Spreading of completely wetting, non-Newtonian fluids with non-power-law rheology.
Min, Qi; Duan, Yuan-Yuan; Wang, Xiao-Dong; Liang, Zhan-Peng; Lee, Duu-Jong; Su, Ay
2010-08-01
Spreading non-Newtonian liquids with non-power-law rheology on completely wetting surfaces are seldom investigated. This study assessed the wetting behavior of polydimethylsiloxane (PDMS), a Newtonian fluid, two carboxymethylcellulose (CMC) sodium solutions, a PDMS+2%w/w silica nanoparticle suspension and three polyethylene glycol (PEG400)+5-10%w/w silica nanoparticle suspensions (non-power-law fluids) on a mica surface. The theta(D)-U and R-t data for spreading drops of the six tested, non-power-law fluids can be described by power-law wetting models. We propose that this behavior is attributable to a uniform shear rate (a few tens to a few hundreds of s(-1)) distributed over the thin-film regime that controls spreading dynamics. Estimated film thickness was below the resolution of an optical microscope for direct observation. Approximating a general non-Newtonian fluid spreading as a power-law fluid greatly simplifies theoretical analysis and data interpretation.
NASA Astrophysics Data System (ADS)
Rabbi, Khan Md.; Rakib, Tawfiqur; Das, Sourav; Mojumder, Satyajit; Saha, Sourav
2016-07-01
This paper demonstrates magneto-hydrodynamic (MHD) mixed convection flow through a channel with a rectangular obstacle at the entrance region using non-Newtonian power law fluid. The obstacle is kept at uniformly high temperature whereas the inlet and top wall of the channel are maintained at a temperature lower than obstacle temperature. Poiseuille flow is implemented as the inlet velocity boundary condition. Grid independency test and code validation are performed to justify the computational accuracy before solving the present problem. Galerkin weighted residual method has been appointed to solve the continuity, momentum and energy equations. The problem has been solved for wide range of pertinent parameters like Richardson number (Ri = 0.1 - 10) at a constant Reynolds number (Re = 100), Hartmann number (Ha = 0 - 100), power index (n = 0.6 - 1.6). The flow and thermal field have been thoroughly discussed through streamline and isothermal lines respectively. The heat transfer performance of the given study has been illustrated by average Nusselt number plots. It is observed that increment of Hartmann number (Ha) tends to decrease the heat transfer rate up to a critical value (Ha = 20) and then let increase the heat transfer performance. Thus maximum heat transfer rate has been recorded for higher Hartmann number and Rayleigh number in case of pseudo-plastic (n = 0.6) non-Newtonian fluid flow.
Propagation of Gravity Currents of non-Newtonian Power-Law Fluids in Porous Media
NASA Astrophysics Data System (ADS)
Di Federico, V.; Longo, S.; Ciriello, V.; Chiapponi, L.
2014-12-01
A comprehensive analytical and experimental framework is presented to describe gravity-driven motions of rheologically complex fluids through porous media. These phenomena are relevant in geophysical, environmental, industrial and biological applications. The fluid is characterized by an Ostwald-DeWaele constitutive equation with behaviour index n. The flow is driven by the release of fluid at the origin of an infinite porous domain. In order to represent several possible spreading scenarios, we consider: i) different domain geometries: plane, radial, and channelized, with the channel shape parameterized by k; ii) instantaneous or continuous injection, depending on the time exponent of the volume of fluid in the current, α; iii) horizontal or inclined impermeable boundaries. Systematic heterogeneity along the streamwise and/or transverse direction is added to the conceptualization upon considering a power-law permeability variation governed by two additional parameters ω and β. Scalings for current length and thickness are derived in self similar form coupling the modified Darcy's law accounting for the fluid rheology with the mass balance equation. The length, thickness, and aspect ratio of the current are studied as functions of model parameters; several different critical values of α emerge and govern the type of dependency, as well as the tendency of the current to accelerate or decelerate and become thicker or thinner at a given point. The asymptotic validity of the solutions is limited to certain ranges of model parameters. Experimental validation is performed under constant volume, constant and variable flux regimes in tanks/channels filled with transparent glass beads of uniform or variable diameter, using shear-thinning suspensions and Newtonian mixtures. The experimental results for the length and profile of the current agree well with the self-similar solutions at intermediate and late times.
Digilov, Rafael M
2008-12-02
The impact of non-Newtonian behavior and the dynamic contact angle on the rise dynamics of a power law liquid in a vertical capillary is studied theoretically and experimentally for quasi-steady-state flow. An analytical solution for the time evolution of the meniscus height is obtained in terms of a Gaussian hypergeometric function, which in the case of a Newtonian liquid reduces to the Lucas-Washburn equation modified by the dynamic contact angle correction. The validity of the solution is checked against experimental data on the rise dynamics of a shear-thinning cmc solution in a glass microcapillary, and excellent agreement is found.
Lee, S.R.; Irvine, T.F. Jr.; Greene, G.A.
1998-04-01
An implicit finite difference method was applied to analyze laminar natural convection in a vertical channel with a modified power law fluid. This fluid model was chosen because it describes the viscous properties of a pseudoplastic fluid over the entire shear rate range likely to be found in natural convection flows since it covers the shear rate range from Newtonian through transition to simple power law behavior. In addition, a dimensionless similarity parameter is identified which specifies in which of the three regions a particular system is operating. The results for the average channel velocity and average Nusselt number in the asymptotic Newtonian and power law regions are compared with numerical data in the literature. Also, graphical results are presented for the velocity and temperature fields and entrance lengths. The results of average channel velocity and Nusselt number are given in the three regions including developing and fully developed flows. As an example, a pseudoplastic fluid (carboxymethyl cellulose) was chosen to compare the different results of average channel velocity and Nusselt number between a modified power law fluid and the conventional power law model. The results show, depending upon the operating conditions, that if the correct model is not used, gross errors can result.
NASA Astrophysics Data System (ADS)
Kishan, N.; Shashidar Reddy, B.
2013-06-01
The problem of a magneto-hydro dynamic flow and heat transfer to a non-Newtonian power-law fluid flow past a continuously moving flat porous plate in the presence of sucion/injection with heat flux by taking into consideration the viscous dissipation is analysed. The non-linear partial differential equations governing the flow and heat transfer are transformed into non-linear ordinary differential equations using appropriate transformations and then solved numerically by an implicit finite difference scheme. The solution is found to be dependent on various governing parameters including the magnetic field parameter M, power-law index n, suction/injection parameter ƒw, Prandtl number Pr and Eckert number Ec. A systematical study is carried out to illustrate the effects of these major parameters on the velocity profiles, temperature profile, skin friction coefficient and rate of heat transfer and the local Nusslet number.
Controlling and minimizing fingering instabilities in non-Newtonian fluids.
Fontana, João V; Dias, Eduardo O; Miranda, José A
2014-01-01
The development of the viscous fingering instability in Hele-Shaw cells has great practical and scientific importance. Recently, researchers have proposed different strategies to control the number of interfacial fingering structures, or to minimize as much as possible the amplitude of interfacial disturbances. Most existing studies address the situation in which an inviscid fluid displaces a viscous Newtonian fluid. In this work, we report on controlling and minimizing protocols considering the situation in which the displaced fluid is a non-Newtonian, power-law fluid. The necessary changes on the controlling schemes due to the shear-thinning and shear thickening nature of the displaced fluid are calculated analytically and discussed.
