explain the relative homogeneity of major elements of MORBs which could be the product of melting a relatively uniform mantle, as commonly accepted, or alternatively a peridotitic mantle with different compositions but in chemical equilibrium.
Equilibrium properties of chemically reacting gases
NASA Technical Reports Server (NTRS)
1976-01-01
The equilibrium energy, enthalpy, entropy, specific heat at constant volume and constant pressure, and the equation of state of the gas are all derived for chemically reacting gas mixtures in terms of the compressibility, the mol fractions, the thermodynamic properties of the pure gas components, and the change in zero point energy due to reaction. Results are illustrated for a simple diatomic dissociation reaction and nitrogen is used as an example. Next, a gas mixture resulting from combined diatomic dissociation and atomic ionization reactions is treated and, again, nitrogen is used as an example. A short discussion is given of the additional complexities involved when precise solutions for high-temperature air are desired, including effects caused by NO produced in shuffle reactions and by other trace species formed from CO2, H2O and Ar found in normal air.
Spectral Quasi-Equilibrium Manifold for Chemical Kinetics.
Kooshkbaghi, Mahdi; Frouzakis, Christos E; Boulouchos, Konstantinos; Karlin, Iliya V
2016-05-26
The Spectral Quasi-Equilibrium Manifold (SQEM) method is a model reduction technique for chemical kinetics based on entropy maximization under constraints built by the slowest eigenvectors at equilibrium. The method is revisited here and discussed and validated through the Michaelis-Menten kinetic scheme, and the quality of the reduction is related to the temporal evolution and the gap between eigenvalues. SQEM is then applied to detailed reaction mechanisms for the homogeneous combustion of hydrogen, syngas, and methane mixtures with air in adiabatic constant pressure reactors. The system states computed using SQEM are compared with those obtained by direct integration of the detailed mechanism, and good agreement between the reduced and the detailed descriptions is demonstrated. The SQEM reduced model of hydrogen/air combustion is also compared with another similar technique, the Rate-Controlled Constrained-Equilibrium (RCCE). For the same number of representative variables, SQEM is found to provide a more accurate description. PMID:27116566
On the Concept "Chemical Equilibrium": The Associative Framework.
ERIC Educational Resources Information Center
Gussarsky, Esther; Gorodetsky, Malka
1990-01-01
Word associations were used to map high school students' concepts of "chemical equilibrium" and "equilibrium." It was found that the preconception of the two concepts was differentiated on noncritical dimensions. (Author/CW)
ERIC Educational Resources Information Center
Niaz, Mansoor
1998-01-01
Reports on a study that constructs a Lakatosian teaching strategy that can facilitate conceptual change in students' understanding of chemical equilibrium. Results indicate that the experimental group performed better on tests. Contains 81 references. (DDR)
Sparse Partial Equilibrium Tables in Chemically Resolved Reactive Flow
Vitello, P; Fried, L E; Pudliner, B; McAbee, T
2003-07-14
The detonation of an energetic material is the result of a complex interaction between kinetic chemical reactions and hydrodynamics. Unfortunately, little is known concerning the detailed chemical kinetics of detonations in energetic materials. CHEETAH uses rate laws to treat species with the slowest chemical reactions, while assuming other chemical species are in equilibrium. CHEETAH supports a wide range of elements and condensed detonation products and can also be applied to gas detonations. A sparse hash table of equation of state values, called the ''cache'' is used in CHEETAH to enhance the efficiency of kinetic reaction calculations. For large-scale parallel hydrodynamic calculations, CHEETAH uses MPI communication to updates to the cache. We present here details of the sparse caching model used in the CHEETAH. To demonstrate the efficiency of modeling using a sparse cache model we consider detonations in energetic materials.
Sparse Partial Equilibrium Tables in Chemically Resolved Reactive Flow
NASA Astrophysics Data System (ADS)
Vitello, Peter; Fried, Laurence E.; Pudliner, Brian; McAbee, Tom
2004-07-01
The detonation of an energetic material is the result of a complex interaction between kinetic chemical reactions and hydrodynamics. Unfortunately, little is known concerning the detailed chemical kinetics of detonations in energetic materials. CHEETAH uses rate laws to treat species with the slowest chemical reactions, while assuming other chemical species are in equilibrium. CHEETAH supports a wide range of elements and condensed detonation products and can also be applied to gas detonations. A sparse hash table of equation of state values is used in CHEETAH to enhance the efficiency of kinetic reaction calculations. For large-scale parallel hydrodynamic calculations, CHEETAH uses parallel communication to updates to the cache. We present here details of the sparse caching model used in the CHEETAH coupled to an ALE hydrocode. To demonstrate the efficiency of modeling using a sparse cache model we consider detonations in energetic materials.
ERIC Educational Resources Information Center
Ghirardi, Marco; Marchetti, Fabio; Pettinari, Claudio; Regis, Alberto; Roletto, Ezio
2015-01-01
A didactic sequence is proposed for the teaching of chemical equilibrium law. In this approach, we have avoided the kinetic derivation and the thermodynamic justification of the equilibrium constant. The equilibrium constant expression is established empirically by a trial-and-error approach. Additionally, students learn to use the criterion of…
Teaching Chemical Equilibrium and Thermodynamics in Undergraduate General Chemistry Classes.
ERIC Educational Resources Information Center
Banerjee, Anil C.
1995-01-01
Discusses some of the conceptual difficulties encountered by undergraduate students in learning certain aspects of chemical equilibrium and thermodynamics. Discusses teaching strategies for dealing with these difficulties. (JRH)
Boltzmann equation solver adapted to emergent chemical non-equilibrium
Birrell, Jeremiah; Wilkening, Jon; Rafelski, Johann
2015-01-15
We present a novel method to solve the spatially homogeneous and isotropic relativistic Boltzmann equation. We employ a basis set of orthogonal polynomials dynamically adapted to allow for emergence of chemical non-equilibrium. Two time dependent parameters characterize the set of orthogonal polynomials, the effective temperature T(t) and phase space occupation factor ϒ(t). In this first paper we address (effectively) massless fermions and derive dynamical equations for T(t) and ϒ(t) such that the zeroth order term of the basis alone captures the particle number density and energy density of each particle distribution. We validate our method and illustrate the reduced computational cost and the ability to easily represent final state chemical non-equilibrium by studying a model problem that is motivated by the physics of the neutrino freeze-out processes in the early Universe, where the essential physical characteristics include reheating from another disappearing particle component (e{sup ±}-annihilation)
Non-equilibrium effects in high temperature chemical reactions
NASA Technical Reports Server (NTRS)
Johnson, Richard E.
1987-01-01
Reaction rate data were collected for chemical reactions occurring at high temperatures during reentry of space vehicles. The principle of detailed balancing is used in modeling kinetics of chemical reactions at high temperatures. Although this principle does not hold for certain transient or incubation times in the initial phase of the reaction, it does seem to be valid for the rates of internal energy transitions that occur within molecules and atoms. That is, for every rate of transition within the internal energy states of atoms or molecules, there is an inverse rate that is related through an equilibrium expression involving the energy difference of the transition.
Chemical Equilibrium Models for the S3 State of the Oxygen-Evolving Complex of Photosystem II.
Isobe, Hiroshi; Shoji, Mitsuo; Shen, Jian-Ren; Yamaguchi, Kizashi
2016-01-19
We have performed hybrid density functional theory (DFT) calculations to investigate how chemical equilibria can be described in the S3 state of the oxygen-evolving complex in photosystem II. For a chosen 340-atom model, 1 stable and 11 metastable intermediates have been identified within the range of 13 kcal mol(-1) that differ in protonation, charge, spin, and conformational states. The results imply that reversible interconversion of these intermediates gives rise to dynamic equilibria that involve processes with relocations of protons and electrons residing in the Mn4CaO5 cluster, as well as bound water ligands, with concomitant large changes in the cluster geometry. Such proton tautomerism and redox isomerism are responsible for reversible activation/deactivation processes of substrate oxygen species, through which Mn-O and O-O bonds are transiently ruptured and formed. These results may allow for a tentative interpretation of kinetic data on substrate water exchange on the order of seconds at room temperature, as measured by time-resolved mass spectrometry. The reliability of the hybrid DFT method for the multielectron redox reaction in such an intricate system is also addressed. PMID:26717045
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, and 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.
The Lewis Chemical Equilibrium Program with parametric study capability
NASA Technical Reports Server (NTRS)
Sevigny, R.
1981-01-01
The program was developed to determine chemical equilibrium in complex systems. Using a free energy minimization technique, the program permits calculations such as: chemical equilibrium for assigned thermodynamic states; theoretical rocket performance for both equilibrium and frozen compositions during expansion; incident and reflected shock properties; and Chapman-Jouget detonation properties. It is shown that the same program can handle solid coal in an entrained flow coal gasification problem.
Using Analogies to Prevent Misconceptions about Chemical Equilibrium
ERIC Educational Resources Information Center
Sahin Pekmez, Esin
2010-01-01
The main purpose of this study was to find the effectiveness of using analogies to prevent misconceptions about chemical equilibrium. Nineteen analogies, which were based on dynamic aspects of chemical equilibrium and application of Le Chatelier's principle, were developed. The participations of this study consisted of 11th grade students (n: 151)…
Conceptual Integration of Chemical Equilibrium by Prospective Physical Sciences Teachers
ERIC Educational Resources Information Center
Ganaras, Kostas; Dumon, Alain; Larcher, Claudine
2008-01-01
This article describes an empirical study concerning the mastering of the chemical equilibrium concept by prospective physical sciences teachers. The main objective was to check whether the concept of chemical equilibrium had become an integrating and unifying concept for them, that is to say an operational and functional knowledge to explain and…
Park, J.Y.; Batchelor, B.
1999-01-01
In the previous paper, SOLTEQ demonstrated its ability to represent chemical speciation in the pure s/s binder systems. The objective of this paper is to provide a method for representing doped waste contaminants in SOLTEQ so that their speciation can be determined. To evaluate this method, model predictions were compared with measured concentrations in the porewaters expressed from cement pastes doped with various metal salts. Among doped metals, only mercury showed concentrations that indicated primary control by precipitation. The other metals, such as Cr(VI), Cd, Pb, and Na, showed behaviors that imply sorption as a major immobilization mechanism. The Langmuir isotherm was found to be well suited to describe the sorption of Na{sup +} ions onto the effective surface of CSH. To support the sorption of metal anions onto presumably negatively charged silica surface in cement porewater, a hypothesis of super-equivalent adsorption is proposed.
Chemical Equilibrium Composition of Aqueous Systems
Energy Science and Technology Software Center (ESTSC)
1996-12-30
MINEQL is a subroutine package to calculate equilibrium composition of an aqueous system, accounting for mass transfer. MINEQL-EIR contains an additional base on enthalpy and heat capacity data and has the option to do calculations at temperatures different from 25 degrees C.
Chan, M.; Yen, T.F.
1980-11-01
A chemical equilibrium model for interfacial activity of crude in aqueous alkaline solution is proposed. The model predicts the observed effects of pH and concentrations of alkali and salt on the interfacial tension (IFT). The model proposed was shown to describe the observed effects of acid content, pH, and sodium ions on the interfacial activity of crude oil in water. Once the pH of the interface reaches the pKa of the acids, sometimes with the help of addition of some salt, the IFT experiences a sudden steep drop to the range of 10/sup -2/ dynes/cm. After that, further addition of sodium either in the form of NaOH or NaCl is going to increase the IFT due to a shift of equilibriumn to the formation of undissociated soap. This was confirmed by the difference in the observed effect of sodium on the IFT of the extracted soap molecules which are dissociated easily and those which are associated highly and precipitated easily. These soap molecules have dissociation constant values ranging from below 10/sup -2/ to above one. 13 references.
Modeling equilibrium Fe isotope fractionation
NASA Astrophysics Data System (ADS)
Anbar, A.; Jarzecki, A.; Spiro, T.
2003-04-01
Research into the stable isotope biogeochemistry of Fe and other transition metals has been driven primarily by analytical innovations which have revealed significant isotope effects in nature and the laboratory. Further development of these new isotope systems requires complementary theoretical research to guide analytical efforts. The results of the first such studies show some discrepancies with experiments. For example, Johnson et al. (2002) report an experimentally-determined 56Fe/54Fe equilibrium fractionation factor between Fe(II) and Fe(III) aquo complexes of ˜1.0025. This effect is ˜50% smaller than predicted theoretically by Schauble et al. (2001). It is important to resolve such discrepancies. Equilibrium isotope fractionation factors can be predicted from vibrational spectroscopic data of isotopically-substituted complexes, or from theoretical predictions of some or all of these frequencies obtained using force field models. The pioneering work of Schauble et al. (2001) utilized a modified Urey-Bradley force field (MUBFF) model. This approach is limiting in at least three ways: First, it is not ab initio, requiring as input some measured vibrational frequencies. Such data are not always available, or may have significant uncertainties. Second, the MUBFF does not include potentially important effects of solvent interaction. Third, because it makes certain assumptions about molecular symmetry, the MUBFF-based approach is not able to model the spectra of mixed-ligand complexes. To address these limitations, we are evaluating the use of density functional theory (DFT) as an ab initio method to predict vibrational frequencies of isotopically-substituted complexes and, hence, equilibrium fractionation factors. In a preliminary examination of the frequency shift upon isotope substitution of the bending and asymmetric stretching modes of the tetrahedral FeCl_42- complex, we find substantial differences between MUBFF and DFT predictions. Results for other Fe
A Better Way of Dealing with Chemical Equilibrium.
ERIC Educational Resources Information Center
Tykodi, Ralph J.
1986-01-01
Discusses how to address the concept of chemical equilibrium through the use of thermodynamic activities. Describes the advantages of setting up an equilibrium constant in terms of activities and demonstrates how to approximate those activities by practical measures such as partial pressures, mole fractions, and molar concentrations. (TW)
Thermodynamic and transport properties of gaseous tetrafluoromethane in chemical equilibrium
NASA Technical Reports Server (NTRS)
Hunt, J. L.; Boney, L. R.
1973-01-01
Equations and in computer code are presented for the thermodynamic and transport properties of gaseous, undissociated tetrafluoromethane (CF4) in chemical equilibrium. The computer code calculates the thermodynamic and transport properties of CF4 when given any two of five thermodynamic variables (entropy, temperature, volume, pressure, and enthalpy). Equilibrium thermodynamic and transport property data are tabulated and pressure-enthalpy diagrams are presented.
Understanding Chemical Reaction Kinetics and Equilibrium with Interlocking Building Blocks
ERIC Educational Resources Information Center
Cloonan, Carrie A.; Nichol, Carolyn A.; Hutchinson, John S.
2011-01-01
Chemical reaction kinetics and equilibrium are essential core concepts of chemistry but are challenging topics for many students, both at the high school and undergraduate university level. Visualization at the molecular level is valuable to aid understanding of reaction kinetics and equilibrium. This activity provides a discovery-based method to…
Evidence-Based Approaches to Improving Chemical Equilibrium Instruction
ERIC Educational Resources Information Center
Davenport, Jodi L.; Leinhardt, Gaea; Greeno, James; Koedinger, Kenneth; Klahr, David; Karabinos, Michael; Yaron, David J.
2014-01-01
Two suggestions for instruction in chemical equilibrium are presented, along with the evidence that supports these suggestions. The first is to use diagrams to connect chemical reactions to the effects of reactions on concentrations. The second is the use of the majority and minority species (M&M) strategy to analyze chemical equilibrium…
Thermal Conductivity of Gas Mixtures in Chemical Equilibrium
NASA Technical Reports Server (NTRS)
Brokaw, Richard S.
1960-01-01
The expression for the thermal conductivity of gas mixtures in chemical equilibrium is presented in a simpler and less restrictive form. This new form is shown to be equivalent to the previous equations.
Speleothems as Examples of Chemical Equilibrium Processes.
ERIC Educational Resources Information Center
Wilson, James R.
1984-01-01
The chemical formation of speleothems such as stalactites and stalagmites is poorly understood by introductory geology instructors and misrepresented in most textbooks. Although evaporation may be a controlling factor in some caves, it is necessary to consider chemical precipitation as more important in controlling the diagenesis of calcium…
ERIC Educational Resources Information Center
Jameson, Cynthia J.
Presented are the teacher's guide and student materials for one of a series of self-instructional, computer-based learning modules for an introductory, undergraduate chemistry course. The student manual for this unit on chemical equilibrium calculations includes objectives, prerequisites, a discussion of the equilibrium constant (K), and ten…
Wave propagation in a quasi-chemical equilibrium plasma
NASA Technical Reports Server (NTRS)
Fang, T.-M.; Baum, H. R.
1975-01-01
Wave propagation in a quasi-chemical equilibrium plasma is studied. The plasma is infinite and without external fields. The chemical reactions are assumed to result from the ionization and recombination processes. When the gas is near equilibrium, the dominant role describing the evolution of a reacting plasma is played by the global conservation equations. These equations are first derived and then used to study the small amplitude wave motion for a near-equilibrium situation. Nontrivial damping effects have been obtained by including the conduction current terms.
Multicomponent Equilibrium Models for Testing Geothermometry Approaches
Cooper, D. Craig; Palmer, Carl D.; Smith, Robert W.; McLing, Travis L.
2013-02-01
Geothermometry is an important tool for estimating deep reservoir temperature from the geochemical composition of shallower and cooler waters. The underlying assumption of geothermometry is that the waters collected from shallow wells and seeps maintain a chemical signature that reflects equilibrium in the deeper reservoir. Many of the geothermometers used in practice are based on correlation between water temperatures and composition or using thermodynamic calculations based a subset (typically silica, cations or cation ratios) of the dissolved constituents. An alternative approach is to use complete water compositions and equilibrium geochemical modeling to calculate the degree of disequilibrium (saturation index) for large number of potential reservoir minerals as a function of temperature. We have constructed several “forward” geochemical models using The Geochemist’s Workbench to simulate the change in chemical composition of reservoir fluids as they migrate toward the surface. These models explicitly account for the formation (mass and composition) of a steam phase and equilibrium partitioning of volatile components (e.g., CO2, H2S, and H2) into the steam as a result of pressure decreases associated with upward fluid migration from depth. We use the synthetic data generated from these simulations to determine the advantages and limitations of various geothermometry and optimization approaches for estimating the likely conditions (e.g., temperature, pCO2) to which the water was exposed in the deep subsurface. We demonstrate the magnitude of errors that can result from boiling, loss of volatiles, and analytical error from sampling and instrumental analysis. The estimated reservoir temperatures for these scenarios are also compared to conventional geothermometers. These results can help improve estimation of geothermal resource temperature during exploration and early development.
NASA Astrophysics Data System (ADS)
Niaz, M.
The main objective of this study is to construct a Lakatosian teaching strategy that can facilitate conceptual change in students'' understanding of chemical equilibrium. The strategy is based on the premise that cognitive conflicts must have been engendered by the students themselves in trying to cope with different problem solving strategies. Results obtained (based on Venezuelan freshman students) show that the performance of the experimental group of students was generally better (especially on the immediate post tests) than that of the control group. It is concluded that a conceptual change teaching strategy must take into consideration the following aspects: a) core beliefs of the students in the topic (cf. ''hard core'', Lakatos 1970); b) exploration of the relationship between core beliefs and student alternative conceptions (misconceptions); c) cognitive complexity of the core belief can be broken down into a series of related and probing questions; d) students resist changes in their core beliefs by postulating ''auxiliary hypotheses'' in order to resolve their contradictions; e) students'' responses based on their alternative conceptions must be considered not as wrong, but rather as models, perhaps in the same sense as used by scientists to break the complexity of a problem; and f) students'' misconceptions be considered as alternative conceptions (theories) that compete with the present scientific theories and at times recapitulate theories scientists held in the past.
QUANTITATIVE ANALYSIS OF AQUEOUS SPECIES USING RAMAN SPECTROMETRY AND EQUILIBRIUM MODEL CALCULATIONS
An analytical approach of quantifying various chemical species, using Raman spectrometry in conjunction with equilibrium modeling, has been tested on aqueous solutions containing Nd, Cu, and dipicolinic acid. Equilibrium modeling was used to select optimum conditions in simple so...