ERIC Educational Resources Information Center
Binous, Housam
2007-01-01
We study four non-Newtonian fluid mechanics problems using Mathematica[R]. Constitutive equations describing the behavior of power-law, Bingham and Carreau models are recalled. The velocity profile is obtained for the horizontal flow of power-law fluids in pipes and annuli. For the vertical laminar film flow of a Bingham fluid we determine the…
Electro-osmotic mobility of non-Newtonian fluids
Zhao, Cunlu; Yang, Chun
2011-01-01
Electrokinetically driven microfluidic devices are usually used to analyze and process biofluids which can be classified as non-Newtonian fluids. Conventional electrokinetic theories resulting from Newtonian hydrodynamics then fail to describe the behaviors of these fluids. In this study, a theoretical analysis of electro-osmotic mobility of non-Newtonian fluids is reported. The general Cauchy momentum equation is simplified by incorporation of the Gouy–Chapman solution to the Poisson–Boltzmann equation and the Carreau fluid constitutive model. Then a nonlinear ordinary differential equation governing the electro-osmotic velocity of Carreau fluids is obtained and solved numerically. The effects of the Weissenberg number (Wi), the surface zeta potential (ψ¯s), the power-law exponent(n), and the transitional parameter (β) on electro-osmotic mobility are examined. It is shown that the results presented in this study for the electro-osmotic mobility of Carreau fluids are quite general so that the electro-osmotic mobility for the Newtonian fluids and the power-law fluids can be obtained as two limiting cases. PMID:21503161
Electro-osmotic mobility of non-Newtonian fluids.
Zhao, Cunlu; Yang, Chun
2011-03-23
Electrokinetically driven microfluidic devices are usually used to analyze and process biofluids which can be classified as non-Newtonian fluids. Conventional electrokinetic theories resulting from Newtonian hydrodynamics then fail to describe the behaviors of these fluids. In this study, a theoretical analysis of electro-osmotic mobility of non-Newtonian fluids is reported. The general Cauchy momentum equation is simplified by incorporation of the Gouy-Chapman solution to the Poisson-Boltzmann equation and the Carreau fluid constitutive model. Then a nonlinear ordinary differential equation governing the electro-osmotic velocity of Carreau fluids is obtained and solved numerically. The effects of the Weissenberg number (Wi), the surface zeta potential (ψ¯s), the power-law exponent(n), and the transitional parameter (β) on electro-osmotic mobility are examined. It is shown that the results presented in this study for the electro-osmotic mobility of Carreau fluids are quite general so that the electro-osmotic mobility for the Newtonian fluids and the power-law fluids can be obtained as two limiting cases.
Theoretical studies of non-Newtonian and Newtonian fluid flow through porous media
Wu, Yu-Shu.
1990-02-01
A comprehensive theoretical study has been carried out on the flow behavior of both single and multiple phase non-Newtonian fluids in porous media. This work is divided into three parts: development of numerical and analytical solutions; theoretical studies of transient flow of non-Newtonian fluids in porous media; and applications of well test analysis and displacement efficiency evaluation to field problems. A fully implicit, integral finite difference model has been developed for simulation of non-Newtonian and Newtonian fluid flow through porous media. Several commonly-used rheological models of power-law and Bingham plastic non-Newtonian fluids have been incorporated in the simulator. A Buckley-Leverett type analytical solution for one-dimensional, immiscible displacement involving non-Newtonian fluids in porous media has been developed. An integral method is also presented for the study of transient flow of Bingham fluids in porous media. In addition, two well test analysis methods have been developed for analyzing pressure transient tests of power-law and Bingham fluids, respectively. Applications are included to demonstrate this new technology. The physical mechanisms involved in immiscible displacement with non-Newtonian fluids in porous media have been studied using the Buckley-Leverett type analytical solution. In another study, an idealized fracture model has been used to obtain some insights into the flow of a power-law fluid in a double-porosity medium. Transient flow of a general pseudoplastic fluid has been studied numerically. 125 refs., 91 figs., 12 tabs.
Electrokinetics of non-Newtonian fluids: a review.
Zhao, Cunlu; Yang, Chun
2013-12-01
This work presents a comprehensive review of electrokinetics pertaining to non-Newtonian fluids. The topic covers a broad range of non-Newtonian effects in electrokinetics, including electroosmosis of non-Newtonian fluids, electrophoresis of particles in non-Newtonian fluids, streaming potential effect of non-Newtonian fluids and other related non-Newtonian effects in electrokinetics. Generally, the coupling between non-Newtonian hydrodynamics and electrostatics not only complicates the electrokinetics but also causes the fluid/particle velocity to be nonlinearly dependent on the strength of external electric field and/or the zeta potential. Shear-thinning nature of liquids tends to enhance electrokinetic phenomena, while shear-thickening nature of liquids leads to the reduction of electrokinetic effects. In addition, directions for the future studies are suggested and several theoretical issues in non-Newtonian electrokinetics are highlighted.
Undulatory swimming in non-Newtonian fluids
NASA Astrophysics Data System (ADS)
Ardekani, Arezoo; Li, Gaojin
2015-11-01
Microorganisms often swim in complex fluids exhibiting both elasticity and shear-thinning viscosity. The motion of low Reynolds number swimmers in complex fluids is important for better understanding the migration of sperms and formation of bacterial biofilms. In this work, we numerically investigate the effects of non-Newtonian fluid properties, including shear-thinning and elasticity, on the undulatory locomotion. Our results show that elasticity hinders the swimming speed, but a shear-thinning viscosity in the absence of elasticity enhances the speed. The combination of the two effects hinders the swimming speed. The swimming boost in a shear-thinning fluid occurs even for an infinitely long flagellum. The swimming speed has a maximum, whose value depends on the flagellum oscillation amplitude and fluid rheological properties. The power consumption, on the other hand, follows a universal scaling law. This work is supported by NSF CBET-1445955 and Indiana CTSI TR001108.
Hachmon, Guy; Mamet, Noam; Sasson, Sapir; Barkai, Tal; Hadar, Nomi; Abu-Horowitz, Almogit; Bachelet, Ido
2016-01-01
New types of robots inspired by biological principles of assembly, locomotion, and behavior have been recently described. In this work we explored the concept of robots that are based on more fundamental physical phenomena, such as fluid dynamics, and their potential capabilities. We report a robot made entirely of non-Newtonian fluid, driven by shear strains created by spatial patterns of audio waves. We demonstrate various robotic primitives such as locomotion and transport of metallic loads-up to 6-fold heavier than the robot itself-between points on a surface, splitting and merging, shapeshifting, percolation through gratings, and counting to 3. We also utilized interactions between multiple robots carrying chemical loads to drive a bulk chemical synthesis reaction. Free of constraints such as skin or obligatory structural integrity, fluid robots represent a radically different design that could adapt more easily to unfamiliar, hostile, or chaotic environments and carry out tasks that neither living organisms nor conventional machines are capable of.
Pressure transient behavior of dilatant non-Newtonian/Newtonian fluid composite reservoirs
Okpobiri, G.A.; Ikoku, C.U.
1983-11-01
This study investigates pressure falloff testing in non-Newtonian/Newtonian fluid composite reservoirs. The non-Newtonian fluids of interest exhibit dilatant behavior. Initial water saturation is accounted for. Application of non-Newtonian well test analysis techniques and conventional Horner (Newtonian) techniques is investigated. The effects of different injection times before shut-in, external radii, flow behavior indexes and non-Newtonian fluid consistencies on the pressure transient behavior constitute the salient features of this work. It is shown that early time falloff pressure data can be analyzed by non-Newtonian techniques while the late shut-in data, under certain conditions, can be analyzed by the conventional Horner method. The time when the Newtonian fluid starts influencing the non-Newtonian falloff curves and the location of the non-Newtonian fluid front can be estimated by using the radius of investigation equation for power-law fluids and volumetric balance equation respectively. Rheological consideration is made to illustrate the pressure transient behavior.
Laminar boundary-layer flow of non-Newtonian fluid
NASA Technical Reports Server (NTRS)
Lin, F. N.; Chern, S. Y.
1979-01-01
A solution for the two-dimensional and axisymmetric laminar boundary-layer momentum equation of power-law non-Newtonian fluid is presented. The analysis makes use of the Merk-Chao series solution method originally devised for the flow of Newtonian fluid. The universal functions for the leading term in the series are tabulated for n from 0.2 to 2. Equations governing the universal functions associated with the second and the third terms are provided. The solution together with either Lighthill's formula or Chao's formula constitutes a simple yet general procedure for the calculation of wall shear and surface heat transfer rate. The theory was applied to flows over a circular cylinder and a sphere and the results compared with published data.
Theoretical Studies of Non-Newtonian and Newtonian Fluid Flowthrough Porous Media
Wu, Y.S.
1990-02-01
A comprehensive theoretical study has been carried out on the flow behavior of both single and multiple phase non-Newtonian fluids in porous media. This work is divided into three parts: (1) development of numerical and analytical solutions; (2) theoretical studies of transient flow of non-Newtonian fluids in porous media; and (3) applications of well test analysis and displacement efficiency evaluation to field problems. A fully implicit, integral finite difference model has been developed for simulation of non-Newtonian and Newtonian fluid flow through porous media. Several commonly-used rheological models of power-law and Bingham plastic non-Newtonian fluids have been incorporated in the simulator. A Buckley-Leverett type analytical solution for one-dimensional, immiscible displacement involving non-Newtonian fluids in porous media has been developed. Based on this solution, a graphic approach for evaluating non-Newtonian displacement efficiency has been developed. The Buckley-Leverett-Welge theory is extended to flow problems with non-Newtonian fluids. An integral method is also presented for the study of transient flow of Bingham fluids in porous media. In addition, two well test analysis methods have been developed for analyzing pressure transient tests of power-law and Bingham fluids, respectively. Applications are included to demonstrate this new technology. The physical mechanisms involved in immiscible displacement with non-Newtonian fluids in porous media have been studied using the Buckley-Leverett type analytical solution. The results show that this kind of displacement is a complicated process and is determined by the rheological properties of the non-Newtonian fluids and the flow conditions, in addition to relative permeability data. In another study, an idealized fracture model has been used to obtain some insights into the flow of a power-law fluid in a double-porosity medium. For flow at a constant rate, non-Newtonian flow behavior in a fractured
Intermittent outgassing through a non-Newtonian fluid.
Divoux, Thibaut; Bertin, Eric; Vidal, Valérie; Géminard, Jean-Christophe
2009-05-01
We report an experimental study of the intermittent dynamics of a gas flowing through a column of a non-Newtonian fluid. In a given range of the imposed constant flow rate, the system spontaneously alternates between two regimes: bubbles emitted at the bottom either rise independently one from the other or merge to create a winding flue which then connects the bottom air entrance to the free surface. The observations are reminiscent of the spontaneous changes in the degassing regime observed on volcanoes and suggest that, in the nature, such a phenomenon is likely to be governed by the non-Newtonian properties of the magma. We focus on the statistical distribution of the lifespans of the bubbling and flue regimes in the intermittent steady state. The bubbling regime exhibits a characteristic time whereas, interestingly, the flue lifespan displays a decaying power-law distribution. The associated exponent, which is significantly smaller than the value 1.5 often reported experimentally and predicted in some standard intermittency scenarios, depends on the fluid properties and can be interpreted as the ratio of two characteristic times of the system.
Coupling electrokinetics and rheology: Electrophoresis in non-Newtonian fluids.
Khair, Aditya S; Posluszny, Denise E; Walker, Lynn M
2012-01-01
We present a theoretical scheme to calculate the electrophoretic motion of charged colloidal particles immersed in complex (non-Newtonian) fluids possessing shear-rate-dependent viscosities. We demonstrate that this non-Newtonian rheology leads to an explicit shape and size dependence of the electrophoretic velocity of a uniformly charged particle in the thin-Debye-layer regime, in contrast to electrophoresis in Newtonian fluids. This dependence is caused by non-Newtonian stresses in the bulk (electroneutral) fluid outside the Debye layer, whose magnitude is naturally characterized in an electrophoretic Deborah number.
Turbulent Entrainment into Non-Newtonian Fluid Mud Gravity Currents
NASA Astrophysics Data System (ADS)
Jacobson, Michael; Testik, Firat
2011-11-01
This study presents insights into turbulent entrainment of ambient water into fluid mud gravity currents. It is well established that fluid mud suspensions exhibit pseudo-plastic behavior. Gravity current laboratory experiments were conducted for constant-volume release configuration with different initial concentrations of fluid mud, representing different rheological properties (i.e. different Power-law model constants). A high quality data set of concentration and velocity profiles of fluid mud gravity currents was collected to calculate the entrainment velocity, we. The entrainment ratio (E =we / U , U - characteristic velocity) was calculated following the well-accepted Morton-Taylor-Turner entrainment hypothesis, which states that the inflow across the edge of a turbulent flow is proportional to some characteristic velocity. The entrainment ratio was further measured qualitatively using a light opaqueness technique. A semi-empirical parameterization for the entrainment ratio is proposed. The findings of this study are expected to be of significance for modeling various non-Newtonian gravity currents, in particular for modeling fluid mud gravity currents generated during dredge disposal operations in coastal waters. Contact Author.
Physical-based non-Newtonian fluid animation using SPH
NASA Astrophysics Data System (ADS)
Mao, Hai
Fluids are commonly seen in our daily lives. They exhibit a wide range of motions, which depend on their physical properties, and often result in amazing visual phenomena. Hence, fluid animation is a popular topic in computer graphics. The animation results not only enrich a computer-generated virtual world but have found applications in generating special effects in motion pictures and in computer games. The three-dimensional (3D) Navier-Stokes (NS) equation is a comprehensive mechanical description of the fluid motions. Smoothed Particle Hydrodynamics (SPH) is a popular particle-based fluid modeling formulation. In physical-based fluid animation, the fluid models are based on the 3D NS equation, which can be solved using SPH based methods. Non-Newtonian fluids form a rich class of fluids. Their physical behavior exhibits a strong and complex stress-strain relationship which falls outside the modeling range of Newtonian fluid mechanics. In physical-based fluid animation, most of the fluid models are based on Newtonian fluids, and hence they cannot realistically animate non-Newtonian fluid motions such as stretching, bending, and bouncing. Based on the 3D NS equation and SPH, three original contributions are presented in this dissertation, which address the following three aspects of fluid animation: (1) particle-based non-Newtonian fluids, (2) immiscible fluid-fluid collision, and (3) heating non-Newtonian fluids. Consequently, more varieties of non-Newtonian fluid motions can be animated, which include stretching, bending, and bouncing.
Optical monitoring for power law fluids during spin coating.
Jardim, P L G; Michels, A F; Horowitz, F
2012-01-30
Optical monitoring is applied, in situ and in real time, to non-newtonian, power law fluids in the spin coating process. An analytical exact solution is presented for thickness evolution that well fits to most measurement data. As result, typical rheological parameters are obtained for several CMC (carboximetilcelullose) concentrations and rotation speeds. Optical monitoring thus precisely indicates applicability of the model to power law fluids under spin coating.
Existence Theory for Stochastic Power Law Fluids
NASA Astrophysics Data System (ADS)
Breit, Dominic
2015-06-01
We consider the equations of motion for an incompressible non-Newtonian fluid in a bounded Lipschitz domain during the time interval (0, T) together with a stochastic perturbation driven by a Brownian motion W. The balance of momentum reads as where v is the velocity, the pressure and f an external volume force. We assume the common power law model and show the existence of martingale weak solution provided . Our approach is based on the -truncation and a harmonic pressure decomposition which are adapted to the stochastic setting.