Lathouri, Maria; Korre, Anna
2015-12-15
Although significant progress has been made in understanding how environmental factors modify the speciation, bioavailability and toxicity of metals such as copper in aquatic environments, the current methods used to establish water quality standards do not necessarily consider the different geological and geochemical characteristics of a given site and the factors that affect copper fate, bioavailability potential and toxicity. In addition, the temporal variation in the concentration and bioavailable metal fraction is also important in freshwater systems. The work presented in this paper illustrates the temporal and seasonal variability of a range of water quality parameters, and Cu speciation, bioavailability and toxicity at four freshwaters sites in the UK. Rivers Coquet, Cree, Lower Clyde and Eden (Kent) were selected to cover a broad range of different geochemical environments and site characteristics. The monitoring data used covered a period of around six years at almost monthly intervals. Chemical equilibrium modelling was used to study temporal variations in Cu speciation and was combined with acute toxicity modelling to assess Cu bioavailability for two aquatic species, Daphnia magna and Daphnia pulex. The estimated copper bioavailability, toxicity levels and the corresponding ecosystem risks were analysed in relation to key water quality parameters (alkalinity, pH and DOC). Although copper concentrations did not vary much during the sampling period or between the seasons at the different sites; copper bioavailability varied markedly. In addition, through the chronic-Cu BLM-based on the voluntary risk assessment approach, the potential environmental risk in terms of the chronic toxicity was assessed. A much higher likelihood of toxicity effects was found during the cold period at all sites. It is suggested that besides the metal (copper) concentration in the surface water environment, the variability and seasonality of other important water quality
Mathematical modeling of non-equilibrium sorption
NASA Astrophysics Data System (ADS)
Kaliev, Ibragim A.; Mukhambetzhanov, Saltanbek T.; Sabitova, Gulnara S.; Sakhit, Anghyz E.
2016-08-01
We consider the system of equations modeling the process of non-equilibrium sorption. Difference approximation of differential problem by the implicit scheme is formulated. The solution of the difference problem is constructed using the sweep method. Based on the numerical results we can conclude the following: when the relaxation time decreases to 0, then the solution of non-equilibrium problem tends with increasing time to solution of the equilibrium problem.
CET89 - CHEMICAL EQUILIBRIUM WITH TRANSPORT PROPERTIES, 1989
NASA Technical Reports Server (NTRS)
Mcbride, B.
1994-01-01
Scientists and engineers need chemical equilibrium composition data to calculate the theoretical thermodynamic properties of a chemical system. This information is essential in the design and analysis of equipment such as compressors, turbines, nozzles, engines, shock tubes, heat exchangers, and chemical processing equipment. The substantial amount of numerical computation required to obtain equilibrium compositions and transport properties for complex chemical systems led scientists at NASA's Lewis Research Center to develop CET89, a program designed to calculate the thermodynamic and transport properties of these systems. CET89 is a general program which will calculate chemical equilibrium compositions and mixture properties for any chemical system with available thermodynamic data. Generally, mixtures may include condensed and gaseous products. CET89 performs the following operations: it 1) obtains chemical equilibrium compositions for assigned thermodynamic states, 2) calculates dilute-gas transport properties of complex chemical mixtures, 3) obtains Chapman-Jouguet detonation properties for gaseous species, 4) calculates incident and reflected shock properties in terms of assigned velocities, and 5) calculates theoretical rocket performance for both equilibrium and frozen compositions during expansion. The rocket performance function allows the option of assuming either a finite area or an infinite area combustor. CET89 accommodates problems involving up to 24 reactants, 20 elements, and 600 products (400 of which may be condensed). The program includes a library of thermodynamic and transport properties in the form of least squares coefficients for possible reaction products. It includes thermodynamic data for over 1300 gaseous and condensed species and transport data for 151 gases. The subroutines UTHERM and UTRAN convert thermodynamic and transport data to unformatted form for faster processing. The program conforms to the FORTRAN 77 standard, except for
ERIC Educational Resources Information Center
Quilez, Juan
2009-01-01
With this paper, our main aim is to contribute to the realisation of the chemical reactivity concept, tracing the historical evolution of the concept of chemical affinity that eventually supported the concept of chemical equilibrium. We will concentrate on searching for the theoretical grounds of three key chemical equilibrium ideas: "incomplete…
ERIC Educational Resources Information Center
Van Driel, Jan H.; De Vos, Wobbe; Verloop, Nico; Dekkers, Hetty
1998-01-01
Describes an empirical study concerning the introduction of the concept of chemical equilibrium in chemistry classrooms in a way which challenges students' initial conceptions of chemical reactions. Contains 23 references. (DDR)
Chemical-equilibrium calculations for aqueous geothermal brines
Kerrisk, J.F.
1981-05-01
Results from four chemical-equilibrium computer programs, REDEQL.EPAK, GEOCHEM, WATEQF, and SENECA2, have been compared with experimental solubility data for some simple systems of interest with geothermal brines. Seven test cases involving solubilities of CaCO/sub 3/, amorphous SiO/sub 2/, CaSO/sub 4/, and BaSO/sub 4/ at various temperatures from 25 to 300/sup 0/C and in NaCl or HCl solutions of 0 to 4 molal have been examined. Significant differences between calculated results and experimental data occurred in some cases. These differences were traced to inaccuracies in free-energy or equilibrium-constant data and in activity coefficients used by the programs. Although currently available chemical-equilibrium programs can give reasonable results for these calculations, considerable care must be taken in the selection of free-energy data and methods of calculating activity coefficients.
Problem Solving and Chemical Equilibrium: Successful versus Unsuccessful Performance.
ERIC Educational Resources Information Center
Camacho, Moises; Good, Ron
1989-01-01
Describes the problem-solving behaviors of experts and novices engaged in solving seven chemical equilibrium problems. Lists 27 behavioral tendencies of successful and unsuccessful problem solvers. Discusses several implications for a problem solving theory, think-aloud techniques, adequacy of the chemistry domain, and chemistry instruction.…
Parameter uncertainty in chemical equilibrium calculations using fuzzy set theory
NASA Astrophysics Data System (ADS)
Schulz, K.; Huwe, B.; Peiffer, S.
1999-04-01
A method based on fuzzy set theory is presented to incorporate imprecise thermodynamic parameters into chemical equilibrium calculations of aqueous systems. Imprecision may arise from uncertainties in experimental parameter determination as well as from inconsistency of available data in the literature. Fuzzy numbers with different shapes of membership functions are used to express imprecision in a non-probabilistic sense. A solution algorithm for a system of nonlinear algebraic equations calculating the chemical equilibrium composition is combined with level set operations to solve the fuzzy chemical equlibrium problem. The method results in multiple minimizing/maximizing procedures from which the membership functions of equilibrium species concentrations are determined. An application of the proposed method to an aqueous cadmium-sulfide system illustrates the acquisition of membership functions for the thermodynamic constants out of given information. Stochastic information on measurement data are appropriately transformed into fuzzy numbers to allow for the combined calculation of different kinds of uncertainty. The results of four calculation scenarios show their strong impact on the resulting membership functions of chemical equilibrium composition and are discussed in the context of data evaluation and decision making in geochemistry.
Treating Chemical Equilibrium Mathematically in Secondary Schools: A Preliminary Investigation.
ERIC Educational Resources Information Center
Case, James B.
This report presents the procedures, results, and conclusions of a study to determine the characteristics of secondary school chemistry students who were successful in grasping a mathematical approach to learning chemical equilibrium. Subjects were eighty-nine students enrolled in chemistry at a rural-suburban high school; each student had…
Modified NASA-Lewis chemical equilibrium code for MHD applications
NASA Technical Reports Server (NTRS)
Sacks, R. A.; Geyer, H. K.; Grammel, S. J.; Doss, E. D.
1979-01-01
A substantially modified version of the NASA-Lewis Chemical Equilibrium Code was recently developed. The modifications were designed to extend the power and convenience of the Code as a tool for performing combustor analysis for MHD systems studies. The effect of the programming details is described from a user point of view.
Computer program determines chemical composition of physical system at equilibrium
NASA Technical Reports Server (NTRS)
Kwong, S. S.
1966-01-01
FORTRAN 4 digital computer program calculates equilibrium composition of complex, multiphase chemical systems. This is a free energy minimization method with solution of the problem reduced to mathematical operations, without concern for the chemistry involved. Also certain thermodynamic properties are determined as byproducts of the main calculations.
Chemical equilibrium of ablation materials including condensed species
NASA Technical Reports Server (NTRS)
Stroud, C. W.; Brinkley, K. L.
1975-01-01
Equilibrium is determined by finding chemical composition with minimum free energy. Method of steepest descent is applied to quadratic representation of free-energy surface. Solution is initiated by selecting arbitrary set of mole fractions, from which point on free-energy surface is computed.
Composition and Thermodynamic Properties of Air in Chemical Equilibrium
NASA Technical Reports Server (NTRS)
Moeckel, W E; Weston, Kenneth C
1958-01-01
Charts have been prepared relating the thermodynamic properties of air in chemical equilibrium for temperatures to 15,000 degrees k and for pressures 10(-5) to 10 (plus 4) atmospheres. Also included are charts showing the composition of air, the isentropic exponent, and the speed of sound. These charts are based on thermodynamic data calculated by the National Bureau of Standards.
Chemical Equilibrium and Polynomial Equations: Beware of Roots.
ERIC Educational Resources Information Center
Smith, William R.; Missen, Ronald W.
1989-01-01
Describes two easily applied mathematical theorems, Budan's rule and Rolle's theorem, that in addition to Descartes's rule of signs and intermediate-value theorem, are useful in chemical equilibrium. Provides examples that illustrate the use of all four theorems. Discusses limitations of the polynomial equation representation of chemical…
Computer Series, 108. Computer Simulation of Chemical Equilibrium.
ERIC Educational Resources Information Center
Cullen, John F., Jr.
1989-01-01
Presented is a computer simulation called "The Great Chemical Bead Game" which can be used to teach the concepts of equilibrium and kinetics to introductory chemistry students more clearly than through an experiment. Discussed are the rules of the game, the application of rate laws and graphical analysis. (CW)
Concept Maps about Chemical Equilibrium and Students' Achievement Scores.
ERIC Educational Resources Information Center
Wilson, Jan
1996-01-01
Examines relationships between structural characteristics of students' concept maps about chemical equilibrium and independent measures of their achievement in chemistry. Results indicate significant relationships between multidimensional scaling coordinates and test scores of recall of knowledge and its application and also reveal structural…
Pre-equilibrium approximation in chemical and photophysical kinetics
NASA Astrophysics Data System (ADS)
Rae, Margaret; Berberan-Santos, Mário N.
2002-07-01
For most mechanisms of chemical reactions and molecular photophysical processes the time evolution of the concentration of the intervening species cannot be obtained analytically. The pre-equilibrium approximation is one of several useful approximation methods that allow the derivation of explicit solutions and simplify numerical solutions. In this work, a general view of the pre-equilibrium approximation is presented, along with the respective analytical solution. It is also shown that the kinetic behavior of systems subject to pre-equilibration can be obtained by the application of perturbation theory. Several photophysical systems are discussed, including excimer formation, thermally activated delayed fluorescence, and external-heavy atom quenching of luminescence.
Rai, D.
1993-12-01
This document is a technical reference manual for FOWL-GH{trademark}, the FOssil Fuel Combustion Waste Leaching Code. FOWL-GH{trademark} predicts the chemical composition of fifteen chemical constituents (Ba, Ca, Cd, CO{sub 3} Cr, Cu, Mo, SO{sub 4}, Sr, As, B, Ni, Se, Zn, and total dissolved solids), plus the pH (H{sup +}), as a function of time at electric utility by-product disposal sites. Boron and Zn are considered only in the ponded site option. These sites may contain fly ash, bottom ash, or flue gas desulfurization (FGD) sludges. FOWL-GH{trademark} considers both landfill and slurry pond disposal sites. FOWL-GH{trademark} is a completely restructured and recoded version of the original FOWL{trademark} model. The major improvements in FOWL-GH{trademark} are the inclusion of a chemical equilibrium model (GMIN) to perform the geochemical calculations, a recoded version of the Hydrologic Evaluation of Landfill Performance (HELP) model for water-balance calculations at landfill sites, the capability to model slurry pond sites, an enhanced user-oriented interface, improved mechanistic (thermodynamic) and empirical data for several elements, and the capability to model concentrations of highly soluble salts. This manual describes the scientific basis for the calculations in FOWL-GH{trademark}. An overview of the structure of the model is also provided. The reliability of the geochemical-module calculations is demonstrated by an extensive comparison of model calculations with experimental data from laboratory batch experiments and data collected at field disposal sites. The results show good agreement with the experimental and field data for most of the chemical constituents included in the model.
Clouds Composition in Super-Earth Atmospheres: Chemical Equilibrium Calculations
NASA Astrophysics Data System (ADS)
Kempton, Eliza M.-R.; Mbarek, Rostom
2015-12-01
Attempts to determine the composition of super-Earth atmospheres have so far been plagued by the presence of clouds. Yet the theoretical framework to understand these clouds is still in its infancy. For the super-Earth archetype GJ 1214b, KCl, Na2S, and ZnS have been proposed as condensates that would form under the condition of chemical equilibrium, if the planet’s atmosphere has a bulk composition near solar. Condensation chemistry calculations have not been presented for a wider range of atmospheric bulk composition that is to be expected for super-Earth exoplanets. Here we provide a theoretical context for the formation of super-Earth clouds in atmospheres of varied composition by determining which condensates are likely to form, under the assumption of chemical equilibrium. We model super-Earth atmospheres assuming they are formed by degassing of volatiles from a solid planetary core of chondritic material. Given the atomic makeup of these atmospheres, we minimize the global Gibbs free energy of over 550 gases and condensates to obtain the molecular composition of the atmospheres over a temperature range of 350-3,000 K. Clouds should form along the temperature-pressure boundaries where the condensed species appear in our calculations. The super-Earth atmospheres that we study range from highly reducing to oxidizing and have carbon to oxygen (C:O) ratios that are both sub-solar and super-solar, thereby spanning a diverse range of atmospheric composition that is appropriate for low-mass exoplanets. Some condensates appear across all of our models. However, the majority of condensed species appear only over specific ranges of H:O and C:O ratios. We find that for GJ 1214b, KCl is the primary cloud-forming condensate at solar composition, in agreement with previous work. However, for oxidizing atmospheres, where H:O is less than unity, K2SO4 clouds form instead. For carbon-rich atmospheres with super-solar C:O ratios, graphite clouds additionally appear. At
MCNP modelling of the PBMR equilibrium core
Albornoz, F.; Korochinsky, S.
2006-07-01
A complete MCNP model of the PBMR equilibrium core is presented, which accounts for the same fuel regions defined in the PBMR core management code, as well as for complete fuel and reflector temperature distributions. This comprehensive 3D model is the means to calculate and characterize the neutron and photon boundary sources of the equilibrium core, and is also used to support some specific core neutronic studies needing detailed geometry modelling. Due to the geometrical modelling approach followed, an unrealistic partial cutting of fuel kernels and pebbles is introduced in the model. The variations introduced by this partial cutting both on the packing fraction and on the uranium load of the modelled core and its corresponding effect on core reactivity and flux levels, have been investigated and quantified. A complete set of high-temperature cross-section data was applied to the calculation of the PBMR equilibrium core, and its effect on the calculated core reactivity is also reported. (authors)
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. PMID:27147197
Rai, D.
1993-12-01
This document is a user`s manual for FOWL-GH{trademark}, the FOssil Fuel Combustion Waste Leaching Code. The necessary input data, model output, installation procedures, and example test cases for FOWL-GH{trademark} are described in this manual. FOWL-GH{trademark} predicts the chemical composition of fifteen chemical constituents (Ba, Ca, Cd, CO{sub 3}, Cr, CU, Mo, SO{sub 4}, Sr, Zn, As, B, Ni, Se, and the total dissolved solids), plus the pH (H{sup +}), as a function of time at electric utility by-product disposal sites. These sites may contain fly ash, bottom ash, or flue gas desulfurization sludges. FOWL-GH{trademark} considers both landfill and slurry-pond disposal sites. FOWL-GH{trademark} is a completely restructured and recoded version of the original FOWL{trademark} model. The major improvements in FOWL-GH{trademark} are the inclusion of a chemical equilibrium model (GMIN) to perform the geochemical calculations, a recoded version of the Hydrologic Evaluation of Landfill Performance (HELP) model for water-balance calculations at landfill sites, the capability to model slurry-pond sites, an enhanced user-oriented interface, improved mechanistic (thermodynamic) and empirical data for several elements, and the capability to model concentrations of highly soluble salts. The actual implementation of these features is described in the accompanying technical manual (Felmy et al. 1993). FOWL-GH{trademark} distributed in executable form for IBM-compatible personal computers by the Electric Power Software Center through an Electric Power Research Institute, Inc. (EPRI) license.
Geometric programming, chemical equilibrium, and the anti-entropy function.
Duffin, R J; Zener, C
1969-07-01
THE CULMINATION OF THIS PAPER IS THE FOLLOWING DUALITY PRINCIPLE OF THERMODYNAMICS: maximum S = minimum S(*). (1) The left side of relation (1) is the classical characterization of equilibrium. It says to maximize the entropy function S with respect to extensive variables which are subject to certain constraints. The right side of (1) is a new characterization of equilibrium and concerns minimization of an anti-entropy function S(*) with respect to intensive variables. Relation (1) is applied to the chemical equilibrium of a mixture of gases at constant temperature and volume. Then (1) specializes to minimum F = maximum F(*), (2) where F is the Helmholtz function for free energy and F(*) is an anti-Helmholtz function. The right-side of (2) is an unconstrained maximization problem and gives a simplified practical procedure for calculating equilibrium concentrations. We also give a direct proof of (2) by the duality theorem of geometric programming. The duality theorem of geometric programming states that minimum cost = maximum anti-cost. (30). PMID:16591769
Exploring Chemical Equilibrium with Poker Chips: A General Chemistry Laboratory Exercise
ERIC Educational Resources Information Center
Bindel, Thomas H.
2012-01-01
A hands-on laboratory exercise at the general chemistry level introduces students to chemical equilibrium through a simulation that uses poker chips and rate equations. More specifically, the exercise allows students to explore reaction tables, dynamic chemical equilibrium, equilibrium constant expressions, and the equilibrium constant based on…
Chemical equilibrium in high pressure molecular fluid mixtures
Shaw, M.S.
1993-09-01
The N{sub atoms}PT Monte Carlo simulation method has been reformulated to incorporate multiple species and chemical reactions with changes in total number of molecules. While maintaining a constant number of each type of atom, the number of molecules is changed by turning on and off the interactions of any particular position with other molecules. Chemical reactions are allowed as a correlated move of atoms to differnt molecular locations. Equilibrium chemical composition is determined as an average over the simulation along with equation of state quantities. A large set of simulations has been made with the system N{sub 2} + O{sub 2} {rightleftharpoons} NO covering a wide range in P and T. Both Hugoniot states and the CJ point have been determined and are shown to be sensitive to the potentials between unlike species.
General Equilibrium Models: Improving the Microeconomics Classroom
ERIC Educational Resources Information Center
Nicholson, Walter; Westhoff, Frank
2009-01-01
General equilibrium models now play important roles in many fields of economics including tax policy, environmental regulation, international trade, and economic development. The intermediate microeconomics classroom has not kept pace with these trends, however. Microeconomics textbooks primarily focus on the insights that can be drawn from the…
ERIC Educational Resources Information Center
Quilez-Pardo, Juan; Solaz-Portoles, Joan Josep
1995-01-01
Study of strategies and procedures of 170 students and 40 teachers when solving chemical equilibrium problems found misconceptions emerging through: misapplication of Le Chatelier's Principle, use of rote-learning recall, incorrect control of variables, limited use of chemical equilibrium law, lack of mastery of chemical equilibrium principles,…
Early quark production and approach to chemical equilibrium
NASA Astrophysics Data System (ADS)
Gelfand, D.; Hebenstreit, F.; Berges, J.
2016-04-01
We perform real-time lattice simulations of out-of-equilibrium quark production in non-Abelian gauge theory in 3 +1 dimensions. Our simulations include the backreaction of quarks onto the dynamical gluon sector, which is particularly relevant for strongly correlated quarks. We observe fast isotropization and universal behavior of quarks and gluons at weak coupling and establish a quantitative connection to previous pure glue results. In order to understand the strongly correlated regime, we perform simulations for a large number of flavors and compare them to those obtained with two light quark flavors. By doing this we are able to provide estimates of the chemical equilibration time.
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.
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.
Concept maps about chemical equilibrium and students' achievement scores
NASA Astrophysics Data System (ADS)
Wilson, Jan
1996-06-01
The purpose of this study was to examine relationships between structural characteristics of students' concept maps about chemical equilibrium and independent measures of their achievement in chemistry. Fifty students in 1991 and seventy students in 1992 completed a concept-mapping task using twenty-four specified concepts. Using similarities in concept map structure, based on the presence or absence of linked pairs of concepts, non-metric multidimensional scaling (MDS) was used to plot the location of the concept maps in coordinate space. The distribution of maps was based on differences in their structure, but also reflected levels of student achievement on independent tests. The relationship between the coordinate location of each student's maps and his or her test scores on independent chemistry achievement tests was sought by canonical correlation analysis of the 1991 data set. This revealed significant relationships between the MDS coordinates and test scores of recall of knowledge and its application. Multiple regression analysis of sixty-one students' maps from the 1992 data set against their percentile rank scores on a national chemistry quiz revealed significant relationships. The results are interpreted as revealing structural differences in conceptual organisation about chemical equilibrium among students with different levels of achievement and thus relative expertise in the domain. The significant relationship between map structure and cognitive process scores in chemistry also supports the view that the organisation of declarative knowledge influences its accessibility in cognitive tasks.