Dynamic characteristics of Non Newtonian fluid Squeeze film damper
NASA Astrophysics Data System (ADS)
Palaksha, C. P.; Shivaprakash, S.; Jagadish, H. P.
2016-09-01
The fluids which do not follow linear relationship between rate of strain and shear stress are termed as non-Newtonian fluid. The non-Newtonian fluids are usually categorized as those in which shear stress depends on the rates of shear only, fluids for which relation between shear stress and rate of shear depends on time and the visco inelastic fluids which possess both elastic and viscous properties. It is quite difficult to provide a single constitutive relation that can be used to define a non-Newtonian fluid due to a great diversity found in its physical structure. Non-Newtonian fluids can present a complex rheological behaviour involving shear-thinning, viscoelastic or thixotropic effects. The rheological characterization of complex fluids is an important issue in many areas. The paper analyses the damping and stiffness characteristics of non-Newtonian fluids (waxy crude oil) used in squeeze film dampers using the available literature for viscosity characterization. Damping and stiffness characteristic will be evaluated as a function of shear strain rate, temperature and percentage wax concentration etc.
Mondal, Sourav; De, Sirshendu
2013-01-01
Mass transport of a neutral solute for a power law fluid in a porous microtube under electro-osmotic flow regime is characterized in this study. Combined electro-osmotic and pressure driven flow is conducted herein. An analytical solution of concentration profile within mass transfer boundary layer is derived from the first principle. The solute transport through the porous wall is also coupled with the electro-osmotic flow to predict the solute concentration in the permeate stream. The effects of non-Newtonian rheology and the operating conditions on the permeation rate and permeate solute concentration are analyzed in detail. Both cases of assisting (electro-osmotic and poiseulle flow are in same direction) and opposing flow (the individual flows are in opposite direction) cases are taken care of. Enhancement of Sherwood due to electro-osmotic flow for a non-porous conduit is also quantified. Effects if non-Newtonian rheology on Sherwood number enhancement are observed. PMID:24404046
Numerical Solution of Hydrodynamics Lubrications with Non-Newtonian Fluid Flow
NASA Astrophysics Data System (ADS)
Osman, Kahar; Sheriff, Jamaluddin Md; Bahak, Mohd. Zubil; Bahari, Adli; Asral
2010-06-01
This paper focuses on solution of numerical model for fluid film lubrication problem related to hydrodynamics with non-Newtonian fluid. A programming code is developed to investigate the effect of bearing design parameter such as pressure. A physical problem is modeled by a contact point of sphere on a disc with certain assumption. A finite difference method with staggered grid is used to improve the accuracy. The results show that the fluid characteristics as defined by power law fluid have led to a difference in the fluid pressure profile. Therefore a lubricant with special viscosity can reduced the pressure near the contact area of bearing.
A comparison of numerical methods for non-Newtonian fluid flows in a sudden expansion
NASA Astrophysics Data System (ADS)
Ilio, G. Di; Chiappini, D.; Bella, G.
2016-06-01
A numerical study on incompressible laminar flow in symmetric channel with sudden expansion is conducted. In this work, Newtonian and non-Newtonian fluids are considered, where non-Newtonian fluids are described by the power-law model. Three different computational methods are employed, namely a semi-implicit Chorin projection method (SICPM), an explicit algorithm based on fourth-order Runge-Kutta method (ERKM) and a Lattice Boltzmann method (LBM). The aim of the work is to investigate on the capabilities of the LBM for the solution of complex flows through the comparison with traditional computational methods. In the range of Reynolds number investigated, excellent agreement with the literature results is found. In particular, the LBM is found to be accurate in the prediction of the fluid flow behavior for the problem under consideration.
Flow Curve Determination for Non-Newtonian Fluids.
ERIC Educational Resources Information Center
Tjahjadi, Mahari; Gupta, Santosh K.
1986-01-01
Describes an experimental program to examine flow curve determination for non-Newtonian fluids. Includes apparatus used (a modification of Walawender and Chen's set-up, but using a 50cc buret connected to a glass capillary through a Tygon tube), theoretical information, procedures, and typical results obtained. (JN)
Non-Newtonian fluid effects on surface reactions in a microfluidic flow cell
NASA Astrophysics Data System (ADS)
Akgül, M. Bahattin; Sarı, Gözde; Pakdemirli, Mehmet
2012-11-01
Mass transfer over a reactive surface in microfluidic flow cells plays a key role in understanding biomoleculer interactions and diagnosis of small molecules for biomedical and environmental applications. The effects of Non-Newtonian power law fluid on the binding reaction kinetic of immunoglobulin G in a flow cell are analyzed in this study. Governing equations for the fluid flow, mass transport and surface reaction are derived. The finite element method is employed to solve resulting equations. In addition, the effects of volumetric flow rate, fluid behavior index and reaction constants on the surface reaction are analyzed and presented graphically.
Non-newtonian fluid flow through three-dimensional disordered porous media.
Morais, Apiano F; Seybold, Hansjoerg; Herrmann, Hans J; Andrade, José S
2009-11-06
We investigate the flow of various non-newtonian fluids through three-dimensional disordered porous media by direct numerical simulation of momentum transport and continuity equations. Remarkably, our results for power-law (PL) fluids indicate that the flow, when quantified in terms of a properly modified permeability-like index and Reynolds number, can be successfully described by a single (universal) curve over a broad range of Reynolds conditions and power-law exponents. We also study the flow behavior of Bingham fluids described in terms of the Herschel-Bulkley model. In this case, our simulations reveal that the interplay of (i) the disordered geometry of the pore space, (ii) the fluid rheological properties, and (iii) the inertial effects on the flow is responsible for a substantial enhancement of the macroscopic hydraulic conductance of the system at intermediate Reynolds conditions.
Verification of vertically rotating flume using non-newtonian fluids
Huizinga, R.J.
1996-01-01
Three tests on non-Newtonian fluids were used to verify the use of a vertically rotating flume (VRF) for the study of the rheological properties of debris flow. The VRF is described and a procedure for the analysis of results of tests made with the VRF is presented. The major advantages of the VRF are a flow field consistent with that found in nature, a large particle-diameter threshold, inexpensive operation, and verification using several different materials; the major limitations are a lack of temperature control and a certain error incurred from the use of the Bingham plastic model to describe a more complex phenomenon. Because the VRF has been verified with non-Newtonian fluids as well as Newtonian fluids, it can be used to measure the rheological properties of coarse-grained debris-flow materials.
CFD simulation of non-Newtonian fluid flow in anaerobic digesters.
Wu, Binxin; Chen, Shulin
2008-02-15
A general mathematical model that predicts the flow fields in a mixed-flow anaerobic digester was developed. In this model, the liquid manure was assumed to be a non-Newtonian fluid, and the flow governed by the continuity, momentum, and k-epsilon standard turbulence equations, and non-Newtonian power law model. The commercial computational fluid dynamics (CFD) software, Fluent, was applied to simulate the flow fields of lab-scale, scale-up, and pilot-scale anaerobic digesters. The simulation results were validated against the experimental data from literature. The flow patterns were qualitatively compared for Newtonian and non-Newtonian fluids flow in a lab-scale digester. Numerical simulations were performed to predict the flow fields in scale-up and pilot-scale anaerobic digesters with different water pump power inputs and different total solid concentration (TS) in the liquid manure. The optimal power inputs were determined for the pilot-scale anaerobic digester. Some measures for reducing dead and low velocity zones were proposed based upon the CFD simulation results.