Network representations of knowledge about chemical equilibrium: Variations with achievement
NASA Astrophysics Data System (ADS)
Wilson, Janice M.
This study examined variation in the organization of domain-specific knowledge by 50 Year-12 chemistry students and 4 chemistry teachers. The study used nonmetric multidimensional scaling (MDS) and the Pathfinder network-generating algorithm to investigate individual and group differences in student concepts maps about chemical equilibrium. MDS was used to represent the individual maps in two-dimensional space, based on the presence or absence of paired propositional links. The resulting separation between maps reflected degree of hierarchical structure, but also reflected independent measures of student achievement. Pathfinder was then used to produce semantic networks from pooled data from high and low achievement groups using proximity matrices derived from the frequencies of paired concepts. The network constructed from maps of higher achievers (coherence measure = 0.18, linked pairs = 294, and number of subjects = 32) showed greater coherence, more concordance in specific paired links, more important specific conceptual relationships, and greater hierarchical organization than did the network constructed from maps of lower achievers (coherence measure = 0.12, linked pairs = 552, and number of subjects = 22). These differences are interpreted in terms of qualitative variation in knowledge organization by two groups of individuals with different levels of relative expertise (as reflected in achievement scores) concerning the topic of chemical equilibrium. The results suggest that the technique of transforming paired links in concept maps into proximity matrices for input to multivariate analyses provides a suitable methodology for comparing and documenting changes in the organization and structure of conceptual knowledge within and between individual students.
Hartman, M.D.; Baron, J.S.; Ojima, D.S.
2007-01-01
Atmospheric deposition of sulfur and nitrogen species have the potential to acidify terrestrial and aquatic ecosystems, but nitrate and ammonium are also critical nutrients for plant and microbial productivity. Both the ecological response and the hydrochemical response to atmospheric deposition are of interest to regulatory and land management agencies. We developed a non-spatial biogeochemical model to simulate soil and surface water chemistry by linking the daily version of the CENTURY ecosystem model (DayCent) with a low temperature aqueous geochemical model, PHREEQC. The coupled model, DayCent-Chem, simulates the daily dynamics of plant production, soil organic matter, cation exchange, mineral weathering, elution, stream discharge, and solute concentrations in soil water and stream flow. By aerially weighting the contributions of separate bedrock/talus and tundra simulations, the model was able to replicate the measured seasonal and annual stream chemistry for most solutes for Andrews Creek in Loch Vale watershed, Rocky Mountain National Park. Simulated soil chemistry, net primary production, live biomass, and soil organic matter for forest and tundra matched well with measurements. This model is appropriate for accurately describing ecosystem and surface water chemical response to atmospheric deposition and climate change. ?? 2006 Elsevier B.V. All rights reserved.
Sugiura, Haruka; Ito, Manami; Okuaki, Tomoya; Mori, Yoshihito; Kitahata, Hiroyuki; Takinoue, Masahiro
2016-01-01
The design, construction and control of artificial self-organized systems modelled on dynamical behaviours of living systems are important issues in biologically inspired engineering. Such systems are usually based on complex reaction dynamics far from equilibrium; therefore, the control of non-equilibrium conditions is required. Here we report a droplet open-reactor system, based on droplet fusion and fission, that achieves dynamical control over chemical fluxes into/out of the reactor for chemical reactions far from equilibrium. We mathematically reveal that the control mechanism is formulated as pulse-density modulation control of the fusion-fission timing. We produce the droplet open-reactor system using microfluidic technologies and then perform external control and autonomous feedback control over autocatalytic chemical oscillation reactions far from equilibrium. We believe that this system will be valuable for the dynamical control over self-organized phenomena far from equilibrium in chemical and biomedical studies. PMID:26786848
NASA Astrophysics Data System (ADS)
Sugiura, Haruka; Ito, Manami; Okuaki, Tomoya; Mori, Yoshihito; Kitahata, Hiroyuki; Takinoue, Masahiro
2016-01-01
The design, construction and control of artificial self-organized systems modelled on dynamical behaviours of living systems are important issues in biologically inspired engineering. Such systems are usually based on complex reaction dynamics far from equilibrium; therefore, the control of non-equilibrium conditions is required. Here we report a droplet open-reactor system, based on droplet fusion and fission, that achieves dynamical control over chemical fluxes into/out of the reactor for chemical reactions far from equilibrium. We mathematically reveal that the control mechanism is formulated as pulse-density modulation control of the fusion-fission timing. We produce the droplet open-reactor system using microfluidic technologies and then perform external control and autonomous feedback control over autocatalytic chemical oscillation reactions far from equilibrium. We believe that this system will be valuable for the dynamical control over self-organized phenomena far from equilibrium in chemical and biomedical studies.
Sugiura, Haruka; Ito, Manami; Okuaki, Tomoya; Mori, Yoshihito; Kitahata, Hiroyuki; Takinoue, Masahiro
2016-01-01
The design, construction and control of artificial self-organized systems modelled on dynamical behaviours of living systems are important issues in biologically inspired engineering. Such systems are usually based on complex reaction dynamics far from equilibrium; therefore, the control of non-equilibrium conditions is required. Here we report a droplet open-reactor system, based on droplet fusion and fission, that achieves dynamical control over chemical fluxes into/out of the reactor for chemical reactions far from equilibrium. We mathematically reveal that the control mechanism is formulated as pulse-density modulation control of the fusion–fission timing. We produce the droplet open-reactor system using microfluidic technologies and then perform external control and autonomous feedback control over autocatalytic chemical oscillation reactions far from equilibrium. We believe that this system will be valuable for the dynamical control over self-organized phenomena far from equilibrium in chemical and biomedical studies. PMID:26786848
A variety of chemical equilibrium models have been developed to help assess environmental chemistry problems, but few were specifically developed as research and teaching tools for use in conjunction with soil chemistry experiments. MANE model was developed to calculate equilibri...
Minimizing the Free Energy: A Computer Method for Teaching Chemical Equilibrium Concepts.
ERIC Educational Resources Information Center
Heald, Emerson F.
1978-01-01
Presents a computer method for teaching chemical equilibrium concepts using material balance conditions and the minimization of the free energy. Method for the calculation of chemical equilibrium, the computer program used to solve equilibrium problems and applications of the method are also included. (HM)
Turbulence modeling for non-equilibrium flow
NASA Technical Reports Server (NTRS)
Durbin, P. A.
1995-01-01
The work performed during this year has involved further assessment and extension of the k-epsilon-v(exp 2) model, and initiation of work on scalar transport. The latter is introduced by the contribution of Y. Shabany to this volume. Flexible, computationally tractable models are needed for engineering CFD. As computational technology has progressed, the ability and need to use elaborate turbulence closure models has increased. The objective of our work is to explore and develop new analytical frameworks that might extend the applicability of the modeling techniques. In past years the development of a method for near-wall modeling was described. The method has been implemented into a CFD code and its viability has been demonstrated by various test cases. Further tests are reported herein. Non-equilibrium near-wall models are needed for some heat transfer applications. Scalar transport seems generally to be more sensitive to non-equilibrium effects than is momentum transport. For some applications turbulence anisotropy plays a role and an estimate of the full Reynolds stress tensor is needed. We have begun work on scalar transport per se, but in this brief I will only report on an extension of the k-epsilon-v(exp 2) model to predict the Reynolds stress tensor.
Transport Coefficients for the NASA Lewis Chemical Equilibrium Program
NASA Technical Reports Server (NTRS)
Svehla, Roger A.
1995-01-01
The new transport property data that will be used in the NASA Lewis Research Center's Chemical Equilibrium and Applications Program (CEA) is presented. It complements a previous publication that documented the thermodynamic and transport property data then in use. Sources of the data and a brief description of the method by which the data were obtained are given. Coefficients to calculate the viscosity, thermal conductivity, and binary interactions are given for either one, or usually, two temperature intervals, typically 300 to 1000 K and 1000 to 5000 K. The form of the transport equation is the same as used previously. The number of species was reduced from the previous database. Many species for which the data were estimated were eliminated from the database. Some ionneutral interactions were added.
Incorporation of a Chemical Equilibrium Equation of State into LOCI-Chem
NASA Technical Reports Server (NTRS)
Cox, Carey F.
2005-01-01
Renewed interest in development of advanced high-speed transport, reentry vehicles and propulsion systems has led to a resurgence of research into high speed aerodynamics. As this flow regime is typically dominated by hot reacting gaseous flow, efficient models for the characteristic chemical activity are necessary for accurate and cost effective analysis and design of aerodynamic vehicles that transit this regime. The LOCI-Chem code recently developed by Ed Luke at Mississippi State University for NASA/MSFC and used by NASA/MSFC and SSC represents an important step in providing an accurate, efficient computational tool for the simulation of reacting flows through the use of finite-rate kinetics [3]. Finite rate chemistry however, requires the solution of an additional N-1 species mass conservation equations with source terms involving reaction kinetics that are not fully understood. In the equilibrium limit, where the reaction rates approach infinity, these equations become very stiff. Through the use of the assumption of local chemical equilibrium the set of governing equations is reduced back to the usual gas dynamic equations, and thus requires less computation, while still allowing for the inclusion of reacting flow phenomenology. The incorporation of a chemical equilibrium equation of state module into the LOCI-Chem code was the primary objective of the current research. The major goals of the project were: (1) the development of a chemical equilibrium composition solver, and (2) the incorporation of chemical equilibrium solver into LOCI-Chem. Due to time and resource constraints, code optimization was not considered unless it was important to the proper functioning of the code.
Equilibrium Model of Precipitation in Microalloyed Steels
NASA Astrophysics Data System (ADS)
Xu, Kun; Thomas, Brian G.; O'Malley, Ron
2011-02-01
The formation of precipitates during thermal processing of microalloyed steels greatly influences their mechanical properties. Precipitation behavior varies with steel composition and temperature history and can lead to beneficial grain refinement or detrimental transverse surface cracks. This work presents an efficient computational model of equilibrium precipitation of oxides, sulfides, nitrides, and carbides in steels, based on satisfying solubility limits including Wagner interaction between elements, mutual solubility between precipitates, and mass conservation of alloying elements. The model predicts the compositions and amounts of stable precipitates for multicomponent microalloyed steels in liquid, ferrite, and austenite phases at any temperature. The model is first validated by comparing with analytical solutions of simple cases, predictions using the commercial package JMat-PRO, and previous experimental observations. Then it is applied to track the evolution of precipitate amounts during continuous casting of two commercial steels (1004 LCAK and 1006Nb HSLA) at two different casting speeds. This model is easy to modify to incorporate other precipitates, or new thermodynamic data, and is a useful tool for equilibrium precipitation analysis.
Thermodynamics and Kinetics of Chemical Equilibrium in Solution.
ERIC Educational Resources Information Center
Leenson, I. A.
1986-01-01
Discusses theory of thermodynamics of the equilibrium in solution and dissociation-dimerization kinetics. Describes experimental procedure including determination of molar absorptivity and equilibrium constant, reaction enthalpy, and kinetics of the dissociation-dimerization reaction. (JM)
NASA Technical Reports Server (NTRS)
Gordon, Sanford; Mcbride, Bonnie J.
1994-01-01
This report presents the latest in a number of versions of chemical equilibrium and applications programs developed at the NASA Lewis Research Center over more than 40 years. These programs have changed over the years to include additional features and improved calculation techniques and to take advantage of constantly improving computer capabilities. The minimization-of-free-energy approach to chemical equilibrium calculations has been used in all versions of the program since 1967. The two principal purposes of this report are presented in two parts. The first purpose, which is accomplished here in part 1, is to present in detail a number of topics of general interest in complex equilibrium calculations. These topics include mathematical analyses and techniques for obtaining chemical equilibrium; formulas for obtaining thermodynamic and transport mixture properties and thermodynamic derivatives; criteria for inclusion of condensed phases; calculations at a triple point; inclusion of ionized species; and various applications, such as constant-pressure or constant-volume combustion, rocket performance based on either a finite- or infinite-chamber-area model, shock wave calculations, and Chapman-Jouguet detonations. The second purpose of this report, to facilitate the use of the computer code, is accomplished in part 2, entitled 'Users Manual and Program Description'. Various aspects of the computer code are discussed, and a number of examples are given to illustrate its versatility.
NASA Astrophysics Data System (ADS)
Quílez, Juan
2009-09-01
With this paper, our main aim is to contribute to the realisation of the chemical reactivity concept, tracing the historical evolution of the concept of chemical affinity that eventually supported the concept of chemical equilibrium. We will concentrate on searching for the theoretical grounds of three key chemical equilibrium ideas: ‚incomplete reaction’, ‚reversibility’ and ‚dynamics’. In addition, the paper aims to promote teachers’ philosophical/historical chemical knowledge. The starting point of this historical reconstruction will be the state of the art in the construction of the first affinity tables, based on the concept of elective affinities, during the 18th century. Berthollet reworked this idea, considering that the amount of the substances involved in a reaction was a key factor accounting for the chemical forces. Guldberg and Waage attempted to measure those forces, formulating the first affinity mathematical equations. Afterwards, the first ideas providing a molecular interpretation of the macroscopic properties of equilibrium reactions are presented. Eventually, theoretical chemists integrated previous findings into a new field: thermodynamics. This historical approach may serve as a base for an appropriate sequencing of the teaching and learning of chemical equilibrium. Hence, this paper tries to go beyond the simple development of teachers’ conceptions of the nature of chemistry, for it gives suggestions about how teachers may translate such understandings into classroom practice.
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.
NASA Astrophysics Data System (ADS)
Kühn, Michael
In order to deal with the complexity of natural systems simplified models are employed to illustrate the principal and regulatory factors controlling a chemical system. Following the aphorism of Albert Einstein: Everything should be made as simple as possible, but not simpler, models need not to be completely realistic to be useful (Stumm and Morgan 1996), but need to meet a successful balance between realism and practicality. Properly constructed, a model is neither too simplified that it is unrealistic nor too detailed that it cannot be readily evaluated and applied to the problem of interest (Bethke 1996). The results of a model have to be at least partially observable or experimentally verifiable (Zhu and Anderson 2002). Geochemical modeling theories are presented here in a sequence of increasing complexity from geochemical equilibrium models to kinetic, reaction path, and finally coupled transport and reaction models. The description is far from complete but provides the needs for the set up of reactive transport models of hydrothermal systems as done within subsequent chapters. Extensive reviews of geochemical models in general can be found in the literature (Appelo and Postma 1999, Bethke 1996, Melchior and Bassett 1990, Nordstrom and Ball 1984, Paschke and van der Heijde 1996).
Closure conditions for non-equilibrium multi-component models
NASA Astrophysics Data System (ADS)
Müller, S.; Hantke, M.; Richter, P.
2016-07-01
A class of non-equilibrium models for compressible multi-component fluids in multi-dimensions is investigated taking into account viscosity and heat conduction. These models are subject to the choice of interfacial pressures and interfacial velocity as well as relaxation terms for velocity, pressure, temperature and chemical potentials. Sufficient conditions are derived for these quantities that ensure meaningful physical properties such as a non-negative entropy production, thermodynamical stability, Galilean invariance and mathematical properties such as hyperbolicity, subcharacteristic property and existence of an entropy-entropy flux pair. For the relaxation of chemical potentials, a two-component and a three-component models for vapor-water and gas-water-vapor, respectively, are considered.
Nguyen, H.D.
1991-11-01
Several of the technologies being evaluated for the treatment of waste material involve chemical reactions. Our example is the in situ vitrification (ISV) process where electrical energy is used to melt soil and waste into a ``glass like`` material that immobilizes and encapsulates any residual waste. During the ISV process, various chemical reactions may occur that produce significant amounts of products which must be contained and treated. The APOLLO program was developed to assist in predicting the composition of the gases that are formed. Although the development of this program was directed toward ISV applications, it should be applicable to other technologies where chemical reactions are of interest. This document presents the mathematical methodology of the APOLLO computer code. APOLLO is a computer code that calculates the products of both equilibrium and kinetic chemical reactions. The current version, written in FORTRAN, is readily adaptable to existing transport programs designed for the analysis of chemically reacting flow systems. Separate subroutines EQREACT and KIREACT for equilibrium ad kinetic chemistry respectively have been developed. A full detailed description of the numerical techniques used, which include both Lagrange multiplies and a third-order integrating scheme is presented. Sample test problems are presented and the results are in excellent agreement with those reported in the literature.
Nguyen, H.D.
1991-11-01
Several of the technologies being evaluated for the treatment of waste material involve chemical reactions. Our example is the in situ vitrification (ISV) process where electrical energy is used to melt soil and waste into a glass like'' material that immobilizes and encapsulates any residual waste. During the ISV process, various chemical reactions may occur that produce significant amounts of products which must be contained and treated. The APOLLO program was developed to assist in predicting the composition of the gases that are formed. Although the development of this program was directed toward ISV applications, it should be applicable to other technologies where chemical reactions are of interest. This document presents the mathematical methodology of the APOLLO computer code. APOLLO is a computer code that calculates the products of both equilibrium and kinetic chemical reactions. The current version, written in FORTRAN, is readily adaptable to existing transport programs designed for the analysis of chemically reacting flow systems. Separate subroutines EQREACT and KIREACT for equilibrium ad kinetic chemistry respectively have been developed. A full detailed description of the numerical techniques used, which include both Lagrange multiplies and a third-order integrating scheme is presented. Sample test problems are presented and the results are in excellent agreement with those reported in the literature.
NASA Technical Reports Server (NTRS)
1976-01-01
The entropy of a gas system with the number of particles subject to external control is maximized to derive relations between the thermodynamic variables that obtain at equilibrium. These relations are described in terms of the chemical potential, defined as equivalent partial derivatives of entropy, energy, enthalpy, free energy, or free enthalpy. At equilibrium, the change in total chemical potential must vanish. This fact is used to derive the equilibrium constants for chemical reactions in terms of the partition functions of the species involved in the reaction. Thus the equilibrium constants can be determined accurately, just as other thermodynamic properties, from a knowledge of the energy levels and degeneracies for the gas species involved. These equilibrium constants permit one to calculate the equilibrium concentrations or partial pressures of chemically reacting species that occur in gas mixtures at any given condition of pressure and temperature or volume and temperature.
NASA Technical Reports Server (NTRS)
Paquette, John A.; Nuth, Joseph A., III
2011-01-01
Classical nucleation theory has been used in models of dust nucleation in circumstellar outflows around oxygen-rich asymptotic giant branch stars. One objection to the application of classical nucleation theory (CNT) to astrophysical systems of this sort is that an equilibrium distribution of clusters (assumed by CNT) is unlikely to exist in such conditions due to a low collision rate of condensable species. A model of silicate grain nucleation and growth was modified to evaluate the effect of a nucleation flux orders of magnitUde below the equilibrium value. The results show that a lack of chemical equilibrium has only a small effect on the ultimate grain distribution.
Cross-coupling effects in chemically non-equilibrium viscous compressible flows
NASA Astrophysics Data System (ADS)
Kustova, E. V.; Giordano, D.
2011-01-01
A closed self-consistent description of a one-temperature non-equilibrium reacting flow is presented on the basis of the kinetic theory methods. A general case including internal degrees of freedom, dissociation-recombination and exchange reactions, and arbitrary values of affinities of chemical reactions is considered. Chemical-reaction rates and mean normal stress in viscous compressible flows are studied and a symmetric cross coupling between these terms is found. It is shown that the rate of each chemical reaction and the mean normal stress depend on velocity divergence and affinities of all chemical reactions; the law of mass action is violated in viscous flows. The results obtained in the frame of linear irreversible thermodynamics can be deduced from the proposed model for the particular case of small affinities. The reciprocal Onsager-Casimir relations are verified, the symmetry of kinetic coefficients is demonstrated, and the entropy production in a viscous flow is studied.
Clouds in Super-Earth Atmospheres: Chemical Equilibrium Calculations
NASA Astrophysics Data System (ADS)
Mbarek, Rostom; Kempton, Eliza M.-R.
2016-08-01
Recent studies have unequivocally proven the existence of clouds in super-Earth atmospheres. Here we provide a theoretical context for the formation of super-Earth clouds by determining which condensates are likely to form under the assumption of chemical equilibrium. We study super-Earth atmospheres of diverse bulk composition, which are assumed to form by outgassing from a solid core of chondritic material, following Schaefer & Fegley. The super-Earth atmospheres that we study arise from planetary cores made up of individual types of chondritic meteorites. They range from highly reducing to oxidizing and have carbon to oxygen (C:O) ratios that are both sub-solar and super-solar, thereby spanning a range of atmospheric composition that is appropriate for low-mass exoplanets. Given the atomic makeup of these atmospheres, we minimize the global Gibbs free energy of formation for over 550 gases and condensates to obtain the molecular composition of the atmospheres over a temperature range of 350–3000 K. Clouds should form along the temperature–pressure boundaries where the condensed species appear in our calculation. We find that the composition of condensate clouds depends strongly on both the H:O and C:O ratios. For the super-Earth archetype GJ 1214b, KCl and ZnS are the primary cloud-forming condensates at solar composition, in agreement with previous work. However, for oxidizing atmospheres, K2SO4 and ZnO condensates are favored instead, and for carbon-rich atmospheres with super-solar C:O ratios, graphite clouds appear. For even hotter planets, clouds form from a wide variety of rock-forming and metallic species.
The Adverse Effects of Le Chatelier's Principle on Teacher Understanding of Chemical Equilibrium
ERIC Educational Resources Information Center
Cheung, Derek
2009-01-01
Although the scientific inadequacy of Le Chatelier's principle has long been documented in the literature, the principle is still treated as a central concept of chemical equilibrium by textbook writers and teachers in many countries. In the past, researchers' interest has focused on student misconceptions about chemical equilibrium and has…
Identification and Analysis of Student Conceptions Used To Solve Chemical Equilibrium Problems.
ERIC Educational Resources Information Center
Voska, Kirk W.; Heikkinen, Henry W.
2000-01-01
Identifies and quantifies the chemistry conceptions used by students when solving chemical equilibrium problems requiring application of LeChatelier's Principle, and explores the feasibility of designing a paper and pencil test to accomplish these purposes. Eleven prevalent incorrect student conceptions about chemical equilibrium were identified…
ERIC Educational Resources Information Center
Niaz, Mansoor
2001-01-01
Illustrates how a novel problem of chemical equilibrium based on a closely related sequence of items can facilitate students' conceptual understanding. Students were presented with a chemical reaction in equilibrium to which a reactant was added as an external effect. Three studies were conducted to assess alternative conceptions. (Author/SAH)
ERIC Educational Resources Information Center
Akkus, Huseyin; Kadayifci, Hakki; Atasoy, Basri; Geban, Omer
2003-01-01
The purpose of this study was to identify misconceptions concerning chemical equilibrium concepts and to investigate the effectiveness of instruction based on the constructivist approach over traditional instruction on 10th grade students' understanding of chemical equilibrium concepts. The subjects of this study consisted of 71 10th grade…
ERIC Educational Resources Information Center
Cheung, Derek; Ma, Hong-jia; Yang, Jie
2009-01-01
The importance of research on misconceptions about chemical equilibrium is well recognized by educators, but in the past, researchers' interest has centered on student misconceptions and has neglected teacher misconceptions. Focusing on the effects of adding more reactants or products on chemical equilibrium, this article discusses the various…
ERIC Educational Resources Information Center
Bilgin, Ibrahim
2006-01-01
The purpose of this study was to investigate the effectiveness of small group discussion on students' conceptual understanding of chemical equilibrium. Students' understanding of chemical equilibrium concepts was measured using the Misconception Identification Test. The test consisted of 30 items and administered as pre-posttests to a total of 81…
Equilibrium Chemistry Calculations for Model Hot-Jupiter Atmospheres
NASA Astrophysics Data System (ADS)
Blumenthal, Sarah; Harrington, Joseph; Bowman, M. Oliver; Blecic, Jasmina
2014-11-01
Every planet in our solar system has different elemental abundances from our sun's. It is thus necessary to explore a variety of elemental abundances when investigating exoplanet atmospheres. Composition is key to unraveling a planet's formation history and determines the radiative behavior of an atmosphere, including its spectrum (Moses et al. 2013). We consider here two commonly discussed situations: [C]/[O] > 1 and 10x and 100x heavy-element enrichment. For planets above 1200 K, equilibrium chemistry is a valid starting point in atmospheric analysis. For HD 209458b, this assumption was verified by comparing the results of a robust kinetics code (non-ideal behavior) to the results of an equilibrium chemistry code (ideal behavior). Both codes output similar results for the dayside of the planet (Agundez et al. 2012). Using NASA's open-source Chemical Equilibrium Abundances code (McBride and Gordon 1996), we calculate the molecular abundances of species of interest across the dayside of model planets with a range of: elemental abundance profiles, degree of redistribution, relevant substellar temperatures, and pressures. We then explore the compositional gradient of each model planet atmosphere layer using synthetic abundance images of target spectroscopic species (water, methane, carbon monoxide). This work was supported by the NASA Planetary Atmospheres grant NNX12AI69G and NASA Astrophysics Data Analysis Program NNX13AF38G.
Chemical evolution of the Earth: Equilibrium or disequilibrium process?
NASA Technical Reports Server (NTRS)
Sato, M.
1985-01-01
To explain the apparent chemical incompatibility of the Earth's core and mantle or the disequilibrium process, various core forming mechanisms have been proposed, i.e., rapid disequilibrium sinking of molten iron, an oxidized core or protocore materials, and meteorite contamination of the upper mantle after separation from the core. Adopting concepts used in steady state thermodynamics, a method is devised for evaluating how elements should distribute stable in the Earth's interior for the present gradients of temperature, pressure, and gravitational acceleration. Thermochemical modeling gives useful insights into the nature of chemical evolution of the Earth without overly speculative assumptions. Further work must be done to reconcile siderophile elements, rare gases, and possible light elements in the outer core.
Modeling rocky coastline evolution and equilibrium
NASA Astrophysics Data System (ADS)
Limber, P. W.; Murray, A. B.
2010-12-01
Many of the world’s rocky coastlines exhibit planform roughness in the form of alternating headlands and embayments. Along cliffed coasts, it is often assumed that headlands consist of rock that is more resistant to wave attack than in neighboring bays, because of either structural or lithologic variations. Bays would then retreat landward faster than headlands, creating the undulating planform profiles characteristic of a rocky coastal landscape. While the interplay between alongshore rock strength and nearshore wave energy is, in some circumstances, a fundamental control on coastline shape, beach sediment is also important. Laboratory experiments and field observations have shown that beach sediment, in small volumes, can act as an abrasive tool to encourage sea cliff retreat. In large volumes, though, sediment discourages wave attack on the cliff face, acting as a protective barrier. This nonlinearity suggests a means for headland persistence, even without alongshore variations in rock strength: bare-rock headlands could retreat more slowly than, or at the same rate as, neighboring sediment-filled embayments because of alongshore variations in the availability of beach sediment. Accordingly, nearshore sediment dynamics (i.e. sediment production from sea cliff retreat and alongshore sediment transport) could promote the development of autogenic planform geometry. To explore these ideas, we present numerical and analytical modeling of large-scale (> one kilometer) and long-term (millennial-scale) planform rocky coastline evolution, in which sediment is supplied by both sea cliff erosion and coastal rivers and is distributed by alongshore sediment transport. We also compare model predictions with real landscapes. Previously, our modeling exercises focused on a basic rocky coastline configuration where lithologically-homogeneous sea cliffs supplied all beach sediment and maintained a constant alongshore height. Results showed that 1) an equilibrium alongshore
Formation of nitric acid hydrates - A chemical equilibrium approach
NASA Technical Reports Server (NTRS)
Smith, Roland H.
1990-01-01
Published data are used to calculate equilibrium constants for reactions of the formation of nitric acid hydrates over the temperature range 190 to 205 K. Standard enthalpies of formation and standard entropies are calculated for the tri- and mono-hydrates. These are shown to be in reasonable agreement with earlier calorimetric measurements. The formation of nitric acid trihydrate in the polar stratosphere is discussed in terms of these equilibrium constants.
The venous equilibrium model is widely used to describe hepatic clearance (CLH) of chemicals metabolized by the liver. If chemical delivery to the tissue does not limit CLH, this model predicts that CLH will approximately equal the product of intrinsic metabolic clearance and a t...
Equilibrium statistical-thermal models in high-energy physics
NASA Astrophysics Data System (ADS)
Tawfik, Abdel Nasser
2014-05-01
We review some recent highlights from the applications of statistical-thermal models to different experimental measurements and lattice QCD thermodynamics that have been made during the last decade. We start with a short review of the historical milestones on the path of constructing statistical-thermal models for heavy-ion physics. We discovered that Heinz Koppe formulated in 1948, an almost complete recipe for the statistical-thermal models. In 1950, Enrico Fermi generalized this statistical approach, in which he started with a general cross-section formula and inserted into it, the simplifying assumptions about the matrix element of the interaction process that likely reflects many features of the high-energy reactions dominated by density in the phase space of final states. In 1964, Hagedorn systematically analyzed the high-energy phenomena using all tools of statistical physics and introduced the concept of limiting temperature based on the statistical bootstrap model. It turns to be quite often that many-particle systems can be studied with the help of statistical-thermal methods. The analysis of yield multiplicities in high-energy collisions gives an overwhelming evidence for the chemical equilibrium in the final state. The strange particles might be an exception, as they are suppressed at lower beam energies. However, their relative yields fulfill statistical equilibrium, as well. We review the equilibrium statistical-thermal models for particle production, fluctuations and collective flow in heavy-ion experiments. We also review their reproduction of the lattice QCD thermodynamics at vanishing and finite chemical potential. During the last decade, five conditions have been suggested to describe the universal behavior of the chemical freeze-out parameters. The higher order moments of multiplicity have been discussed. They offer deep insights about particle production and to critical fluctuations. Therefore, we use them to describe the freeze-out parameters
Behera, Sailesh N; Betha, Raghu; Liu, Ping; Balasubramanian, Rajasekhar
2013-05-01
Aerosol acidity is one of the most important parameters that can influence atmospheric visibility, climate change and human health. Based on continuous field measurements of inorganic aerosol species and their thermodynamic modeling on a time resolution of 1h, this study has investigated the acidic properties of PM2.5 and their relation with the formation of secondary inorganic aerosols (SIA). The study was conducted by taking into account the prevailing ambient temperature (T) and relative humidity (RH) in a tropical urban atmosphere. The in-situ aerosol pH (pH(IS)) on a 12h basis ranged from -0.20 to 1.46 during daytime with an average value of 0.48 and 0.23 to 1.53 during nighttime with an average value of 0.72. These diurnal variations suggest that the daytime aerosol was more acidic than that caused by the nighttime aerosol. The hourly values of pH(IS) showed a reverse trend as compared to that of in-situ aerosol acidity ([H(+)]Ins). The pH(IS) had its maximum values at 3:00 and at 20:00 and its minimum during 11:00 to 12:00. Correlation analyses revealed that the molar concentration ratio of ammonium to sulfate (R(N/S)), equivalent concentration ratio of cations to anions (RC/A), T and RH can be used as independent variables for prediction of pH(IS). A multi-linear regression model consisting of RN/S, RC/A, T and RH was developed to estimate aerosol pH(IS). PMID:23523726
NASA Astrophysics Data System (ADS)
Jain, Priyanka; Varshney, Shilpa; Srivastava, Shalini
2015-10-01
Site-specific functionalizations are the emergent attention for the enhancement of sorption latent of heavy metals. Limited chemistry has been applied for the fabrication of diafunctionalized materials having potential to tether both environmentally stable oxidation states of chromium (Cr(III) and Cr(VI). Polyaniline impregnated nanocellulose composite (PANI-NCC) has been fabricated using click chemistry and explored for the removal of Cr(III) and Cr(VI) from hydrological environment. The structure, stability, morphology, particle size, surface area, hydrophilicity, and porosity of fabricated PANI-NCC were characterized comprehensively using analytical techniques and mathematical tools. The maximum sorption performance of PANI-NCC was procured for (Cr(III): 47.06 mg g-1; 94.12 %) and (Cr(VI): 48.92 mg g-1; 97.84 %) by equilibrating 0.5 g sorbent dose with 1000 mL of 25 mg L-1 chromium conc. at pH 6.5 and 2.5 for Cr(III) and Cr(VI), respectively. The sorption data showed a best fit to the Langmuir isotherm and pseudo-second-order kinetic model. The negative value of ∆ G° (-8.59 and -11.16 kJ mol-1) and ∆ H° (66.46 × 10-1 and 17.84 × 10-1 kJ mol-1), and positive value of ∆ S° (26.66 and 31.46 J mol-1K-1) for Cr(III) and Cr(VI), respectively, reflect the spontaneous, feasibility, and exothermic nature of the sorption process. The application of fabricated PANI-NCC for removing both the forms of chromium in the presence of other heavy metals was also tested at laboratory and industrial waste water regime. These findings open up new avenues in the row of high performance, scalable, and economic nanobiomaterial for the remediation of both forms of chromium from water streams.
Rate-Controlled Constrained-Equilibrium Theory of Chemical Reactions
NASA Astrophysics Data System (ADS)
Keck, James C.
2008-08-01
The Rate-Controlled Constrained-Equilibrium (RCCE) method for simplifying the treatment of reactions in complex systems is summarized and the selection of constraints for both close-to and far-from equilibrium systems is discussed. Illustrative examples of RCCE calculations of carbon monoxide concentrations in the exhaust products of an internal combustion engine and ignition delays for methane-oxygen mixtures in a constant volume adiabatic chamber are given and compared with "detailed" calculations. The advantages of RCCE calculations over "detailed" calculations are discussed.
An unstructured shock-fitting solver for hypersonic plasma flows in chemical non-equilibrium
NASA Astrophysics Data System (ADS)
Pepe, R.; Bonfiglioli, A.; D'Angola, A.; Colonna, G.; Paciorri, R.
2015-11-01
A CFD solver, using Residual Distribution Schemes on unstructured grids, has been extended to deal with inviscid chemical non-equilibrium flows. The conservative equations have been coupled with a kinetic model for argon plasma which includes the argon metastable state as independent species, taking into account electron-atom and atom-atom processes. Results in the case of an hypersonic flow around an infinite cylinder, obtained by using both shock-capturing and shock-fitting approaches, show higher accuracy of the shock-fitting approach.
A rapid method for the computation of equilibrium chemical composition of air to 15000 K
NASA Technical Reports Server (NTRS)
Prabhu, Ramadas K.; Erickson, Wayne D.
1988-01-01
A rapid computational method has been developed to determine the chemical composition of equilibrium air to 15000 K. Eleven chemically reacting species, i.e., O2, N2, O, NO, N, NO+, e-, N+, O+, Ar, and Ar+ are included. The method involves combining algebraically seven nonlinear equilibrium equations and four linear elemental mass balance and charge neutrality equations. Computational speeds for determining the equilibrium chemical composition are significantly faster than the often used free energy minimization procedure. Data are also included from which the thermodynamic properties of air can be computed. A listing of the computer program together with a set of sample results are included.
Balistrieri, L.S.; Blank, R.G.
2008-01-01
In order to evaluate thermodynamic speciation calculations inherent in biotic ligand models, the speciation of dissolved Cd, Cu, Pb, and Zn in aquatic systems influenced by historical mining activities is examined using equilibrium computer models and the diffusive gradients in thin films (DGT) technique. Several metal/organic-matter complexation models, including WHAM VI, NICA-Donnan, and Stockholm Humic model (SHM), are used in combination with inorganic speciation models to calculate the thermodynamic speciation of dissolved metals and concentrations of metal associated with biotic ligands (e.g., fish gills). Maximum dynamic metal concentrations, determined from total dissolved metal concentrations and thermodynamic speciation calculations, are compared with labile metal concentrations measured by DGT to assess which metal/organic-matter complexation model best describes metal speciation and, thereby, biotic ligand speciation, in the studied systems. Results indicate that the choice of model that defines metal/organic-matter interactions does not affect calculated concentrations of Cd and Zn associated with biotic ligands for geochemical conditions in the study area, whereas concentrations of Cu and Pb associated with biotic ligands depend on whether the speciation calculations use WHAM VI, NICA-Donnan, or SHM. Agreement between labile metal concentrations and dynamic metal concentrations occurs when WHAM VI is used to calculate Cu speciation and SHM is used to calculate Pb speciation. Additional work in systems that contain wide ranges in concentrations of multiple metals should incorporate analytical speciation methods, such as DGT, to constrain the speciation component of biotic ligand models. ?? 2008 Elsevier Ltd.
NASA Astrophysics Data System (ADS)
Leal, Allan M. M.; Kulik, Dmitrii A.; Kosakowski, Georg
2016-02-01
We present a numerical method for multiphase chemical equilibrium calculations based on a Gibbs energy minimization approach. The method can accurately and efficiently determine the stable phase assemblage at equilibrium independently of the type of phases and species that constitute the chemical system. We have successfully applied our chemical equilibrium algorithm in reactive transport simulations to demonstrate its effective use in computationally intensive applications. We used FEniCS to solve the governing partial differential equations of mass transport in porous media using finite element methods in unstructured meshes. Our equilibrium calculations were benchmarked with GEMS3K, the numerical kernel of the geochemical package GEMS. This allowed us to compare our results with a well-established Gibbs energy minimization algorithm, as well as their performance on every mesh node, at every time step of the transport simulation. The benchmark shows that our novel chemical equilibrium algorithm is accurate, robust, and efficient for reactive transport applications, and it is an improvement over the Gibbs energy minimization algorithm used in GEMS3K. The proposed chemical equilibrium method has been implemented in Reaktoro, a unified framework for modeling chemically reactive systems, which is now used as an alternative numerical kernel of GEMS.
A Hybrid Method for Flows in Local Chemical Equilibrium and Nonequilibrium
NASA Astrophysics Data System (ADS)
Currier, Nicholas G.
The primary objective of this work is to develop a more efficient chemically active compressible Euler equation solver. Currently, a choice between the physical accuracy of a finite-rate solver or the computational efficiency of an equilibrium flow solver must be made. The number of species modeled continues to increase with available computational resources. A method of further leveraging the increase in computational power is desired. The hybrid chemistry scheme proposed here attempts to maintain the accuracy of finite-rate schemes while retaining some of the cost savings associated with equilibrium chemistry solvers. The method given uses a full finite-rate flux in regions where chemistry is slow compared to the advection rate and an equilibrium chemistry scheme in regions where the chemistry outpaces the fluid transport. Control volume switching is based on a locally defined Damkohler number. This method could be extremely useful for full reaction path modeling or the tracking of a very large number of species. The cost of symmetric Gauss-Seidel iterations grows like the number of species plus four, quantity squared. Thus, eliminating the increased cost of solving for a large number of unknowns in regions where it is unjustified can be very useful. Tenasi, a University of Tennessee SimCenter research code, is used as a base for the new solver. The hybrid method is implemented and tested with an explicit solution technique in one dimension. In combination with a five species air chemistry model, a high-temperature shock tube is used as a verification test case. Results are compared with those from pure equilibrium, full finite-rate, perfect gas Euler, and exact perfect gas Riemann solvers. Timings are also given, suggesting the cost savings that would be possible should the hybrid method be extended using implicit algorithms.
Effect of a Perturbation on the Chemical Equilibrium: Comparison with Le Chatelier's Principle
ERIC Educational Resources Information Center
Torres, Emilio Martinez
2007-01-01
This article develops a general thermodynamic treatment to predict the direction of shift in a chemical equilibrium when it is subjected to a stress. This treatment gives an inequality that relates the change in the perturbed variable and the change that the equilibrium shift produces in the conjugated variable. To illustrate the generality of…
A two-dimensional, TVD numerical scheme for inviscid, high Mach number flows in chemical equilibrium
NASA Technical Reports Server (NTRS)
Eberhardt, S.; Palmer, G.
1986-01-01
A new algorithm has been developed for hypervelocity flows in chemical equilibrium. Solutions have been achieved for Mach numbers up to 15 with no adverse effect on convergence. Two methods of coupling an equilibrium chemistry package have been tested, with the simpler method proving to be more robust. Improvements in boundary conditions are still required for a production-quality code.
Relating Students' Reasoning To the History of Science: The Case of Chemical Equilibrium.
ERIC Educational Resources Information Center
Van Driel, Jan H.; De Vos, Wobbe; Verloop, Nico
1998-01-01
Relates the reasoning of students introduced to the concept of chemical equilibrium to the historical development of the concept. Concludes that the study of authentic historical sources may inspire the design of effective teaching activities. Contains 33 references. (DDR)
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
Chemical Equilibrium in Supramolecular Systems as Studied by NMR Spectrometry
ERIC Educational Resources Information Center
Gonzalez-Gaitano, Gustavo; Tardajos, Gloria
2004-01-01
Undergraduate students are required to study the chemical balance in supramolecular assemblies constituting two or more interacting species, by using proton NMR spectrometry. A good knowledge of physical chemistry, fundamentals of chemical balance, and NMR are pre-requisites for conducting this study.