NASA Technical Reports Server (NTRS)
DiSalvo, Roberto; Deaconu, Stelu; Majumdar, Alok
2006-01-01
One of the goals of this program was to develop the experimental and analytical/computational tools required to predict the flow of non-Newtonian fluids through the various system components of a propulsion system: pipes, valves, pumps etc. To achieve this goal we selected to augment the capabilities of NASA's Generalized Fluid System Simulation Program (GFSSP) software. GFSSP is a general-purpose computer program designed to calculate steady state and transient pressure and flow distributions in a complex fluid network. While the current version of the GFSSP code is able to handle various systems components the implicit assumption in the code is that the fluids in the system are Newtonian. To extend the capability of the code to non-Newtonian fluids, such as silica gelled fuels and oxidizers, modifications to the momentum equations of the code have been performed. We have successfully implemented in GFSSP flow equations for fluids with power law behavior. The implementation of the power law fluid behavior into the GFSSP code depends on knowledge of the two fluid coefficients, n and K. The determination of these parameters for the silica gels used in this program was performed experimentally. The n and K parameters for silica water gels were determined experimentally at CFDRC's Special Projects Laboratory, with a constant shear rate capillary viscometer. Batches of 8:1 (by weight) water-silica gel were mixed using CFDRC s 10-gallon gelled propellant mixer. Prior to testing the gel was allowed to rest in the rheometer tank for at least twelve hours to ensure that the delicate structure of the gel had sufficient time to reform. During the tests silica gel was pressure fed and discharged through stainless steel pipes ranging from 1", to 36", in length and three diameters; 0.0237", 0.032", and 0.047". The data collected in these tests included pressure at tube entrance and volumetric flowrate. From these data the uncorrected shear rate, shear stress, residence time
Relaxation Dynamics of Non-Power-Law Fluids
NASA Astrophysics Data System (ADS)
Min, Qi; Duan, Yuan-Yuan; Wang, Xiao-Dong; Liang, Zhan-Peng; Lee, Duu-Jong
2013-12-01
The relaxation of non-Newtonian liquids with non-power-law rheology on partially wetted surfaces is rarely investigated. This study assesses the relaxation behavior of 14 partial wetting systems with non-power-law fluids by sessile drop method. These systems are two carboxymethylcellulose sodium solutions on two kinds of slides, cover glass, and silicon wafer surfaces; three polyethylene glycol (PEG400) + silica nanoparticle suspensions on polymethyl methacrylate and polystyrene surfaces. The dynamic contact angle and moving velocity of contact line relationship data for relaxation drops of the 14 tested systems demonstrate a power-law fluid-like behavior, and the equivalent power exponent for a certain fluid on different solid substrates are uniform. By analyzing the relationship between the equivalent power exponent and shear rate, it is proposed that a fluid regime with shear rates of a few tens of s controls relaxation dynamics.
Dynamic wetting with viscous Newtonian and non-Newtonian fluids.
Wei, Y; Rame, E; Walker, L M; Garoff, S
2009-11-18
We examine various aspects of dynamic wetting with viscous Newtonian and non-Newtonian fluids. Rather than concentrating on the mechanisms that relieve the classic contact line stress singularity, we focus on the behavior in the wedge flow near the contact line which has the dominant influence on wetting with these fluids. Our experiments show that a Newtonian polymer melt composed of highly flexible molecules exhibits dynamic wetting behavior described very well by hydrodynamic models that capture the critical properties of the Newtonian wedge flow near the contact line. We find that shear thinning has a strong impact on dynamic wetting, by reducing the drag of the solid on the fluid near the contact line, while the elasticity of a Boger fluid has a weaker impact on dynamic wetting. Finally, we find that other polymeric fluids, nominally Newtonian in rheometric measurements, exhibit deviations from Newtonian dynamic wetting behavior.
Group invariant solution for a pre-existing fracture driven by a power-law fluid in permeable rock
NASA Astrophysics Data System (ADS)
Fareo, A. G.; Mason, D. P.
2016-06-01
Group invariant analytical and numerical solutions for the evolution of a two-dimensional fracture with nonzero initial length in permeable rock and driven by an incompressible non-Newtonian fluid of power-law rheology are obtained. The effect of fluid leak-off on the evolution of the power-law fluid fracture is investigated.
Electro-osmosis of non-Newtonian fluids in porous media using lattice Poisson-Boltzmann method.
Chen, Simeng; He, Xinting; Bertola, Volfango; Wang, Moran
2014-12-15
Electro-osmosis in porous media has many important applications in various areas such as oil and gas exploitation and biomedical detection. Very often, fluids relevant to these applications are non-Newtonian because of the shear-rate dependent viscosity. The purpose of this study was to investigate the behaviors and physical mechanism of electro-osmosis of non-Newtonian fluids in porous media. Model porous microstructures (granular, fibrous, and network) were created by a random generation-growth method. The nonlinear governing equations of electro-kinetic transport for a power-law fluid were solved by the lattice Poisson-Boltzmann method (LPBM). The model results indicate that: (i) the electro-osmosis of non-Newtonian fluids exhibits distinct nonlinear behaviors compared to that of Newtonian fluids; (ii) when the bulk ion concentration or zeta potential is high enough, shear-thinning fluids exhibit higher electro-osmotic permeability, while shear-thickening fluids lead to the higher electro-osmotic permeability for very low bulk ion concentration or zeta potential; (iii) the effect of the porous medium structure depends significantly on the constitutive parameters: for fluids with large constitutive coefficients strongly dependent on the power-law index, the network structure shows the highest electro-osmotic permeability while the granular structure exhibits the lowest permeability on the entire range of power law indices considered; when the dependence of the constitutive coefficient on the power law index is weaker, different behaviors can be observed especially in case of strong shear thinning.
Steady flow of a non-Newtonian fluid through a contraction
NASA Technical Reports Server (NTRS)
Gatski, T. B.; Lumley, J. L.
1978-01-01
A steady-state analysis is conducted to examine the basic flow structure of a non-Newtonian fluid in a domain including an inflow region, a contraction region, and an outflow region. A Cartesian grid system is used throughout the entire flow domain, including the contraction region, thus creating an irregular grid cell structure adjacent to the curved boundary. At node points adjacent to the curved boundary symmetry conditions are derived for the different flow variables in order to solve the governing difference equations. Attention is given to the motion and non-Newtonian constitutive equations, the boundary conditions, the numerical modeling of the non-Newtonian equations, the stream function contour lines for the non-Newtonian fluid, the vorticity contour lines for the non-Newtonian fluid, the velocity profile across the contraction, and the shear stress contour lines for the non-Newtonian fluid.
Morphological stability of an interface between two non-Newtonian fluids moving in a Hele-Shaw cell.
Martyushev, L M; Birzina, A I
2015-01-01
The problem of the morphological stability of an interface in the case of the displacement of one non-Newtonian fluid by another non-Newtonian fluid in a radial Hele-Shaw cell has been considered. Both fluids have been described by the two-parameter Ostwald-de Waele power-law model. The nonzero viscosity of the displacing fluid has been taken into account. A generalized Darcy's law for the system under consideration, as well as an equation for the determination of the critical size of morphological stability with respect to harmonic perturbations (linear analysis), has been derived. Morphological phase diagrams have been constructed, and the region of the parameters in which nonequilibrium reentrant morphological transitions are possible has been revealed.
Electrokinetically modulated peristaltic transport of power-law fluids.
Goswami, Prakash; Chakraborty, Jeevanjyoti; Bandopadhyay, Aditya; Chakraborty, Suman
2016-01-01
The electrokinetically modulated peristaltic transport of power-law fluids through a narrow confinement in the form of a deformable tube is investigated. The fluid is considered to be divided into two regions - a non-Newtonian core region (described by the power-law behavior) which is surrounded by a thin wall-adhering layer of Newtonian fluid. This division mimics the occurrence of a wall-adjacent cell-free skimming layer in blood samples typically handled in microfluidic transport. The pumping characteristics and the trapping of the fluid bolus are studied by considering the effect of fluid viscosities, power-law index and electroosmosis. It is found that the zero-flow pressure rise is strongly dependent on the relative viscosity ratio of the near-wall depleted fluid and the core fluid as well as on the power-law index. The effect of electroosmosis on the pressure rise is strongly manifested at lower occlusion values, thereby indicating its importance in transport modulation for weakly peristaltic flow. It is also established that the phenomenon of trapping may be controlled on-the-fly by tuning the magnitude of the electric field: the trapping vanishes as the magnitude of the electric field is increased. Similarly, the phenomenon of reflux is shown to disappear due to the action of the applied electric field. These findings may be applied for the modulation of pumping in bio-physical environments by means of external electric fields.
Mathematical simulation of nonisothermal filling of plane channel with non-Newtonian fluid
NASA Astrophysics Data System (ADS)
Borzenko, E.; Ryltseva, K.; Frolov, O.; Shrager, G.
2016-10-01
In this paper, the fountain flow of a non-Newtonian fluid during the filling of a plane vertical channel with due account of dissipative heating is investigated. The rheological features of the medium are defined by Ostwald de Waele power-law with exponential temperature dependence of viscosity. The numerical solution of the problem is obtained using a finite-difference method, based on the SIMPLE algorithm, and the method of invariants for compliance with the natural boundary conditions on free surface. It was shown that the flow separates into a two-dimensional flow zone in the vicinity of the free surface and a onedimensional flow zone away from it. The parametrical investigations of kinematic and thermophysical properties of the flow and the dependence of the free surface behavior on the basic criteria and rheological parameters are implemented.
Similarity solution for unsteady gravity-driven dry patch in a non-Newtonian fluid flow
NASA Astrophysics Data System (ADS)
Abas, Siti Sabariah; Mohd Yatim, Yazariah
2013-04-01
We consider an unsteady thin-film flow of a non-Newtonian fluid around a dry patch subject to gravitational acceleration on an inclined plane. The general governing partial differential equation is transformed into the second-order ordinary differential equation using a unique travelling-wave similarity transformation. The analysis shows that the dry patch has a parabolic shape and the film thickness was found to increase monotonically away from the dry patch. Numerical solutions of the similarity equation are obtained for the velocity of the dry patch. These numerical solutions are also compared with the asymptotic solutions in the certain limits. The effects of power-law index on the behavior and patterns of the solutions are also discussed.
NASA Astrophysics Data System (ADS)
Zheng, L. C.; Zhang, X. X.; Boubaker, K.; Yücel, U.; Gargouri-Ellouze, E.; Yıldırım, A.
2011-08-01
In this paper, a new model is proposed for the heat transfer characteristics of power law non- Newtonian fluids. The effects of power law viscosity on temperature field were taken into account by assuming that the temperature field is similar to the velocity field with modified Fourier's law of heat conduction for power law fluid media. The solutions obtained by using Boubaker Polynomials Expansion Scheme (BPES) technique are compared with those of the recent related similarity method in the literature with good agreement to verify the protocol exactness.
Using ultrasonic Doppler velocimetry to investigate the mixing of non-Newtonian fluids
NASA Astrophysics Data System (ADS)
Patel, Dineshkumar; Ein-Mozaffari, Farhad; Mehrvar, Mehrab
2012-12-01
Mixing is a critical unit operation, which is widely used in chemical and allied industries. Mixing of non-Newtonian fluids is a challenging task due to the complex rheology exhibited by these fluids. Pseudoplastic fluids with yield stress are an important class of non-Newtonian fluids. In this study, we utilized ultrasonic Doppler velocimetry (UDV) to explore the flow field generated by different impellers in the agitation of xanthan gum solutions and pulp suspensions, which are yield-pseudoplastic fluids.
Bandopadhyay, Aditya; Chakraborty, Suman
2015-03-21
By considering an ion moving inside an imaginary sphere filled with a power-law fluid, we bring out the implications of the fluid rheology and the influence of the proximity of the other ions towards evaluating the conduction current in an ionic solution. We show that the variation of the conductivity as a function of the ionic concentration is both qualitatively and quantitatively similar to that predicted by the Kohlrausch law. We then utilize this consideration for estimating streaming potentials developed across narrow fluidic confinements as a consequence of the transport of ions in a convective medium constituting a power-law fluid. These estimates turn out to be in sharp contrast to the classical estimates of streaming potential for non-Newtonian fluids, in which the effect of rheology of the solvent is merely considered to affect the advection current, disregarding its contributions to the conduction current. Our results have potential implications of devising a new paradigm of consistent estimation of streaming potentials for non-Newtonian fluids, with combined considerations of the confinement effect and fluid rheology in the theoretical calculations.
NASA Astrophysics Data System (ADS)
Adam, Saad; Premnath, Kannan
2016-11-01
Fluid mechanics of non-Newtonian fluids, which arise in numerous settings, are characterized by non-linear constitutive models that pose certain unique challenges for computational methods. Here, we consider the lattice Boltzmann method (LBM), which offers some computational advantages due to its kinetic basis and its simpler stream-and-collide procedure enabling efficient simulations. However, further improvements are necessary to improve its numerical stability and accuracy for computations involving broader parameter ranges. Hence, in this study, we extend the cascaded LBM formulation by modifying its moment equilibria and relaxation parameters to handle a variety of non-Newtonian constitutive equations, including power-law and Bingham fluids, with improved stability. In addition, we include corrections to the moment equilibria to obtain an inertial frame invariant scheme without cubic-velocity defects. After preforming its validation study for various benchmark flows, we study the physics of non-Newtonian flow over pairs of circular and square cylinders in a tandem arrangement, especially the wake structure interactions and their effects on resulting forces in each cylinder, and elucidate the effect of the various characteristic parameters.
Phenomenological Blasius-type friction equation for turbulent power-law fluid flows
NASA Astrophysics Data System (ADS)
Anbarlooei, H. R.; Cruz, D. O. A.; Ramos, F.; Silva Freire, A. P.
2015-12-01
We propose a friction formula for turbulent power-law fluid flows, a class of purely viscous non-Newtonian fluids commonly found in applications. Our model is derived through an extension of the friction factor analysis based on Kolmogorov's phenomenology, recently proposed by Gioia and Chakraborty. Tests against classical empirical data show excellent agreement over a significant range of Reynolds number. Limits of the model are also discussed.
Khali, S; Nebbali, R; Ameziani, D E; Bouhadef, K
2013-05-01
In this work the instability of the Taylor-Couette flow for Newtonian and non-Newtonian fluids (dilatant and pseudoplastic fluids) is investigated for cases of finite aspect ratios. The study is conducted numerically using the lattice Boltzmann method (LBM). In many industrial applications, the apparatuses and installations drift away from the idealized case of an annulus of infinite length, and thus the end caps effect can no longer be ignored. The inner cylinder is rotating while the outer one and the end walls are maintained at rest. The lattice two-dimensional nine-velocity (D2Q9) Boltzmann model developed from the Bhatnagar-Gross-Krook approximation is used to obtain the flow field for fluids obeying the power-law model. The combined effects of the Reynolds number, the radius ratio, and the power-law index n on the flow characteristics are analyzed for an annular space of finite aspect ratio. Two flow modes are obtained: a primary Couette flow (CF) mode and a secondary Taylor vortex flow (TVF) mode. The flow structures so obtained are different from one mode to another. The critical Reynolds number Re(c) for the passage from the primary to the secondary mode exhibits the lowest value for the pseudoplastic fluids and the highest value for the dilatant fluids. The findings are useful for studies of the swirling flow of non-Newtonians fluids in axisymmetric geometries using LBM. The flow changes from the CF to TVF and its structure switches from the two-cells to four-cells regime for both Newtonian and dilatant fluids. Contrariwise for pseudoplastic fluids, the flow exhibits 2-4-2 structure passing from two-cells to four cells and switches again to the two-cells configuration. Furthermore, the critical Reynolds number presents a monotonic increase with the power-law index n of the non-Newtonian fluid, and as the radius ratio grows, the transition flow regimes tend to appear for higher critical Reynolds numbers.