NASA Astrophysics Data System (ADS)
Kamimura, Atsushi; Yukawa, Satoshi; Ito, Nobuyasu
2006-02-01
As a first step to study reaction dynamics in far-from-equilibrium open systems, we propose a stochastic protocell model in which two mutually catalyzing chemicals are replicating depending on the external flow of energy resources J. This model exhibits an Arrhenius type reaction; furthermore, it produces a non-Arrhenius reaction that exhibits a power-law reaction rate with regard to the activation energy. These dependences are explained using the dynamics of J; the asymmetric random walk of J results in the Arrhenius equation and conservation of J results in a power-law dependence. Further, we find that the discreteness of molecules results in the power change. Effects of cell divisions are also discussed in our model.
Arjmand, N; Shirazi-Adl, A; Parnianpour, M
2007-05-01
Accurate estimation of muscle forces in various occupational tasks is critical for a reliable evaluation of spinal loads and subsequent assessment of risk of injury and management of back disorders. The majority of biomechanical models of multi-segmental spine estimate muscle forces and spinal loads based on the balance of net moments at a single level with no consideration for the equilibrium at remaining levels. This work aimed to quantify the extent of equilibrium violation and alterations in estimations when such models are performed at different levels. Results are compared with those of kinematics-driven model that satisfies equilibrium at all levels and EMG data. Regardless of the method used (optimization or EMG-assisted), single-level free body diagram models yielded estimations that substantially altered depending on the level considered (i.e., level dependency). Equilibrium of net moment was also grossly violated at remaining levels with the error increasing in more demanding tasks. These models may, however, be used to estimate spinal compression forces. PMID:17136359
Features of the chemical equilibrium of dimerization in a system of solid spheres
NASA Astrophysics Data System (ADS)
Tkachev, N. K.; Zinatullina, A. R.
2013-09-01
Statistical and thermodynamic analyses of the equilibrium of dimerization in solid-phase systems is performed for a model of the Van der Waals type and the Perkus-Yevik approximation. For the model of Van der Waals type, the simple equation γ = exp[ p 0(2-λ3)] is obtained for an average activity coefficient ( p 0 is reduced pressure and λ is bond length in dimer) that describes both positive and negative deviations from the ideal, depending on the change in volume after the elementary act of chemical reaction. It is found that the Perkus-Yevik approximation predicts similar results with more pronounced deviations from the ideal, and the activity coefficient depends on the degree of dissociation as well.
A Unified Graphical Representation of Chemical Thermodynamics and Equilibrium
ERIC Educational Resources Information Center
Hanson, Robert M.
2012-01-01
During the years 1873-1879, J. Willard Gibbs published his now-famous set of articles that form the basis of the current perspective on chemical thermodynamics. The second article of this series, "A Method of Geometrical Representation of the Thermodynamic Properties of Substances by Means of Surfaces," published in 1873, is particularly notable…
Rapid computation of chemical equilibrium composition - An application to hydrocarbon combustion
NASA Technical Reports Server (NTRS)
Erickson, W. D.; Prabhu, R. K.
1986-01-01
A scheme for rapidly computing the chemical equilibrium composition of hydrocarbon combustion products is derived. A set of ten governing equations is reduced to a single equation that is solved by the Newton iteration method. Computation speeds are approximately 80 times faster than the often used free-energy minimization method. The general approach also has application to many other chemical systems.
Achieving Chemical Equilibrium: The Role of Imposed Conditions in the Ammonia Formation Reaction
ERIC Educational Resources Information Center
Tellinghuisen, Joel
2006-01-01
Under conditions of constant temperature T and pressure P, chemical equilibrium occurs in a closed system (fixed mass) when the Gibbs free energy G of the reaction mixture is minimized. However, when chemical reactions occur under other conditions, other thermodynamic functions are minimized or maximized. For processes at constant T and volume V,…
The assumption of equilibrium in models of migration.
Schachter, J; Althaus, P G
1993-02-01
In recent articles Evans (1990) and Harrigan and McGregor (1993) (hereafter HM) scrutinized the equilibrium model of migration presented in a 1989 paper by Schachter and Althaus. This model used standard microeconomics to analyze gross interregional migration flows based on the assumption that gross flows are in approximate equilibrium. HM criticized the model as theoretically untenable, while Evans summoned empirical as well as theoretical objections. HM claimed that equilibrium of gross migration flows could be ruled out on theoretical grounds. They argued that the absence of net migration requires that either all regions have equal populations or that unsustainable regional migration propensities must obtain. In fact some moves are inter- and other are intraregional. It does not follow, however, that the number of interregional migrants will be larger for the more populous region. Alternatively, a country could be divided into a large number of small regions that have equal populations. With uniform propensities to move, each of these analytical regions would experience in equilibrium zero net migration. Hence, the condition that net migration equal zero is entirely consistent with unequal distributions of population across regions. The criticisms of Evans were based both on flawed reasoning and on misinterpretation of the results of a number of econometric studies. His reasoning assumed that the existence of demand shifts as found by Goldfarb and Yezer (1987) and Topel (1986) invalidated the equilibrium model. The equilibrium never really obtains exactly, but economic modeling of migration properly begins with a simple equilibrium model of the system. A careful reading of the papers Evans cited in support of his position showed that in fact they affirmed rather than denied the appropriateness of equilibrium modeling. Zero net migration together with nonzero gross migration are not theoretically incompatible with regional heterogeneity of population, wages, or
A time-accurate algorithm for chemical non-equilibrium viscous flows at all speeds
NASA Technical Reports Server (NTRS)
Shuen, J.-S.; Chen, K.-H.; Choi, Y.
1992-01-01
A time-accurate, coupled solution procedure is described for the chemical nonequilibrium Navier-Stokes equations over a wide range of Mach numbers. This method employs the strong conservation form of the governing equations, but uses primitive variables as unknowns. Real gas properties and equilibrium chemistry are considered. Numerical tests include steady convergent-divergent nozzle flows with air dissociation/recombination chemistry, dump combustor flows with n-pentane-air chemistry, nonreacting flow in a model double annular combustor, and nonreacting unsteady driven cavity flows. Numerical results for both the steady and unsteady flows demonstrate the efficiency and robustness of the present algorithm for Mach numbers ranging from the incompressible limit to supersonic speeds.
Modeling of bi-equilibrium states in dielectric elastomer
NASA Astrophysics Data System (ADS)
Peng, Longgui
2014-03-01
Dielectric elastomer is a soft active material, producing fast deformation under voltage-activation. Under a specific boundary condition, trussed dielectric elastomer elongates mimicking the behavior of biological muscle. During this process, dielectric elastomer experiences a snap from one deformation mode to another, though both at the electromechanical equilibrium states. Based on thermodynamics, models are established to investigate electromechanical coupling at the two equilibrium states. Particular emphasis is devoted to establishing the governing equations of the two deformation modes with physical interpretations. The transition of equilibrium state is discussed, to predict the attainable stable state for application.
Michal P. Glazer; Nafees A. Khan; Wiebren de Jong; Hartmut Spliethoff; Heiko Schuermann; Penelope Monkhouse
2005-10-01
Combustion and co-combustion experiments with four kinds of straw, specially selected for their different alkali, Cl, and Si contents, and Colombian black coal were carried out in a circulating fluidized bed (CFB) reactor at Delft University of Technology. The influence of operating conditions and fuel composition on the release of the alkali compounds to the gas phase was investigated. The amount of the total gas-phase sodium and potassium compounds in the flue gases was measured with excimer laser induced fluorescence (ELIF). The results show that the release of gaseous alkali species depends on fuel composition, in particular the K/Cl and K/Si ratios in the fuel. The fuels with high K and Cl values show higher concentrations of the gaseous alkalis. A synergetic effect of the co-combustion with coal was observed, which led to a strong decrease in gaseous alkali concentrations. Together with experiments, chemical equilibrium modeling was performed to help in interpreting the experimental data. The calculations confirmed that the equilibrium is very strongly influenced by the composition of the fuel blend. Moreover, the simulations provided more information on sequestering of alkali species. 22 refs., 5 figs., 4 tabs.
Turbulence modeling for non-equilibrium flows
NASA Technical Reports Server (NTRS)
Durbin, Paul A.
1993-01-01
Two projects are reported. The first is the development and testing of an eddy viscosity transport model. This project also is a starting point for our work on developing computational tools for solving turbulence models in complex geometries. The second project is a stochastic analysis of the realizability of Reynolds stress transport models.
Modeling MOSFET surface capacitance behavior under non-equilibrium
NASA Astrophysics Data System (ADS)
Kapoor, Abhishek; Jindal, R. P.
2005-06-01
A normalized analytical solution for the capacitance associated with a MOSFET surface under non-equilibrium conditions is presented. It is shown that this model can be mapped into an equivalent equilibrium problem with 98% accuracy for near intrinsic samples (UB ≅ 2). The precision becomes even better for highly doped semiconductors. The physics behind this transformation is explained and nomograms generated to present data in a highly normalized form.
A continuum model for flocking: Obstacle avoidance, equilibrium, and stability
NASA Astrophysics Data System (ADS)
Mecholsky, Nicholas Alexander
The modeling and investigation of the dynamics and configurations of animal groups is a subject of growing attention. In this dissertation, we present a partial-differential-equation based continuum model of flocking and use it to investigate several properties of group dynamics and equilibrium. We analyze the reaction of a flock to an obstacle or an attacking predator. We show that the flock response is in the form of density disturbances that resemble Mach cones whose configuration is determined by the anisotropic propagation of waves through the flock. We investigate the effect of a flock 'pressure' and pairwise repulsion on an equilibrium density distribution. We investigate both linear and nonlinear pressures, look at the convergence to a 'cold' (T → 0) equilibrium solution, and find regions of parameter space where different models produce the same equilibrium. Finally, we analyze the stability of an equilibrium density distribution to long-wavelength perturbations. Analytic results for the stability of a constant density solution as well as stability regimes for constant density solutions to the equilibrium equations are presented.
MODELING CHEMICAL INTERACTIONS IN ANAEROBIC BIOFILM SYSTEMS
Rigorous steady-state models of acetate- and methanol-utilizing methanogenic biofilms are developed taking into account the mass transfer of neutral and ionic species, pH changes within the biofilm, pH-dependent Monod kinetics, chemical equilibrium,, electronueutrality, gas produ...
Effects of angular-momentum conservation in unified pre-equilibrium and equilibrium reaction models
NASA Astrophysics Data System (ADS)
Shi, Xiangjun; Gruppelaar, H.; Akkermans, J. M.
1987-05-01
The master-equation theory of precompound and compound nuclear decay is generalized to the inclusion of the conservation of angular momentum. It is demonstrated that the constructed model contains the Hauser-Feshbach, Weisskopf-Ewing as well as standard exciton models as limiting cases. This unified pre-equilibrium/Hauser-Feshbach model, which may be considered as a practicable version of the quantum-statistical, so-called AWM theory of Agassi et al., has been computationally optimized, such that the related numerical effort has become comparable to or less than that of a standard Hauser-Feshbach calculation. With this unified model the nature and importance of some spin effects in pre-equilibrium reactions has been investigated. The main conclusion from numerical calculations is that the standard precompound-model results are close to those of the angular-momentum conserving model, implying that the popular semi-classical models are quite reliable in this respect from a practical point of view.
Modeling non-equilibrium phase transitions in isentropically compressed Bi
Kane, J; Smith, R
2005-09-19
We report here on modeling of non-equilibrium phase transitions in Bi samples isentropically compressed to 120 GPa by a ramped drive, which is produced using the Janus laser. In the experiments, the Bi samples are attached to windows of LiF or sapphire, and the velocity history of the sample-window interface is recorded with line VISAR. The 1D response of the targets is modeled using a multiphase Bi EOS, the Andrews-Hayes method for non-equilibrium transitions, and a Boettger-Wallace kinetics model. The pressure drive is deduced by back integration of VISAR data from shots performed with Al samples.
Freight Network Equilibrium Model revisited: the Freight Network Modeling System
Tobin, R.L.
1984-01-01
The Freight Network Equilibrium Model (FNEM) was developed to study potential coal transportation impacts that could result from widespread conversion of boilers to use coal for fuel, as mandated under the Powerplant and Industrial Fuel Use Act of 1978. Continued improvement of FNEM and creation of auxiliary software and data during applications of the model in various transportation analyses led to the development of the Freight Network Modeling System, a general and flexible modeling system designed to have wide applicability to a variety of freight transportation analyses. It consists of compatible network data bases, data management software, models of freight transportation, report generators, and graphics output. The network data include US rail, water, highway, and pipeline systems. Data management software automates the task of setting up a study network of appropriate detail in appropriate regions of the country. The major analytical tools in the system are FNEM and Shortest Path Analysis and Display (SPAD); FNEM is predictive and simulates decisions of both shippers and carriers, taking into account the competition for transportation facilities; SPAD is a simpler model that optimizes routings of single shipments. Output for both FNEM and SPAD includes detailed routings, cost and delay estimates for all shipments, and data on total traffic levels. SPAD can be used interactively with routes displayed graphically. 13 references, 10 figures, 2 tables.
A kinetic and equilibrium analysis of silicon carbide chemical vapor deposition on monofilaments
NASA Technical Reports Server (NTRS)
Gokoglu, S. A.; Kuczmarski, M. A.
1993-01-01
Chemical kinetics of atmospheric pressure silicon carbide (SiC) chemical vapor deposition (CVD) from dilute silane and propane source gases in hydrogen is numerically analyzed in a cylindrical upflow reactor designed for CVD on monofilaments. The chemical composition of the SiC deposit is assessed both from the calculated total fluxes of carbon and silicon and from chemical equilibrium considerations for the prevailing temperatures and species concentrations at and along the filament surface. The effects of gas and surface chemistry on the evolution of major gas phase species are considered in the analysis.
Modelling spectral properties of non-equilibrium atomic hydrogen plasma
NASA Astrophysics Data System (ADS)
D'Ammando, G.; Pietanza, L. D.; Colonna, G.; Longo, S.; Capitelli, M.
2010-02-01
A model to predict the emissivity and absorption coefficient of atomic hydrogen plasma is presented in detail. Non-equilibrium plasma is studied through coupling of the model with a collisional-radiative code for the excited states population as well as with the Boltzmann equation for the electron energy distribution function.
Heavy ion collisions and the pre-equilibrium exciton model
Betak, E.
2012-10-20
We present a feasible way to apply the pre-equilibrium exciton model in its masterequation formulation to heavy-ion induced reactions including spin variables. Emission of nucleons, {gamma}'s and also light clusters is included in our model.
A novel local equilibrium model for shaped tokamak plasmas
Yu Weihong; Zhou Deng; Xiang Nong
2012-07-15
A model is proposed for a local up-down symmetric equilibrium in the vicinity of a specified magnetic surface with given elongation and triangularity. Different from the Miller's model [R. L. Miller et al., Phys. Plasmas 5, 973 (1998)], the derivative of the Shafranov shift in the present model is self-consistently determined. The equilibrium accounts for all the essential features, like the elongation, the triangularity, and the Shafranov shift etc., of a shaped cross section. Hence, it can be used for investigation of radially localized plasma modes, like reversed shear Alfvenic eigenmodes and ballooning mode, etc., and it is also suitable for local equilibrium construction used for flux tube plasma simulations.
ERIC Educational Resources Information Center
Aydeniz, Mehmet; Dogan, Alev
2016-01-01
This study examines the impact of argumentation on pre-service science teachers' (PST) conceptual understanding of chemical equilibrium. The sample consisted of 57 first-year PSTs enrolled in a teacher education program in Turkey. Thirty two of the 57 PSTs who participated in this study were in the experimental group and 25 in the control group.…
ERIC Educational Resources Information Center
Atasoy, Basri; Akkus, Huseyin; Kadayifci, Hakki
2009-01-01
The purpose of this study was to compare the effects of a conceptual change approach over traditional instruction on tenth-grade students' conceptual achievement in understanding chemical equilibrium. The study was conducted in two classes of the same teacher with participation of a total of 44 tenth-grade students. In this study, a…
ERIC Educational Resources Information Center
Vargas, Francisco M.
2014-01-01
The temperature dependence of the Gibbs energy and important quantities such as Henry's law constants, activity coefficients, and chemical equilibrium constants is usually calculated by using the Gibbs-Helmholtz equation. Although, this is a well-known approach and traditionally covered as part of any physical chemistry course, the required…
ERIC Educational Resources Information Center
Kaya, Ebru
2013-01-01
This study examines the impact of argumentation practices on pre-service teachers' understanding of chemical equilibrium. The sample consisted of 100 pre-service teachers in two classes of a public university. One of these classes was assigned as experimental and the other as control group, randomly. In the experimental group, the subject of…
ERIC Educational Resources Information Center
Piquette, Jeff S.; Heikkinen, Henry W.
2005-01-01
This study explores general-chemistry instructors' awareness of and ability to identify and address common student learning obstacles in chemical equilibrium. Reported instructor strategies directed at remediating student alternate conceptions were investigated and compared with successful, literature-based conceptual change methods. Fifty-two…
Control of Chemical Equilibrium by Solvent: A Basis for Teaching Physical Chemistry of Solutions
ERIC Educational Resources Information Center
Prezhdo, Oleg V.; Craig, Colleen F.; Fialkov, Yuriy; Prezhdo, Victor V.
2007-01-01
The study demonstrates that the solvent present in a system can highly alter and control the chemical equilibrium of a system. The results show that the dipole moment and polarizibility of a system can be highly altered by using different mixed solvents.
ERIC Educational Resources Information Center
Ozmen, Haluk
2007-01-01
This study investigated the effectiveness of conceptual change texts in remediating high school students' alternative conceptions concerning chemical equilibrium. A quasi-experimental design was used in this study. The subjects for this study consisted of a total 78 tenth-grade students, 38 of them in the experimental group and 40 of them in the…
Analogies in the Teaching of Chemical Equilibrium: A Synthesis/Analysis of the Literature
ERIC Educational Resources Information Center
Raviolo, Andres; Garritz, Andoni
2009-01-01
This paper presents a thorough literature review of the analogies used to teach chemical equilibrium. The main objective is to compile all the analogies that have been found to be of service to the teacher and the student. Additionally, we categorize and analyze analogies in relation to the following aspects: representation of the dynamic nature…
ERIC Educational Resources Information Center
Cheung, Derek
2009-01-01
Secondary school chemistry teachers' understanding of chemical equilibrium was investigated through interviews using the think-aloud technique. The interviews were conducted with twelve volunteer chemistry teachers in Hong Kong. Their teaching experience ranged from 3 to 18 years. They were asked to predict what would happen to the equilibrium…
A time-accurate implicit method for chemical non-equilibrium flows at all speeds
NASA Technical Reports Server (NTRS)
Shuen, Jian-Shun
1992-01-01
A new time accurate coupled solution procedure for solving the chemical non-equilibrium Navier-Stokes equations over a wide range of Mach numbers is described. The scheme is shown to be very efficient and robust for flows with velocities ranging from M less than or equal to 10(exp -10) to supersonic speeds.
A Teaching Sequence for Learning the Concept of Chemical Equilibrium in Secondary School Education
ERIC Educational Resources Information Center
Ghirardi, Marco; Marchetti, Fabio; Pettinari, Claudio; Regis, Alberto; Roletto, Ezio
2014-01-01
A novel didactic sequence is proposed for the teaching of chemical equilibrium. This teaching sequence takes into account the historical and epistemological evolution of the concept, the alternative conceptions and learning difficulties highlighted by teaching science and research in education, and the need to focus on both the students'…
Systematic Approach to Calculate the Concentration of Chemical Species in Multi-Equilibrium Problems
ERIC Educational Resources Information Center
Baeza-Baeza, Juan Jose; Garcia-Alvarez-Coque, Maria Celia
2011-01-01
A general systematic approach is proposed for the numerical calculation of multi-equilibrium problems. The approach involves several steps: (i) the establishment of balances involving the chemical species in solution (e.g., mass balances, charge balance, and stoichiometric balance for the reaction products), (ii) the selection of the unknowns (the…
NASA Astrophysics Data System (ADS)
Hadi, Fatemeh; Janbozorgi, Mohammad; Sheikhi, Reza H.; Metghalchi, Hameed
2014-11-01
The Rate-Controlled Constrained-Equilibrium (RCCE) method is applied to study the interaction between mixing and chemical reaction in a constant pressure Partially-Stirred Reactor (PaSR). The objective is to understand the influence of mixing on RCCE predictions. The RCCE is a computationally efficient method based on thermodynamics to implement the combustion chemistry. In the RCCE the dynamics of reacting systems is described by a small number of rate-controlling reactions and slowly-varying constraints. The method is applied to study methane combustion via 12 constraints and 133 reaction steps. Simulations are carried out over a wide range of initial temperatures and equivalence ratios. The RCCE predictions are assessed by comparing with those of detailed kinetics model, in which the same kinetics, involving 29 species and 133 reaction steps, is integrated directly. Chemical kinetics and mixing interactions are studied for different residence and mixing time scales. Results show that the RCCE accurately represents the effect of mixing with different mixing strengths. An assessment of numerical performance of the RCCE is also performed. It is shown that the method is effective to reduce the stiffness of the kinetics and thus allows simulations with much lower computation costs.
A numerical model of non-equilibrium thermal plasmas. II. Governing equations
Li HePing; Zhang XiaoNing; Xia Weidong
2013-03-15
Governing equations and the corresponding physical properties of the plasmas are both prerequisites for studying the fundamental processes in a non-equilibrium thermal plasma system numerically. In this paper, a kinetic derivation of the governing equations used for describing the complicated thermo-electro-magneto-hydrodynamic-chemical coupling effects in non-equilibrium thermal plasmas is presented. This derivation, which is achieved using the Chapman-Enskog method, is completely consistent with the theory of the transport properties reported in the previous paper by the same authors. It is shown, based on this self-consistent theory, that the definitions of the specific heat at constant pressure and the reactive thermal conductivity of two-temperature plasmas are not necessary. The governing equations can be reduced to their counterparts under local thermodynamic equilibrium (LTE) and local chemical equilibrium (LCE) conditions. The general method for the determination of the boundary conditions of the solved variables is also discussed briefly. The two papers establish a self-consistent physical-mathematical model that describes the complicated physical and chemical processes in a thermal plasma system for the cases both in LTE or LCE conditions and under non-equilibrium conditions.
Evaluation of the Diffusive Equilibrium Models by the IMAGE RPI
NASA Astrophysics Data System (ADS)
Ozhogin, Pavel; Reinisch, Bodo W.; Song, Paul; Tu, Jiannan
2013-04-01
Using measured field-aligned electron density profiles, this study investigates the validity of the diffusive equilibrium model in Earth's plasmasphere. This model which describes the electron and ion densities along a magnetic field line in the plasmasphere has been widely used for ray tracing and pitch-angle scattering calculations. It is based on the hydrostatic equilibrium with the electrostatic force that acts on ions and electrons along geomagnetic field lines while actually there is no motion or diffusion of the plasma involved. The model requires multiple input parameters: electron density and ion composition (H+, He+, O+) at a base level for a magnetic field line in the ionosphere, and the (electron or ion) temperature in the plasmasphere. It has been recognized that these input parameters have to be flexible from one field line to another so that the model output does not contradict some known observed relationships. However, while the flexibility provides the possibility to fit any individual observed density distribution which is measured across many different field lines, the model prediction becomes questionable along a single field line. Before the launch of the IMAGE satellite in 2000 no plasma density measurements along a single field line were available, and therefore the validity of the diffusive equilibrium models had not been independently verified. Our qualitative and quantitative analysis shows that the fundamental functional form of the diffusive equilibrium model is inconsistent with the large database of field-aligned electron density distributions obtained by the radio plasma imager (RPI) instrument onboard the IMAGE satellite. Review of the procedures used in the derivation of the original diffusive equilibrium model suggests that the physical processes described by the mathematical procedures are fundamentally incorrect.
NASA Astrophysics Data System (ADS)
Spencer, Ronald J.; Møller, Nancy; Weare, John H.
1990-03-01
A low temperature thermochemical model for the system NaKCaMgClSO 4H 2O is presented. Aqueous species and standard chemical potentials of solid-solution reactions are modeled from published data for binary and ternary solutions. The temperature range below 25°C (to near -60°C) is emphasized, although the model parameters are fitted to merge smoothly with those of higher temperature models at temperatures between 25 and 100°C. Binary and ternary specific ion interaction terms vary independently with temperature and are modeled using freezing point depression and mineral solubility measurements. The standard chemical potential of the ice-water reaction is fitted independent of the model (from vapor pressure and free energy data). Remaining standard chemical potentials of solidsolution reactions are fitted along with the specific ion interaction terms. Model predictions are tested against published data for minerals formed and brine compositions obtained by chilling seawater to the eutectic (about -54°C). The model predicts the sequence of solid phases observed to precipitate from chilled seawater (mice-mirabilite-hydrohalite-sylvite-MgCl 2 · 12H 2Oantarcticite). For all but mirabilite model temperatures are within the uncertainty of the measured temperature. The compositions of brines predicted by the model also closely follow the observed compositions. The model allows accurate predictions of the freezing points of simple and complex solutions in the system. Low temperature phase equilibria and mineral solubilities may also be predicted. The model may be used to determine the composition of brines in fluid inclusions in the multicomponent system based on low temperature phase equilibria.
Derivation of the chemical-equilibrium rate coefficient using scattering theory
NASA Technical Reports Server (NTRS)
Mickens, R. E.
1977-01-01
Scattering theory is applied to derive the equilibrium rate coefficient for a general homogeneous chemical reaction involving ideal gases. The reaction rate is expressed in terms of the product of a number of normalized momentum distribution functions, the product of the number of molecules with a given internal energy state, and the spin-averaged T-matrix elements. An expression for momentum distribution at equilibrium for an arbitrary molecule is presented, and the number of molecules with a given internal-energy state is represented by an expression which includes the partition function.
An implicit flux-split algorithm to calculate hypersonic flowfields in chemical equilibrium
NASA Technical Reports Server (NTRS)
Palmer, Grant
1987-01-01
An implicit, finite-difference, shock-capturing algorithm that calculates inviscid, hypersonic flows in chemical equilibrium is presented. The flux vectors and flux Jacobians are differenced using a first-order, flux-split technique. The equilibrium composition of the gas is determined by minimizing the Gibbs free energy at every node point. The code is validated by comparing results over an axisymmetric hemisphere against previously published results. The algorithm is also applied to more practical configurations. The accuracy, stability, and versatility of the algorithm have been promising.
NASA Astrophysics Data System (ADS)
Birrer, Marcel; Stemmer, Christian; Adams, Nikolaus N.
2011-05-01
Investigations of hypersonic boundary-layer flows around a cubical obstacle with a height in the order of half the boundary layer thickness were carried out in this work. Special interest was laid on the influence of chemical non-equilibrium effects on the wake flow of the obstacle. Direct numerical simulations were conducted using three different gas models, a caloric perfect, an equilibrium and a chemical non-equilibrium gas model. The geometry was chosen as a wedge with a six degree half angle, according to the aborted NASA HyBoLT free flight experiment. At 0.5 m downstream of the leading edge, a surface trip was positioned. The free-stream flow was set to Mach 8.5 with air conditions taken from the 1976 standard atmosphere at an altitude of 42 km according to the predicted flight path. The simulations were done in three steps for all models. First, two-dimensional calculations of the whole configuration including the leading edge and the obstacle were conducted. These provide constant span-wise profiles for detailed, steady three-dimensional simulations around the close vicinity of the obstacle. A free-stream Mach number of about 6.3 occurs behind the shock. A cross-section in the wake of the object then delivers the steady inflow for detailed unsteady simulations of the wake. Perturbations at unstable frequencies, obtained from a bi-global secondary stability analysis, were added to these profiles. The solutions are time-Fourier transformed to investigate the unsteady downstream development of the different modes due to the interaction with the base-flow containing two counter-rotating vortices. Results will be presented that show the influence of the presence of chemical non-equilibrium on the instability in the wake of the object leading to a laminar or a turbulent wake.
IDES: an integrated demand and energy supply equilibrium model. [IDES
Macal, C.M.
1985-01-01
The IDES (Integrated Demand and Energy Supply) Model is a price-quantity equilibrium model similar to the Long-Term Energy Analysis Package (LEAP) for projecting energy quantities and prices over a 30-year time horizon. The model integrates resource production activities, petroleum refining, electricity generation, fuel processing, and demand modules. The design objectives, mathematical formulation, iterative solution algorithm, and computer implementation are described in this paper.
GROUNDWATER MASS TRANSPORT AND EQUILIBRIUM CHEMISTRY MODEL FOR MULTICOMPONENT SYSTEMS
A mass transport model, TRANQL, for a multicomponent solution system has been developed. The equilibrium interaction chemistry is posed independently of the mass transport equations which leads to a set of algebraic equations for the chemistry coupled to a set of differential equ...
Approach to equilibrium in accelerated global oceanic models
Danabasoglu, G.; McWilliams, J.C.; Large, W.G.
1996-05-01
The approach to equilibrium of a coarse-resolution, seasonally forced, global oceanic general circulation model is investigated, considering the effects of a widely used acceleration technique that distorts the dynamics by using unequal time steps in the governing equations. A measure of the equilibration time for any solution property is defined as the time it takes to go 90% of the way from its present value to its equilibrium value. This measure becomes approximately time invariant only after sufficiently long integration. It indicates that the total kinetic energy and most mass transport rates attain equilibrium within about 90 and 40 calendar years, respectively. The upper-ocean potential temperature and salinity equilibrium times are about 480 and 380 calender years, following 150- and 20-year initial adjustments, respectively. In the abyssal ocean, potential temperature and salinity equilibration take about 4500 and 3900 calender years, respectively. These longer equilibration times are due to the slow diffusion of tracers both along and across the isopycnal surfaces in stably stratified regions, and these times vary with the associated diffusivities. An analysis of synchronous (i.e., not accelerated) integrations shows that there is a complex interplay between convective, advective, and diffusive timescales. Because of the distortion by acceleration of the seasonal cycle, the solutions display some significant adjustments upon switching to synchronous integration. However, the proper seasonal cycle is recovered within five years. Provided that a sufficient equilibrium state has been achieved with acceleration, the model must be integrated synchronously for only about 15 years thereafter to closely approach synchronous equilibrium. 16 refs., 11 figs., 1 tab.
New Simulator for Non-Equilibrium Modeling of Hydrate Reservoirs
NASA Astrophysics Data System (ADS)
Kvamme, B.; Qorbani Nashaqi, K.; Jemai, K.; Vafaei, M.
2014-12-01
Due to Gibbs phase rule and combination of first and second law of thermodynamics, hydrate in nature cannot be in equilibrium since they come from different parent phases. In this system hydrate formation and dissociation is affected by local variables such as pressure, temperature and composition with mass and energy transport restrictions. Available simulators have attempted to model hydrate phase transition as an equilibrium reaction. Although those which treated the processes of formation and dissociation as kinetics used model of Kim and Bishnoi based on laboratory PVT experiment, and consequently hard to accept up scaling to real reservoirs condition. Additionally, they merely check equilibrium in terms of pressure and temperature projections and disregard thermodynamic requirements for equilibrium especially along axes of concentrations in phases. Non-equilibrium analysis of hydrate involves putting aside all the phase transitions which are not possible and use kinetic evaluation to measure phase transitions progress in each grid block for each time step. This procedure is Similar to geochemical reservoir simulators logic. As a result RetrasoCodeBright has been chosen as hydrate reservoir simulator and our work involves extension of this code. RetrasoCodeBright (RCB) is able to handle competing processes of formation and dissociation of hydrates as pseudo reactions at each node and each time step according to the temperature, pressure and concentration. Hydrates can therefore be implemented into the structure as pseudo minerals, with appropriate kinetic models. In order to implement competing nature of phase transition kinetics of hydrate formation, we use classical nucleation theory based on Kvamme et al. as a simplified model inside RCB and use advanced theories to fit parameters for the model (PFT). Hydrate formation and dissociation can directly be observed through porosity changes in the specific areas of the porous media. In this work which is in
Radiative-convective equilibrium models of Jupiter and Saturn
NASA Astrophysics Data System (ADS)
Appleby, J. F.; Hogan, J. S.
1984-09-01
Radiative-convective equilibrium models for Jupiter and Saturn have been produced in a study concentrating on the stratospheric energy balance and the possible role of aerosol heating. These models are compared directly with the thermal structure profiles obtained from Voyager radio occultation measurements. The method is based on a straightforward flux divergence formulation derived from earlier work. The balance between absorbed and emitted energies is computed iteratively at each level in the atmosphere, assuming local thermodynamic equilibrium and employing a standard treatment of opacities. Results for Jupiter indicate that a dust-free model furnishes a good mean thermal profile for the stratosphere when compared with the Voyager 1 radio occultation measurements. Observations of the equatorial region exhibit periodic vertical structure. The Saturn models are relatively simple and in good agreement with the Voyager 2 radio occultation temperature profiles at all levels. Aerosol heating played a minor role in Saturn's midlatitude stratospheric energy balance at the time of the Voyager 2 encounter.
Equilibrium and Disequilibrium Dynamics in Cobweb Models with Time Delays
NASA Astrophysics Data System (ADS)
Gori, Luca; Guerrini, Luca; Sodini, Mauro
2015-06-01
This paper aims to study price dynamics in two different continuous time cobweb models with delays close to [Hommes, 1994]. In both cases, the stationary equilibrium may be not representative of the long-term dynamics of the model, since it is possible to observe endogenous and persistent fluctuations (supercritical Hopf bifurcations) even if a deterministic context without external shocks is considered. In the model in which markets are in equilibrium every time, we show that the existence of time delays in the expectations formation mechanism may cause chaotic dynamics similar to those obtained in [Hommes, 1994] in a discrete time context. From a mathematical point of view, we apply the Poincaré-Lindstedt perturbation method to study the local dynamic properties of the models. In addition, several numerical experiments are used to investigate global properties of the systems.
Knowledge Management through the Equilibrium Pattern Model for Learning
NASA Astrophysics Data System (ADS)
Sarirete, Akila; Noble, Elizabeth; Chikh, Azeddine
Contemporary students are characterized by having very applied learning styles and methods of acquiring knowledge. This behavior is consistent with the constructivist models where students are co-partners in the learning process. In the present work the authors developed a new model of learning based on the constructivist theory coupled with the cognitive development theory of Piaget. The model considers the level of learning based on several stages and the move from one stage to another requires learners' challenge. At each time a new concept is introduced creates a disequilibrium that needs to be worked out to return back to its equilibrium stage. This process of "disequilibrium/equilibrium" has been analyzed and validated using a course in computer networking as part of Cisco Networking Academy Program at Effat College, a women college in Saudi Arabia. The model provides a theoretical foundation for teaching especially in a complex knowledge domain such as engineering and can be used in a knowledge economy.
Felmy, Andrew R.; Mason, Marvin J.; Qafoku, Odeta; Dixon, David A.
2005-04-19
This symposium manuscript describes the development of an accurate aqueous thermodynamic model for predicting the speciation of Sr in the waste tanks at the Hanford site. A systematic approach is described that details the studies performed to define the most important inorganic and organic complexation reactions as well as the effects of other important metal ions that compete with Sr for complexation reactions with the chelates. By using this approach we were able to define a reduced set of inorganic complexation, organic complexation, and competing metal reactions that best represent the much more complex waste tank chemical system. A summary is presented of the final thermodynamic model for the system Na-Ca-Sr-OH-CO3-NO3-EDTA-HEDTA-H2O from 25 to 75 ºC that was previously published in a variety of sources. Previously unpublished experimental data are also given for the competing metal Ni as well for certain chemical systems, Na-Sr-CO3-PO4-H2O, and for the solubility of amorphous iron hydroxide in the presence of several organic chelating agents. These data were not used in model development but were key to the final selection of the specific chemical systems prioritized for detailed study.
Viscous-shock-layer solutions for turbulent flow of radiating gas mixtures in chemical equilibrium
NASA Technical Reports Server (NTRS)
Anderson, E. C.; Moss, J. N.
1975-01-01
The viscous-shock-layer equations for hypersonic laminar and turbulent flows of radiating or nonradiating gas mixtures in chemical equilibrium are presented for two-dimensional and axially-symmetric flow fields. Solutions were obtained using an implicit finite-difference scheme and results are presented for hypersonic flow over spherically-blunted cone configurations at freestream conditions representative of entry into the atmosphere of Venus. These data are compared with solutions obtained using other methods of analysis.
Viscous shock layer solutions for turbulent flow of radiating gas mixtures in chemical equilibrium
NASA Technical Reports Server (NTRS)
Anderson, E. C.; Moss, J. N.
1975-01-01
The viscous shock layer equations for hypersonic laminar and turbulent flows of radiating or nonradiating gas mixtures in chemical equilibrium are presented for two-dimensional and axially symmetric flow fields. Solutions are obtained using an implicit finite difference scheme and results are presented for hypersonic flow over spherically blunted cone configurations at free stream conditions representative of entry into the atmosphere of Venus. These data are compared with solutions obtained using other methods of analysis.
NASA Astrophysics Data System (ADS)
Marques, Wilson, Jr.; Jacinta Soares, Ana; Pandolfi Bianchi, Miriam; Kremer, Gilberto M.
2015-06-01
A shock wave structure problem, like the one which can be formulated for the planar detonation wave, is analyzed here for a binary mixture of ideal gases undergoing the symmetric reaction {{A}1}+{{A}1}\\rightleftharpoons {{A}2}+{{A}2}. The problem is studied at the hydrodynamic Euler limit of a kinetic model of the reactive Boltzmann equation. The chemical rate law is deduced in this frame with a second-order reaction rate, in a chemical regime such that the gas flow is not far away from the chemical equilibrium. The caloric and the thermal equations of state for the specific internal energy and temperature are employed to close the system of balance laws. With respect to other approaches known in the kinetic literature for detonation problems with a reversible reaction, this paper aims to improve some aspects of the wave solution. Within the mathematical analysis of the detonation model, the equation of the equilibrium Hugoniot curve of the final states is explicitly derived for the first time and used to define the correct location of the equilibrium Chapman-Jouguet point in the Hugoniot diagram. The parametric space is widened to investigate the response of the detonation solution to the activation energy of the chemical reaction. Finally, the mathematical formulation of the linear stability problem is given for the wave detonation structure via a normal-mode approach, when bidimensional disturbances perturb the steady solution. The stability equations with their boundary conditions and the radiation condition of the considered model are explicitly derived for small transversal deviations of the shock wave location. The paper shows how a second-order chemical kinetics description, derived at the microscopic level, and an analytic deduction of the equilibrium Hugoniot curve, lead to an accurate picture of the steady detonation with reversible reaction, as well as to a proper bidimensional linear stability analysis.
NASA Technical Reports Server (NTRS)
Steinberger, Craig J.
1991-01-01
The effects of compressibility, chemical reaction exothermicity, and non-equilibrium chemical modeling in a reacting plane mixing layer were investigated by means of two dimensional direct numerical simulations. The chemical reaction was irreversible and second order of the type A + B yields Products + Heat. The general governing fluid equations of a compressible reacting flow field were solved by means of high order finite difference methods. Physical effects were then determined by examining the response of the mixing layer to variation of the relevant non-dimensionalized parameters. The simulations show that increased compressibility generally results in a suppressed mixing, and consequently a reduced chemical reaction conversion rate. Reaction heat release was found to enhance mixing at the initial stages of the layer growth, but had a stabilizing effect at later times. The increased stability manifested itself in the suppression or delay of the formation of large coherent structures within the flow. Calculations were performed for a constant rate chemical kinetics model and an Arrhenius type kinetic prototype. The choice of the model was shown to have an effect on the development of the flow. The Arrhenius model caused a greater temperature increase due to reaction than the constant kinetic model. This had the same effect as increasing the exothermicity of the reaction. Localized flame quenching was also observed when the Zeldovich number was relatively large.
Non-Equilibrium Turbulence and Two-Equation Modeling
NASA Technical Reports Server (NTRS)
Rubinstein, Robert
2011-01-01
Two-equation turbulence models are analyzed from the perspective of spectral closure theories. Kolmogorov theory provides useful information for models, but it is limited to equilibrium conditions in which the energy spectrum has relaxed to a steady state consistent with the forcing at large scales; it does not describe transient evolution between such states. Transient evolution is necessarily through nonequilibrium states, which can only be found from a theory of turbulence evolution, such as one provided by a spectral closure. When the departure from equilibrium is small, perturbation theory can be used to approximate the evolution by a two-equation model. The perturbation theory also gives explicit conditions under which this model can be valid, and when it will fail. Implications of the non-equilibrium corrections for the classic Tennekes-Lumley balance in the dissipation rate equation are drawn: it is possible to establish both the cancellation of the leading order Re1/2 divergent contributions to vortex stretching and enstrophy destruction, and the existence of a nonzero difference which is finite in the limit of infinite Reynolds number.
NASA Astrophysics Data System (ADS)
Salvage, Karen M.; Yeh, Gour-Tsyh
1998-08-01
This paper presents the conceptual and mathematical development of the numerical model titled BIOKEMOD, and verification simulations performed using the model. BIOKEMOD is a general computer model for simulation of geochemical and microbiological reactions in batch aqueous solutions. BIOKEMOD may be coupled with hydrologic transport codes for simulation of chemically and biologically reactive transport. The chemical systems simulated may include any mixture of kinetic and equilibrium reactions. The pH, pe, and ionic strength may be specified or simulated. Chemical processes included are aqueous complexation, adsorption, ion-exchange and precipitation/dissolution. Microbiological reactions address growth of biomass and degradation of chemicals by microbial metabolism of substrates, nutrients, and electron acceptors. Inhibition or facilitation of growth due to the presence of specific chemicals and a lag period for microbial acclimation to new substrates may be simulated if significant in the system of interest. Chemical reactions controlled by equilibrium are solved using the law of mass action relating the thermodynamic equilibrium constant to the activities of the products and reactants. Kinetic chemical reactions are solved using reaction rate equations based on collision theory. Microbiologically mediated reactions for substrate removal and biomass growth are assumed to follow Monod kinetics modified for the potentially limiting effects of substrate, nutrient, and electron acceptor availability. BIOKEMOD solves the ordinary differential and algebraic equations of mixed geochemical and biogeochemical reactions using the Newton-Raphson method with full matrix pivoting. Simulations may be either steady state or transient. Input to the program includes the stoichiometry and parameters describing the relevant chemical and microbiological reactions, initial conditions, and sources/sinks for each chemical species. Output includes the chemical and biomass concentrations
Reactive solute transport in streams. 1. Development of an equilibrium- based model
Runkel, R.L.; Bencala, K.E.; Broshears, R.E.; Chapra, S.C.