Effect of non-Newtonian viscosity on the fluid-dynamic characteristics in stenotic vessels
NASA Astrophysics Data System (ADS)
Huh, Hyung Kyu; Ha, Hojin; Lee, Sang Joon
2015-08-01
Although blood is known to have shear-thinning and viscoelastic properties, the effects of such properties on the hemodynamic characteristics in various vascular environments are not fully understood yet. For a quantitative hemodynamic analysis, the refractive index of a transparent blood analogue needs to be matched with that of the flowing conduit in order to minimize the errors according to the distortion of the light. In this study, three refractive index-matched blood analogue fluids with different viscosities are prepared—one Newtonian and two non-Newtonian analogues—which correspond to healthy blood with 45 % hematocrit (i.e., normal non-Newtonian) and obese blood with higher viscosity (i.e., abnormal non-Newtonian). The effects of the non-Newtonian rheological properties of the blood analogues on the hemodynamic characteristics in the post-stenosis region of an axisymmetric stenosis model are experimentally investigated using particle image velocimetry velocity field measurement technique and pathline flow visualization. As a result, the centerline jet flow from the stenosis apex is suppressed by the shear-thinning feature of the blood analogues when the Reynolds number is smaller than 500. The lengths of the recirculation zone for abnormal and normal non-Newtonian blood analogues are 3.67 and 1.72 times shorter than that for the Newtonian analogue at Reynolds numbers smaller than 200. The Reynolds number of the transition from laminar to turbulent flow for all blood analogues increases as the shear-thinning feature increases, and the maximum wall shear stresses in non-Newtonian fluids are five times greater than those in Newtonian fluids. However, the shear-thinning effect on the hemodynamic characteristics is not significant at Reynolds numbers higher than 1000. The findings of this study on refractive index-matched non-Newtonian blood analogues can be utilized in other in vitro experiments, where non-Newtonian features dominantly affect the flow
Characterising the rheology of non-Newtonian fluids using PFG-NMR and cumulant analysis.
Blythe, T W; Sederman, A J; Mitchell, J; Stitt, E H; York, A P E; Gladden, L F
2015-06-01
Conventional rheological characterisation using nuclear magnetic resonance (NMR) typically utilises spatially-resolved measurements of velocity. We propose a new approach to rheometry using pulsed field gradient (PFG) NMR which readily extends the application of MR rheometry to single-axis gradient hardware. The quantitative use of flow propagators in this application is challenging because of the introduction of artefacts during Fourier transform, which arise when realistic sampling strategies are limited by experimental and hardware constraints and when particular spatial and temporal resolution are required. The method outlined in this paper involves the cumulant analysis of the acquisition data directly, thereby preventing the introduction of artefacts and reducing data acquisition times. A model-dependent approach is developed to enable the pipe-flow characterisation of fluids demonstrating non-Newtonian power-law rheology, involving the use of an analytical expression describing the flow propagator in terms of the flow behaviour index. The sensitivity of this approach was investigated and found to be robust to the signal-to-noise ratio (SNR) and number of acquired data points, enabling an increase in temporal resolution defined by the SNR. Validation of the simulated results was provided by an experimental case study on shear-thinning aqueous xanthan gum solutions, whose rheology could be accurately characterised using a power-law model across the experimental shear rate range of 1-100 s(-1). The flow behaviour indices calculated using this approach were observed to be within 8% of those obtained using spatially-resolved velocity imaging and within 5% of conventional rheometry. Furthermore, it was shown that the number of points sampled could be reduced by a factor of 32, when compared to the acquisition of a volume-averaged flow propagator with 128 gradient increments, without negatively influencing the accuracy of the characterisation, reducing the
The Rayleigh-Taylor instability of Newtonian and non-Newtonian fluids
NASA Astrophysics Data System (ADS)
Doludenko, A. N.; Fortova, S. V.; Son, E. E.
2016-10-01
Along with Newtonian fluids (for example, water), fluids with non-Newtonian rheology are widespread in nature and industry. The characteristic feature of a non-Newtonian fluid is the non-linear dependence between the shear stress and shear rate tensors. The form of this relation defines the types of non-Newtonian behavior: viscoplastic, pseudoplastic, dilatant and viscoelastic. The present work is devoted to the study of the Rayleigh-Taylor instability in pseudoplastic fluids. The main aim of the work is to undertake a direct three-dimensional numerical simulation of the mixing of two media with various rheologies and obtain the width of the mixing layer and the kinetic energy spectra, depending on the basic properties of the shear thinning liquids and the Atwood number. A theoretical study is carried out on the basis of the Navier-Stokes equation system for weakly compressible media.
Non-Newtonian fluid flow over a heterogeneously slippery surface
NASA Astrophysics Data System (ADS)
Haase, A. Sander; Wood, Jeffery A.; Sprakel, Lisette M. J.; Lammertink, Rob G. H.
2015-11-01
The no-slip boundary condition does not always hold. In the past, we have investigated the influence of effective wall slip on interfacial transport for a bubble mattress - a superhydrophobic surface consisting of an array of transverse gas-filled grooves. We proved experimentally that the amount of effective wall slip depends on the bubble protrusion angle and the surface porosity (Karatay et al., PNAS 110, 2013), and predicted that mass transport can be enhanced significantly (Haase et al., Soft Matter 9, 2013). Both studies involve the flow of water. In practise, however, many liquids encountered are non-Newtonian, like blood and polymer solutions. This raises some interesting questions. How does interfacial transport depend on the rheological properties of the liquid? Does the time-scale of the experiment matter? A bubble mattress is a suitable platform to investigate this, due to local variations in shear rate. We predict that for shear-thinning liquids, compared to water, the amount of wall slip can be enhanced considerably, although this depends on the applied flow rate. Experiments are performed to proof this behaviour. Simulations are used to assess what will happen when the characteristic time-scale of the system matches the relaxation time of the visco-elastic liquid. R.G.H.L. acknowledges the European Research Council for the ERC starting grant 307342-TRAM.
Effect of non-Newtonian fluid properties on bovine sperm motility.
Hyakutake, Toru; Suzuki, Hiroki; Yamamoto, Satoru
2015-09-18
The swimming process by which mammal spermatozoa progress towards an egg within the reproductive organs is important in achieving successful internal fertilization. The viscosity of oviductal mucus is more than two orders of magnitude greater than that of water, and oviductal mucus also has non-Newtonian properties. In this study, we experimentally observed sperm motion in fluids with various fluid rheological properties and investigated the influence of varying the viscosity and whether the fluid was Newtonian or non-Newtonian on the sperm motility. We selected polyvinylpyrrolidone and methylcellulose as solutes to create solutions with different rheological properties. We used the semen of Japanese cattle and investigated the following parameters: the sperm velocity, the straight-line velocity and the amplitude from the trajectory, and the beat frequency from the fragellar movement. In a Newtonian fluid environment, as the viscosity increased, the motility of the sperm decreased. However, in a non-Newtonian fluid, the straight-line velocity and beat frequency were significantly higher than in a Newtonian fluid with comparable viscosity. As a result, the linearity of the sperm movement increased. Additionally, increasing the viscosity brought about large changes in the sperm flagellar shape. At low viscosities, the entire flagellum moved in a curved flapping motion, whereas in the high-viscosity, only the tip of the flagellum flapped. These results suggest that the bovine sperm has evolved to swim toward the egg as quickly as possible in the actual oviduct fluid, which is a high-viscosity non-Newtonian fluid.
Revisiting Newtonian and Non-Newtonian Fluid Mechanics Using Computer Algebra
ERIC Educational Resources Information Center
Knight, D. G.