1996-01-01
An equilibrium-based solute transport model is developed for the simulation of trace metal fate and transport in streams. The model is formed by coupling a solute transport model with a chemical equilibrium submodel based on MINTEQ. The solute transport model considers the physical processes of advection, dispersion, lateral inflow, and transient storage, while the equilibrium submodel considers the speciation and complexation of aqueous species, precipitation/dissolution and sorption. Within the model, reactions in the water column may result in the formation of solid phases (precipitates and sorbed species) that are subject to downstream transport and settling processes. Solid phases on the streambed may also interact with the water column through dissolution and sorption/desorption reactions. Consideration of both mobile (water-borne) and immobile (streambed) solid phases requires a unique set of governing differential equations and solution techniques that are developed herein. The partial differential equations describing physical transport and the algebraic equations describing chemical equilibria are coupled using the sequential iteration approach.
Rates of coalescence for common epidemiological models at equilibrium
Koelle, Katia; Rasmussen, David A.
2012-01-01
Coalescent theory provides a mathematical framework for quantitatively interpreting gene genealogies. With the increased availability of molecular sequence data, disease ecologists now regularly apply this body of theory to viral phylogenies, most commonly in attempts to reconstruct demographic histories of infected individuals and to estimate parameters such as the basic reproduction number. However, with few exceptions, the mathematical expressions at the core of coalescent theory have not been explicitly linked to the structure of epidemiological models, which are commonly used to mathematically describe the transmission dynamics of a pathogen. Here, we aim to make progress towards establishing this link by presenting a general approach for deriving a model's rate of coalescence under the assumption that the disease dynamics are at their endemic equilibrium. We apply this approach to four common families of epidemiological models: standard susceptible-infected-susceptible/susceptible-infected-recovered/susceptible-infected-recovered-susceptible models, models with individual heterogeneity in infectivity, models with an exposed but not yet infectious class and models with variable distributions of the infectious period. These results improve our understanding of how epidemiological processes shape viral genealogies, as well as how these processes affect levels of viral diversity and rates of genetic drift. Finally, we discuss how a subset of these coalescent rate expressions can be used for phylodynamic inference in non-equilibrium settings. For the ones that are limited to equilibrium conditions, we also discuss why this is the case. These results, therefore, point towards necessary future work while providing intuition on how epidemiological characteristics of the infection process impact gene genealogies. PMID:21920961
Equilibrium slab models of Lyman-alpha clouds
NASA Technical Reports Server (NTRS)
Charlton, Jane C.; Salpeter, Edwin E.; Hogan, Craig J.
1993-01-01
Solutions for the equilibrium configuration of a slab with ionizing radiation incident equally from both sides are explored. Radiation effects (photoionization, Ly-alpha photon trapping, and mock gravity) as well as external pressure and self gravity (with and without dark matter) are included. The general formalism is applied to structure growth on small scales at very high z due to mock gravity on dust. Emphasis is placed on the application of slab models at z of less than 5, particularly those that may correspond to Ly-alpha forest, Lyman limit, and damped Ly-alpha systems. The regime with a dominant outward force contributed by trapping of Ly-alpha photons is discussed. General expressions are given for the equilibrium, including dark matter, assuming various relationships between the density of the dark matter halo and the total gas column density.
ERIC Educational Resources Information Center
Bindel, Thomas H.
2010-01-01
Entropy analyses as a function of the extent of reaction are presented for a number of physicochemical processes, including vaporization of a liquid, dimerization of nitrogen dioxide, and the autoionization of water. Graphs of the total entropy change versus the extent of reaction give a visual representation of chemical equilibrium and the second…
Facilitated Oriented Spin Models: Some Non Equilibrium Results
NASA Astrophysics Data System (ADS)
Cancrini, N.; Martinelli, F.; Schonmann, R.; Toninelli, C.
2010-03-01
We perform the rigorous analysis of the relaxation to equilibrium for some facilitated or kinetically constrained spin models (KCSM) when the initial distribution ν is different from the reversible one, μ. This setting has been intensively studied in the physics literature to analyze the slow dynamics which follows a sudden quench from the liquid to the glass phase. We concentrate on two basic oriented KCSM: the East model on ℤ, for which the constraint requires that the East neighbor of the to-be-update vertex is vacant and the AD model on the binary tree introduced in Aldous and Diaconis (J. Stat. Phys. 107(5-6):945-975, 2002), for which the constraint requires the two children to be vacant. It is important to observe that, while the former model is ergodic at any p≠1, the latter displays an ergodicity breaking transition at p c =1/2. For the East we prove exponential convergence to equilibrium with rate depending on the spectral gap if ν is concentrated on any configuration which does not contain a forever blocked site or if ν is a Bernoulli( p') product measure for any p'≠1. For the model on the binary tree we prove similar results in the regime p, p'< p c and under the (plausible) assumption that the spectral gap is positive for p< p c . By constructing a proper test function, we also prove that if p'> p c and p≤ p c convergence to equilibrium cannot occur for all local functions. Finally, in a short appendix, we present a very simple argument, different from the one given in Aldous and Diaconis (J. Stat. Phys. 107(5-6):945-975, 2002), based on a combination of some combinatorial results together with "energy barrier" considerations, which yields the sharp upper bound for the spectral gap of East when p↑1.
Pharmaceutical Industry and Trade Liberalization Using Computable General Equilibrium Model
Barouni, M; Ghaderi, H; Banouei, AA
2012-01-01
Background Computable general equilibrium models are known as a powerful instrument in economic analyses and widely have been used in order to evaluate trade liberalization effects. The purpose of this study was to provide the impacts of trade openness on pharmaceutical industry using CGE model. Methods: Using a computable general equilibrium model in this study, the effects of decrease in tariffs as a symbol of trade liberalization on key variables of Iranian pharmaceutical products were studied. Simulation was performed via two scenarios in this study. The first scenario was the effect of decrease in tariffs of pharmaceutical products as 10, 30, 50, and 100 on key drug variables, and the second was the effect of decrease in other sectors except pharmaceutical products on vital and economic variables of pharmaceutical products. The required data were obtained and the model parameters were calibrated according to the social accounting matrix of Iran in 2006. Results: The results associated with simulation demonstrated that the first scenario has increased import, export, drug supply to markets and household consumption, while import, export, supply of product to market, and household consumption of pharmaceutical products would averagely decrease in the second scenario. Ultimately, society welfare would improve in all scenarios. Conclusion: We presents and synthesizes the CGE model which could be used to analyze trade liberalization policy issue in developing countries (like Iran), and thus provides information that policymakers can use to improve the pharmacy economics. PMID:23641393
NASA Astrophysics Data System (ADS)
Maulois, Melissa; Ribière, Maxime; Eichwald, Olivier; Yousfi, Mohammed; Azaïs, Bruno
2016-04-01
The comprehension of electromagnetic perturbations of electronic devices, due to air plasma-induced electromagnetic field, requires a thorough study on air plasma. In the aim to understand the phenomena at the origin of the formation of non-equilibrium air plasma, we simulate, using a volume average chemical kinetics model (0D model), the time evolution of a non-equilibrium air plasma generated by an energetic X-ray flash. The simulation is undertaken in synthetic air (80% N2 and 20% O2) at ambient temperature and atmospheric pressure. When the X-ray flash crosses the gas, non-relativistic Compton electrons (low energy) and a relativistic Compton electron beam (high energy) are simultaneously generated and interact with the gas. The considered chemical kinetics scheme involves 26 influent species (electrons, positive ions, negative ions, and neutral atoms and molecules in their ground or metastable excited states) reacting following 164 selected reactions. The kinetics model describing the plasma chemistry was coupled to the conservation equation of the electron mean energy, in order to calculate at each time step of the non-equilibrium plasma evolution, the coefficients of reactions involving electrons while the energy of the heavy species (positive and negative ions and neutral atoms and molecules) is assumed remaining close to ambient temperature. It has been shown that it is the relativistic Compton electron beam directly created by the X-ray flash which is mainly responsible for the non-equilibrium plasma formation. Indeed, the low energy electrons (i.e., the non-relativistic ones) directly ejected from molecules by Compton collisions contribute to less than 1% on the creation of electrons in the plasma. In our simulation conditions, a non-equilibrium plasma with a low electron mean energy close to 1 eV and a concentration of charged species close to 1013 cm-3 is formed a few nanoseconds after the peak of X-ray flash intensity. 200 ns after the flash
Model fitting and inference under Latent Equilibrium Processes
Bhattacharya, Sourabh; Gelfand, Alan E.; Holsinger, Kent E.
2008-01-01
This paper presents a methodology for model fitting and inference in the context of Bayesian models of the type f(Y | X, θ)f(X | θ)f(θ), where Y is the (set of) observed data, θ is a set of model parameters and X is an unobserved (latent) stationary stochastic process induced by the first order transition model f(X(t+1) | X(t), θ), where X(t) denotes the state of the process at time (or generation) t. The crucial feature of the above type of model is that, given θ, the transition model f(X(t+1) | X(t), θ) is known but the distribution of the stochastic process in equilibrium, that is f(X | θ), is, except in very special cases, intractable, hence unknown. A further point to note is that the data Y has been assumed to be observed when the underlying process is in equilibrium. In other words, the data is not collected dynamically over time. We refer to such specification as a latent equilibrium process (LEP) model. It is motivated by problems in population genetics (though other applications are discussed), where it is of interest to learn about parameters such as mutation and migration rates and population sizes, given a sample of allele frequencies at one or more loci. In such problems it is natural to assume that the distribution of the observed allele frequencies depends on the true (unobserved) population allele frequencies, whereas the distribution of the true allele frequencies is only indirectly specified through a transition model. As a hierarchical specification, it is natural to fit the LEP within a Bayesian framework. Fitting such models is usually done via Markov chain Monte Carlo (MCMC). However, we demonstrate that, in the case of LEP models, implementation of MCMC is far from straightforward. The main contribution of this paper is to provide a methodology to implement MCMC for LEP models. We demonstrate our approach in population genetics problems with both simulated and real data sets. The resultant model fitting is computationally intensive
LLNL Chemical Kinetics Modeling Group
Pitz, W J; Westbrook, C K; Mehl, M; Herbinet, O; Curran, H J; Silke, E J
2008-09-24
The LLNL chemical kinetics modeling group has been responsible for much progress in the development of chemical kinetic models for practical fuels. The group began its work in the early 1970s, developing chemical kinetic models for methane, ethane, ethanol and halogenated inhibitors. Most recently, it has been developing chemical kinetic models for large n-alkanes, cycloalkanes, hexenes, and large methyl esters. These component models are needed to represent gasoline, diesel, jet, and oil-sand-derived fuels.
Formation of copper porous structures under near-equilibrium chemical vapor deposition
NASA Astrophysics Data System (ADS)
Kornyushchenko, A. S.; Natalich, V. V.; Perekrestov, V. I.
2016-05-01
The mechanism of copper structure formation under near-equilibrium conditions in a chemically-active medium-condensate system has been investigated. The desired conditions have been implemented using CVD system. Copper chloride CuCl2 was used as a source material, and mixture of hydrogen with nitrogen served as a working gas. The influence of the evaporation temperature, condensation temperature and state of the growth surface on the porous structures formation has been investigated. It has been established, that the structure formation mechanism is determined by layer-by-layer or normal crystal growth, nucleation and growth of whiskers, and also by partial intergrowth of structural elements.
Runkel, Robert L.
2010-01-01
OTEQ is a mathematical simulation model used to characterize the fate and transport of waterborne solutes in streams and rivers. The model is formed by coupling a solute transport model with a chemical equilibrium submodel. The solute transport model is based on OTIS, a model that considers the physical processes of advection, dispersion, lateral inflow, and transient storage. The equilibrium submodel is based on MINTEQ, a model that considers the speciation and complexation of aqueous species, acid-base reactions, precipitation/dissolution, and sorption. Within OTEQ, reactions in the water column may result in the formation of solid phases (precipitates and sorbed species) that are subject to downstream transport and settling processes. Solid phases on the streambed may also interact with the water column through dissolution and sorption/desorption reactions. Consideration of both mobile (waterborne) and immobile (streambed) solid phases requires a unique set of governing differential equations and solution techniques that are developed herein. The partial differential equations describing physical transport and the algebraic equations describing chemical equilibria are coupled using the sequential iteration approach. The model's ability to simulate pH, precipitation/dissolution, and pH-dependent sorption provides a means of evaluating the complex interactions between instream chemistry and hydrologic transport at the field scale. This report details the development and application of OTEQ. Sections of the report describe model theory, input/output specifications, model applications, and installation instructions. OTEQ may be obtained over the Internet at http://water.usgs.gov/software/OTEQ.
Westbrook, C.K.; Pitz, W.J.
1993-12-01
This project emphasizes numerical modeling of chemical kinetics of combustion, including applications in both practical combustion systems and in controlled laboratory experiments. Elementary reaction rate parameters are combined into mechanisms which then describe the overall reaction of the fuels being studied. Detailed sensitivity analyses are used to identify those reaction rates and product species distributions to which the results are most sensitive and therefore warrant the greatest attention from other experimental and theoretical research programs. Experimental data from a variety of environments are combined together to validate the reaction mechanisms, including results from laminar flames, shock tubes, flow systems, detonations, and even internal combustion engines.
Modeling Inflation Using a Non-Equilibrium Equation of Exchange
NASA Technical Reports Server (NTRS)
Chamberlain, Robert G.
2013-01-01
Inflation is a change in the prices of goods that takes place without changes in the actual values of those goods. The Equation of Exchange, formulated clearly in a seminal paper by Irving Fisher in 1911, establishes an equilibrium relationship between the price index P (also known as "inflation"), the economy's aggregate output Q (also known as "the real gross domestic product"), the amount of money available for spending M (also known as "the money supply"), and the rate at which money is reused V (also known as "the velocity of circulation of money"). This paper offers first a qualitative discussion of what can cause these factors to change and how those causes might be controlled, then develops a quantitative model of inflation based on a non-equilibrium version of the Equation of Exchange. Causal relationships are different from equations in that the effects of changes in the causal variables take time to play out-often significant amounts of time. In the model described here, wages track prices, but only after a distributed lag. Prices change whenever the money supply, aggregate output, or the velocity of circulation of money change, but only after a distributed lag. Similarly, the money supply depends on the supplies of domestic and foreign money, which depend on the monetary base and a variety of foreign transactions, respectively. The spreading of delays mitigates the shocks of sudden changes to important inputs, but the most important aspect of this model is that delays, which often have dramatic consequences in dynamic systems, are explicitly incorporated.macroeconomics, inflation, equation of exchange, non-equilibrium, Athena Project
NASA Technical Reports Server (NTRS)
Gokoglu, Suleyman A.
1988-01-01
This paper investigates the role played by vapor-phase chemical reactions on CVD rates by comparing the results of two extreme theories developed to predict CVD mass transport rates in the absence of interfacial kinetic barrier: one based on chemically frozen boundary layer and the other based on local thermochemical equilibrium. Both theories consider laminar convective-diffusion boundary layers at high Reynolds numbers and include thermal (Soret) diffusion and variable property effects. As an example, Na2SO4 deposition was studied. It was found that gas phase reactions have no important role on Na2SO4 deposition rates and on the predictions of the theories. The implications of the predictions of the two theories to other CVD systems are discussed.
A tightly coupled non-equilibrium model for inductively coupled radio-frequency plasmas
Munafò, A. Alfuhaid, S. A. Panesi, M.; Cambier, J.-L.
2015-10-07
The objective of the present work is the development of a tightly coupled magneto-hydrodynamic model for inductively coupled radio-frequency plasmas. Non Local Thermodynamic Equilibrium (NLTE) effects are described based on a hybrid State-to-State approach. A multi-temperature formulation is used to account for thermal non-equilibrium between translation of heavy-particles and vibration of molecules. Excited electronic states of atoms are instead treated as separate pseudo-species, allowing for non-Boltzmann distributions of their populations. Free-electrons are assumed Maxwellian at their own temperature. The governing equations for the electro-magnetic field and the gas properties (e.g., chemical composition and temperatures) are written as a coupled system of time-dependent conservation laws. Steady-state solutions are obtained by means of an implicit Finite Volume method. The results obtained in both LTE and NLTE conditions over a broad spectrum of operating conditions demonstrate the robustness of the proposed coupled numerical method. The analysis of chemical composition and temperature distributions along the torch radius shows that: (i) the use of the LTE assumption may lead to an inaccurate prediction of the thermo-chemical state of the gas, and (ii) non-equilibrium phenomena play a significant role close the walls, due to the combined effects of Ohmic heating and macroscopic gradients.
A tightly coupled non-equilibrium model for inductively coupled radio-frequency plasmas
NASA Astrophysics Data System (ADS)
Munafò, A.; Alfuhaid, S. A.; Cambier, J.-L.; Panesi, M.
2015-10-01
The objective of the present work is the development of a tightly coupled magneto-hydrodynamic model for inductively coupled radio-frequency plasmas. Non Local Thermodynamic Equilibrium (NLTE) effects are described based on a hybrid State-to-State approach. A multi-temperature formulation is used to account for thermal non-equilibrium between translation of heavy-particles and vibration of molecules. Excited electronic states of atoms are instead treated as separate pseudo-species, allowing for non-Boltzmann distributions of their populations. Free-electrons are assumed Maxwellian at their own temperature. The governing equations for the electro-magnetic field and the gas properties (e.g., chemical composition and temperatures) are written as a coupled system of time-dependent conservation laws. Steady-state solutions are obtained by means of an implicit Finite Volume method. The results obtained in both LTE and NLTE conditions over a broad spectrum of operating conditions demonstrate the robustness of the proposed coupled numerical method. The analysis of chemical composition and temperature distributions along the torch radius shows that: (i) the use of the LTE assumption may lead to an inaccurate prediction of the thermo-chemical state of the gas, and (ii) non-equilibrium phenomena play a significant role close the walls, due to the combined effects of Ohmic heating and macroscopic gradients.
Model of opacity and emissivity of non-equilibrium plasma
NASA Astrophysics Data System (ADS)
Politov, V. Y.
2008-05-01
In this work the model describing absorption and emission properties of the non-equilibrium plasma is presented. It is based on the kinetics equations for populations of the ground, singly and doubly excited states of multi-charged ions. After solving these equations, the states populations together with the spectroscopic data, supplied in the special database for a lot ionization stages, are used for building the spectral distributions of plasma opacity and emissivity in STA approximation. Results of kinetics simulation are performed for such important X-ray converter as gold, which is investigated intensively in ICF-experiments.
On equilibrium parameters of a radiation-compression model pinch
Afonin, V.I.
1994-12-31
Up to date, the micropinch effect in high-current axially symmetric electric discharges was the subject of extensive theoretical and experimental research. The radiation compression mechanism proved to fit the experimental data better than any other model. It assumes the pinch equilibrium to occur when the surface radiation emission replaces the surface emission mode. The aim of the present work is to show that a quasi-stationary pinch state can exist in the case of an optically thin plasma as well. 8 figs.
A Quasi-Equilibrium Tropical Circulation Model--Formulation*.
NASA Astrophysics Data System (ADS)
Neelin, J. David; Zeng, Ning
2000-06-01
A class of model for simulation and theory of the tropical atmospheric component of climate variations is introduced. These models are referred to as quasi-equilibrium tropical circulation models, or QTCMs, because they make use of approximations associated with quasi-equilibrium (QE) convective parameterizations. Quasi-equilibrium convective closures tend to constrain the vertical temperature profile in convecting regions. This can be used to generate analytical solutions for the large-scale flow under certain approximations. A tropical atmospheric model of intermediate complexity is constructed by using the analytical solutions as the first basis function in a Galerkin representation of vertical structure. This retains much of the simplicity of the analytical solutions, while retaining full nonlinearity, vertical momentum transport, departures from QE, and a transition between convective and nonconvective zones based on convective available potential energy. The atmospheric model is coupled to a one-layer land surface model with interactive soil moisture and simulates its own tropical climatology. In the QTCM version presented here, the vertical structure of temperature variations is truncated to a single profile associated with deep convection. Though designed to be accurate in and near regions dominated by deep convection, the model simulates the tropical and subtropical climatology reasonably well, and even has a qualitative representation of midlatitude storm tracks.The model is computationally economical, since part of the solution has been carried out analytically, but the main advantage is relative simplicity of analysis under certain conditions. The formulation suggests a slightly different way of looking at the tropical atmosphere than has been traditional in tropical meteorology. While convective scales are unstable, the large-scale motions evolve with a positive effective stratification that takes into account the partial cancellation of adiabatic
NASA Astrophysics Data System (ADS)
Shannon, Joseph Charles
Much of the research concerning pedagogical content knowledge (PCK) in science education has been focused on its nature and development rather than how it is dynamically employed in the classroom with respect to specific topics. Research on how PCK is linked with actual classroom decisions has been limited since its tacit nature makes it challenging to identify what dimensions of PCK a teacher employs in various aspects of their practice. This study, using a multi-method case study design, examined four chemistry teachers' (two 1 st year and two 3rd year) decision-making during the planning, teaching, and reflection stages of their practice to determine PCK's influence for the topic of chemical equilibrium. The research occurred in undergraduate chemistry classrooms and special emphasis was placed on examining discourse to illuminate the relationships between how a teacher recognizes the need for a decision, what pedagogical 'moves' were chosen for implementation, and how talk was utilized to execute it. Findings indicated there were distinct differences between 1st and 3rd year teachers' PCK and how they employed it in their practice. The various types of knowledge and beliefs supporting the teachers' model of PCK such as subject matter knowledge, knowledge of student understanding, knowledge of instructional strategies as well as knowledge and beliefs about teaching and their learners influenced their decision-making ability during pre-lesson planning which subsequently influenced their communicative approach in the classroom. Two patterns were observed. Teachers with less teaching experience displayed a model of PCK characterized by an underdeveloped and sometimes fragmented understanding of the topic as well as a fragile knowledge of student understanding. As a result of having limited resources to draw on in the classroom they relied on a controlling communicative approach, thereby inhibiting the elicitation and incorporation of student thinking and
Chemicals loading in acetylated bamboo assisted by supercritical CO2 based on phase equilibrium data
NASA Astrophysics Data System (ADS)
Silviana, Petermann, M.
2015-12-01
Indonesia has a large tropical forest. However, the deforestation still appears annually and vastly. This reason drives a use of bamboo as wood alternative. Recently, there are many modifications of bamboo in order to prolong the shelf life. Unfortunately, the processes need more chemicals and time. Based on wood modification, esterifying of bamboo was undertaken in present of a dense gas, i.e. supercritical CO2. Calculation of chemicals loading referred to ASTM D1413-99 by using the phase equilibrium data at optimum condition by a statistical design. The results showed that the acetylation of bamboo assisted by supercritical CO2 required 14.73 kg acetic anhydride/m3 of bamboo for a treatment of one hour.
Equilibrium model constraints on baryon cycling across cosmic time
NASA Astrophysics Data System (ADS)
Mitra, Sourav; Davé, Romeel; Finlator, Kristian
2015-09-01
Galaxies strongly self-regulate their growth via energetic feedback from stars, supernovae, and black holes, but these processes are among the least understood aspects of galaxy formation theory. We present an analytic galaxy evolution model that directly constrains such feedback processes from observed galaxy scaling relations. The equilibrium model, which is broadly valid for star-forming central galaxies that dominate cosmic star formation, is based on the ansatz that galaxies live in a slowly evolving equilibrium between inflows, outflows, and star formation. Using a Bayesian Monte Carlo Markov chain approach, we constrain our model to match observed galaxy scaling relations between stellar mass and halo mass, star formation rate, and metallicity from 0 < z < 2. A good fit (χ2 ≈ 1.6) is achieved with eight free parameters. We further show that constraining our model to any two of the three data sets also produces a fit to the third that is within reasonable systematic uncertainties. The resulting best-fitting parameters that describe baryon cycling suggest galactic outflow scalings intermediate between energy and momentum-driven winds, a weak dependence of wind recycling time on mass, and a quenching mass scale that evolves modestly upwards with redshift. This model further predicts a stellar mass-star formation rate relation that is in good agreement with observations to z ˜ 6. Our results suggest that this simple analytic framework captures the basic physical processes required to model the mean evolution of stars and metals in galaxies, despite not incorporating many canonical ingredients of galaxy formation models such as merging or disc formation.
Dimension reduction of non-equilibrium plasma kinetic models using principal component analysis
NASA Astrophysics Data System (ADS)
Peerenboom, Kim; Parente, Alessandro; Kozák, Tomáš; Bogaerts, Annemie; Degrez, Gérard
2015-04-01
The chemical complexity of non-equilibrium plasmas poses a challenge for plasma modeling because of the computational load. This paper presents a dimension reduction method for such chemically complex plasmas based on principal component analysis (PCA). PCA is used to identify a low-dimensional manifold in chemical state space that is described by a small number of parameters: the principal components. Reduction is obtained since continuity equations only need to be solved for these principal components and not for all the species. Application of the presented method to a CO2 plasma model including state-to-state vibrational kinetics of CO2 and CO demonstrates the potential of the PCA method for dimension reduction. A manifold described by only two principal components is able to predict the CO2 to CO conversion at varying ionization degrees very accurately.
A Metastable Equilibrium Model for the Relative Abundances of Microbial Phyla in a Hot Spring
Dick, Jeffrey M.; Shock, Everett L.
2013-01-01
Many studies link the compositions of microbial communities to their environments, but the energetics of organism-specific biomass synthesis as a function of geochemical variables have rarely been assessed. We describe a thermodynamic model that integrates geochemical and metagenomic data for biofilms sampled at five sites along a thermal and chemical gradient in the outflow channel of the hot spring known as “Bison Pool” in Yellowstone National Park. The relative abundances of major phyla in individual communities sampled along the outflow channel are modeled by computing metastable equilibrium among model proteins with amino acid compositions derived from metagenomic sequences. Geochemical conditions are represented by temperature and activities of basis species, including pH and oxidation-reduction potential quantified as the activity of dissolved hydrogen. By adjusting the activity of hydrogen, the model can be tuned to closely approximate the relative abundances of the phyla observed in the community profiles generated from BLAST assignments. The findings reveal an inverse relationship between the energy demand to form the proteins at equal thermodynamic activities and the abundance of phyla in the community. The distance from metastable equilibrium of the communities, assessed using an equation derived from energetic considerations that is also consistent with the information-theoretic entropy change, decreases along the outflow channel. Specific divergences from metastable equilibrium, such as an underprediction of the relative abundances of phototrophic organisms at lower temperatures, can be explained by considering additional sources of energy and/or differences in growth efficiency. Although the metabolisms used by many members of these communities are driven by chemical disequilibria, the results support the possibility that higher-level patterns of chemotrophic microbial ecosystems are shaped by metastable equilibrium states that depend on both the
A metastable equilibrium model for the relative abundances of microbial phyla in a hot spring.
Dick, Jeffrey M; Shock, Everett L
2013-01-01
Many studies link the compositions of microbial communities to their environments, but the energetics of organism-specific biomass synthesis as a function of geochemical variables have rarely been assessed. We describe a thermodynamic model that integrates geochemical and metagenomic data for biofilms sampled at five sites along a thermal and chemical gradient in the outflow channel of the hot spring known as "Bison Pool" in Yellowstone National Park. The relative abundances of major phyla in individual communities sampled along the outflow channel are modeled by computing metastable equilibrium among model proteins with amino acid compositions derived from metagenomic sequences. Geochemical conditions are represented by temperature and activities of basis species, including pH and oxidation-reduction potential quantified as the activity of dissolved hydrogen. By adjusting the activity of hydrogen, the model can be tuned to closely approximate the relative abundances of the phyla observed in the community profiles generated from BLAST assignments. The findings reveal an inverse relationship between the energy demand to form the proteins at equal thermodynamic activities and the abundance of phyla in the community. The distance from metastable equilibrium of the communities, assessed using an equation derived from energetic considerations that is also consistent with the information-theoretic entropy change, decreases along the outflow channel. Specific divergences from metastable equilibrium, such as an underprediction of the relative abundances of phototrophic organisms at lower temperatures, can be explained by considering additional sources of energy and/or differences in growth efficiency. Although the metabolisms used by many members of these communities are driven by chemical disequilibria, the results support the possibility that higher-level patterns of chemotrophic microbial ecosystems are shaped by metastable equilibrium states that depend on both the
Modeling dune response using measured and equilibrium bathymetric profiles
Fauver, Laura A.; Thompson, David M.; Sallenger, Asbury H.
2007-01-01
Coastal engineers typically use numerical models such as SBEACH to predict coastal change due to extreme storms. SBEACH model inputs include pre-storm profiles, wave heights and periods, and water levels. This study focuses on the sensitivity of SBEACH to the details of pre-storm bathymetry. The SBEACH model is tested with two initial conditions for bathymetry, including (1) measured bathymetry from lidar, and (2) calculated equilibrium profiles. Results show that longshore variability in the predicted erosion signal is greater over measured bathymetric profiles, due to longshore variations in initial surf zone bathymetry. Additionally, patterns in predicted erosion can be partially explained by the configuration of the inner surf zone from the shoreline to the trough, with surf zone slope accounting for 67% of the variability in predicted erosion volumes.
Equilibrium Analysis of a Yellow Fever Dynamical Model with Vaccination
Martorano Raimundo, Silvia
2015-01-01
We propose an equilibrium analysis of a dynamical model of yellow fever transmission in the presence of a vaccine. The model considers both human and vector populations. We found thresholds parameters that affect the development of the disease and the infectious status of the human population in the presence of a vaccine whose protection may wane over time. In particular, we derived a threshold vaccination rate, above which the disease would be eradicated from the human population. We show that if the mortality rate of the mosquitoes is greater than a given threshold, then the disease is naturally (without intervention) eradicated from the population. In contrast, if the mortality rate of the mosquitoes is less than that threshold, then the disease is eradicated from the populations only when the growing rate of humans is less than another threshold; otherwise, the disease is eradicated only if the reproduction number of the infection after vaccination is less than 1. When this reproduction number is greater than 1, the disease will be eradicated from the human population if the vaccination rate is greater than a given threshold; otherwise, the disease will establish itself among humans, reaching a stable endemic equilibrium. The analysis presented in this paper can be useful, both to the better understanding of the disease dynamics and also for the planning of vaccination strategies. PMID:25834634
Non-Equilibrium Zeldovich-Von Neumann-Doring Theory and Reactive Flow Modeling of Detonation
Tarver, C M; Forbes, J W; Urtiew, P A
2002-05-02
This paper discusses the Non-Equilibrium Zeldovich - von Neumann - Doring (NEZND) theory of self-sustaining detonation waves and the Ignition and Growth reactive flow model of shock initiation and detonation wave propagation in solid explosives. The NEZND theory identified the non-equilibrium excitation processes that precede and follow the exothermic decomposition of a large high explosive molecule into several small reaction product molecules. The thermal energy deposited by the leading shock wave must be distributed to the vibrational modes of the explosive molecule before chemical reactions can occur. The induction time for the onset of the initial endothermic reactions can be calculated using high pressure, high temperature transition state theory. Since the chemical energy is released well behind the leading shock front of a detonation wave, a physical mechanism is required for this chemical energy to reinforce the leading shock front and maintain its overall constant velocity. This mechanism is the amplification of pressure wavelets in the reaction zone by the process of de-excitation of the initially highly vibrationally excited reaction product molecules. This process leads to the development of the three-dimensional structure of detonation waves observed for all explosives. For practical predictions of shock initiation and detonation in hydrodynamic codes, phenomenological reactive flow models have been developed. The Ignition and Growth reactive flow model of shock initiation and detonation in solid explosives has been very successful in describing the overall flow measured by embedded gauges and laser interferometry. This reactive flow model uses pressure and compression dependent reaction rates, because time resolved experimental temperature data is not yet available. Since all chemical reaction rates are ultimately controlled by temperature, the next generation of reactive flow models will use temperature dependent reaction rates. Progress on a
NASA Technical Reports Server (NTRS)
Prinn, R. G.
1992-01-01
The differences in atmospheric composition over the globe and the short- and long-term variations in this composition are the net effect of several atmospheric and biospheric processes: biospheric emissions, atmospheric circulation, atmospheric chemical transformations and finally deposition back to the surface. Accurate and realistic atmospheric chemistry and circulation models are essential to interpret the observed global distributions and trends of atmospheric species in terms of these underlying processes. Comparisons between model predictions and observations test current understanding of these processes and models used in conjunction with inverse methods allow deductions of the rates of these processes from the observations. With the planned inclusion of at least CO and CH4 observations on the Earth Observing System (EOS) satellites, together with the large global data set expected from in situ observations under the International Global Atmospheric Chemistry (IGAC) Project, the further development of global three-dimensional high-resolution atmospheric chemistry and circulation models in order to interpret this new data is a high-priority endeavor.
A radial non-uniform helicon equilibrium discharge model
NASA Astrophysics Data System (ADS)
Cheng, Yu-Guo; Cheng, Mou-Sen; Wang, Mo-Ge; Li, Xiao-Kang
2014-10-01
Helicon discharges have attracted great attention in the electric propulsion community in recent years. To acquire the equilibrium properties, a self-consistent model is developed, which combines the helicon/Trivelpiece—Gould (TG) waves-plasma interaction mechanism and the plasma flow theory under the confinement of the magnetic field. The calculations reproduce the central peak density phenomenon observed in the experiments. The results show that when operating in the wave coupling mode, high magnetic field strength B0 results in the deviation of the central density versus B0 from the linear relationship, while the density rise becomes flatter as the radiofrequency (rf) input power Prf grows, and the electron temperature Te radial profile is mainly determined by the characteristic of the rf energy deposition. The model could provide suggestions in choosing the B0 and Prf for medium power helicon thrusters.
Local Thermal Equilibrium for Certain Stochastic Models of Heat Transport
NASA Astrophysics Data System (ADS)
Li, Yao; Nándori, Péter; Young, Lai-Sang
2016-04-01
This paper is about nonequilibrium steady states (NESS) of a class of stochastic models in which particles exchange energy with their "local environments" rather than directly with one another. The physical domain of the system can be a bounded region of R^d for any d ge 1. We assume that the temperature at the boundary of the domain is prescribed and is nonconstant, so that the system is forced out of equilibrium. Our main result is local thermal equilibrium in the infinite volume limit. In the Hamiltonian context, this would mean that at any location x in the domain, local marginal distributions of NESS tend to a probability with density 1/Z e^{-β (x) H}, permitting one to define the local temperature at x to be β (x)^{-1}. We prove also that in the infinite volume limit, the mean energy profile of NESS satisfies Laplace's equation for the prescribed boundary condition. Our method of proof is duality: by reversing the sample paths of particle movements, we convert the problem of studying local marginal energy distributions at x to that of joint hitting distributions of certain random walks starting from x, and prove that the walks in question become increasingly independent as system size tends to infinity.
Stellar and gaseous disc structures in cosmological galaxy equilibrium models
NASA Astrophysics Data System (ADS)
Rathaus, Ben; Sternberg, Amiel
2016-05-01
We present `radially resolved equilibrium models' for the growth of stellar and gaseous discs in cosmologically accreting massive haloes. Our focus is on objects that evolve to redshifts z ˜ 2. We solve the time-dependent equations that govern the radially dependent star formation rates, inflows and outflows from and to the inter- and circumgalactic medium, and inward radial gas flows within the discs. The stellar and gaseous discs reach equilibrium configurations on dynamical time-scales much shorter than variations in the cosmological dark matter halo growth and baryonic accretions rates. We show analytically that mass and global angular momentum conservation naturally give rise to exponential gas and stellar discs over many radial length-scales. As expected, the gaseous discs are more extended as set by the condition Toomre Q < 1 for star formation. The discs rapidly become baryon dominated. For massive, 5 × 1012 M⊙ haloes at redshift z = 2, we reproduced the typical observed star formation rates of ˜100 M⊙ yr-1, stellar masses ˜9 × 1010 M⊙, gas contents ˜1011 M⊙, half-mass sizes of 4.5 and 5.8 kpc for the stars and gas, and characteristic surface densities of 500 and 400 M⊙ pc-2 for the stars and gas.
CHEMICAL REACTIONS SIMULATED BY GROUND-WATER-QUALITY MODELS.
Grove, David B.; Stollenwerk, Kenneth G.
1987-01-01
Recent literature concerning the modeling of chemical reactions during transport in ground water is examined with emphasis on sorption reactions. The theory of transport and reactions in porous media has been well documented. Numerous equations have been developed from this theory, to provide both continuous and sequential or multistep models, with the water phase considered for both mobile and immobile phases. Chemical reactions can be either equilibrium or non-equilibrium, and can be quantified in linear or non-linear mathematical forms. Non-equilibrium reactions can be separated into kinetic and diffusional rate-limiting mechanisms. Solutions to the equations are available by either analytical expressions or numerical techniques. Saturated and unsaturated batch, column, and field studies are discussed with one-dimensional, laboratory-column experiments predominating. A summary table is presented that references the various kinds of models studied and their applications in predicting chemical concentrations in ground waters.
Radiative-convective equilibrium models of Uranus and Neptune
Appleby, J.F.
1986-03-01
The present study of Uranus and Neptune radiative-convective equilibrium models gives emphasis to such aspects of the stratospheric energy balance as the influence of aerosol heating and convective penetration. The results obtained for Uranus imply that a continuum absorber may be a significant factor in the stratosphere despite the great distance from the sun. The results obtained for Neptune show that such a continuum absorber could significantly contribute to the energy balance within a localized stratospheric region, although it probably cannot furnish sufficient power to account for the observed IR spectrum irrespective of its vertical distribution. Attention is accordingly given to the convective penetration that could arise under such rapid vertical mixing that CH4's condensation cannot occur before the gas is carried above the condensation region. 64 references.
Equilibrium Slab Models of Lyman-Alpha Clouds
NASA Technical Reports Server (NTRS)
Charlton, Jane C.; Salpeter, Edwin E.; Hogan, Craig J.
1993-01-01
We model the L(sub y(alpha)) clouds as slabs of hydrogen with an ionizing extragalactic radiation field incident from both sides. In general, the equilibrium configuration of a slab at redshift z approx. less than 5 is determined by a balance of the gas pressure, gravity (including the effects of a dark matter halo), and the pressure exerted by the inter-galactic medium, P(sub ext). These models have been used to make predictions of the number of slabs as a function of the neutral hydrogen column density, N(sub H). A break in the curve is predicted at the transition between regimes where gravity and pressure are the dominant confining forces, with a less rapid decrease at larger N(sub H). The transition from optically thin to optically thick slabs leads to a gap in the distribution, whose location is governed largely by the spectrum of ionizing radiation. There are certain parallels between lines of sight through the outer HI disk of spiral galaxy with increasing radius, and the progression from damped, to Lyman limit, to forest clouds. We discuss briefly the possibility that at least some of the observed low z forest clouds may be a separate population, associated with galaxies, as suggested by the observations of Bahcall et al. This population could dominate the forest at present if the dark matter attached to galaxies should lead to gravity confinement for this disk population, while the isolated clouds remain pressure confined. The formalism developed in this paper will allow a more detailed study. We also discuss a more general parameter study of the equilibrium configuration of slabs, including mock gravity and L(sub y(alpha)) photon trapping.
Estimated Performance of Radial-Flow Exit Nozzles for Air in Chemical Equilibrium
NASA Technical Reports Server (NTRS)
Englert, Gerald W.; Kochendorfer, Fred D.
1959-01-01
The thrust, boundary-layer, and heat-transfer characteristics were computed for nozzles having radial flow in the divergent part. The working medium was air in chemical equilibrium, and the boundary layer was assumed to be all turbulent. Stagnation pressure was varied from 1 to 32 atmospheres, stagnation temperature from 1000 to 6000 R, and wall temperature from 1000 to 3000 R. Design pressure ratio was varied from 5 to 320, and operating pressure ratio was varied from 0.25 to 8 times the design pressure ratio. Results were generalized independent of divergence angle and were also generalized independent of stagnation pressure in the temperature range of 1000 to 3000 R. A means of determining the aerodynamically optimum wall angle is provided.
NASA Technical Reports Server (NTRS)
Johnson, R. E.
1986-01-01
Chemical reactions at high temperatures have been considered extensively because of their importance to the heating effects on re-entry of space vehicles. Data on these reactions however, are not abundant and even when found there are discrepancies in data collected by various investigators. In particular, data for recombination reactions are calculated from the dissociation reactions or vice versa through the equilibrium constant. This involves the use of the principle of detailed balancing. This principle is discussed in reference to conditions where it is valid as well as to those where it is not valid. Related topics that merit further study or for which applicable information was available are briefly mentioned in an appendix to this report.