2006-01-01
This article illustrates how a computer algebra system, such as Maple[R], can assist in the study of theoretical fluid mechanics, for both Newtonian and non-Newtonian fluids. The continuity equation, the stress equations of motion, the Navier-Stokes equations, and various constitutive equations are treated, using a full, but straightforward,…
Learning about Non-Newtonian Fluids in a Student-Driven Classroom
ERIC Educational Resources Information Center
Dounas-Frazer, D. R.; Lynn, J.; Zaniewski, A. M.; Roth, N.
2013-01-01
We describe a simple, low-cost experiment and corresponding pedagogical strategies for studying fluids whose viscosities depend on shear rate, referred to as "non-Newtonian fluids." We developed these materials teaching for the Compass Project, an organization that fosters a creative, diverse, and collaborative community of science…
Yih, K.A.
1998-10-01
Convective heat transfer in a porous medium has a number of thermal engineering applications such as ceramic processing, nuclear reactor cooling system, crude oil drilling, chemical reactor design, ground water pollution and filtration processes. In this paper, the authors have investigated a boundary layer analysis for uniform lateral mass flux effect on natural convection of non-Newtonian power-law fluids along an isothermal or isoflux vertical cone embedded in a porous medium. Numerical results for the dimensionless temperature profiles as well as the local Nusselt number are presented for the mass flux parameter, viscosity index n and geometry shape parameter {lambda}. The local surface heat transfer increases for the case withdrawal of fluid, the increase of the value of {lambda}. The local Nusselt number is found to be significantly affected by the surface mass flux than the viscosity index.
Stretch flow of confined non-Newtonian fluids: nonlinear fingering dynamics.
Brandão, Rodolfo; Fontana, João V; Miranda, José A
2013-12-01
We employ a weakly nonlinear perturbative scheme to investigate the stretch flow of a non-Newtonian fluid confined in Hele-Shaw cell for which the upper plate is lifted. A generalized Darcy's law is utilized to model interfacial fingering formation in both the weak shear-thinning and weak shear-thickening limits. Within this context, we analyze how the interfacial finger shapes and the nonlinear competition dynamics among fingers are affected by the non-Newtonian nature of the stretched fluid.
Helton, Kristen L; Yager, Paul
2007-11-01
As part of a project to develop an integrated microfluidic biosensor for the detection of small molecules in saliva, practical issues of extraction of analytes from non-Newtonian samples using an H-filter were explored. The H-filter can be used to rapidly and efficiently extract small molecules from a complex sample into a simpler buffer. The location of the interface between the sample and buffer streams is a critical parameter in the function of the H-filter, so fluorescence microscopy was employed to monitor the interface position; this revealed apparently anomalous fluorophore diffusion from the samples into the buffer solutions. Using confocal microscopy to understand the three-dimensional distribution of the fluorophore, it was found that the interface between the non-Newtonian sample and Newtonian buffer was both curved and unstable. The core of the non-Newtonian sample extended into the Newtonian buffer and its position was unstable, producing a fluorescence intensity profile that gave rise to the apparently anomalously fast fluorophore transport. These instabilities resulted from the pairing of rheologically dissimilar fluid streams and were flowrate dependent. We conclude that use of non-Newtonian fluids, such as saliva, in the H-filter necessitates pretreatment to reduce viscoelasticity. The interfacial variation in position, stability and shape caused by the non-Newtonian samples has substantial implications for the use of biological samples for quantitative analysis and analyte extraction in concurrent flow extraction devices.
NASA Astrophysics Data System (ADS)
De Rosis, Alessandro
2014-11-01
In this paper, the fluid dynamics induced by a rigid lamina undergoing harmonic oscillations in a non-Newtonian calm fluid is investigated. The fluid is modelled through the lattice Boltzmann method and the flow is assumed to be nearly incompressible. An iterative viscosity-correction based procedure is proposed to properly account for the non-Newtonian fluid feature and its accuracy is evaluated. In order to handle the mutual interaction between the lamina and the encompassing fluid, the Immersed Boundary method is adopted. A numerical campaign is performed. In particular, the effect of the non-Newtonian feature is highlighted by investigating the fluid forces acting on a harmonically oscillating lamina for different values of the Reynolds number. The findings prove that the non-Newtonian feature can drastically influence the behaviour of the fluid and, as a consequence, the forces acting upon the lamina. Several considerations are carried out on the time history of the drag coefficient and the results are used to compute the added mass through the hydrodynamic function. Moreover, the computational cost involved in the numerical simulations is discussed. Finally, two applications concerning water resources are investigated: the flow through an obstructed channel and the particle sedimentation. Present findings highlight a strong coupling between the body shape, the Reynolds number, and the flow behaviour index.
Passive mechanical behavior of human neutrophils: power-law fluid.
Tsai, M A; Frank, R S; Waugh, R E
1993-01-01
The mechanical behavior of the neutrophil plays an important role in both the microcirculation and the immune system. Several laboratories in the past have developed mechanical models to describe different aspects of neutrophil deformability. In this study, the passive mechanical properties of normal human neutrophils have been further characterized. The cellular mechanical properties were assessed by single cell micropipette aspiration at fixed aspiration pressures. A numerical simulation was developed to interpret the experiments in terms of cell mechanical properties based on the Newtonian liquid drop model (Yeung and Evans, Biophys. J., 56: 139-149, 1989). The cytoplasmic viscosity was determined as a function of the ratio of the initial cell size to the pipette radius, the cortical tension, aspiration pressure, and the whole cell aspiration time. The cortical tension of passive neutrophils was measured to be about 2.7 x 10(-5) N/m. The apparent viscosity of neutrophil cytoplasm was found to depend on aspiration pressure, and ranged from approximately 500 Pa.s at an aspiration pressure of 98 Pa (1.0 cm H2O) to approximately 50 Pa.s at 882 Pa (9.0 cm H2O) when tested with a 4.0-micron pipette. These data provide the first documentation that the neutrophil cytoplasm exhibits non-Newtonian behavior. To further characterize the non-Newtonian behavior of human neutrophils, a mean shear rate gamma m was estimated based on the numerical simulation. The apparent cytoplasmic viscosity appears to decrease as the mean shear rate increases. The dependence of cytoplasmic viscosity on the mean shear rate can be approximated as a power-law relationship described by mu = mu c(gamma m/gamma c)-b, where mu is the cytoplasmic viscosity, gamma m is the mean shear rate, mu c is the characteristic viscosity at characteristic shear rate gamma c, and b is a material coefficient. When gamma c was set to 1 s-1, the material coefficients for passive neutrophils were determined to be mu c
Smart Fluids in Hydrology: Use of Non-Newtonian Fluids for Pore Structure Characterization
NASA Astrophysics Data System (ADS)
Abou Najm, Majdi; Atallah, Nabil; Selker, John; Roques, Clément; Stewart, Ryan; Rupp, David; Saad, George; El-Fadel, Mutasem
2016-04-01
Classic porous media characterization relies on typical infiltration experiments with Newtonian fluids (i.e., water) to estimate hydraulic conductivity. However, such experiments are generally not able to discern important characteristics such as pore size distribution or pore structure. We show that introducing non-Newtonian fluids provides additional unique flow signatures that can be used for improved pore structure characterization. We present a new method that transforms results of N infiltration experiments using water and N-1 non-Newtonian solutions into a system of equations that yields N representative radii (Ri) and their corresponding percent contribution to flow (wi). Those radii and weights are optimized in terms of flow and porosity to represent the functional hydraulic behavior of real porous media. The method also allows for estimating the soil retention curve using only saturated experiments. Experimental and numerical validation revealed the ability of the proposed method to represent the water retention and functional infiltration behavior of real soils. The experimental results showed the ability of such fluids to outsmart Newtonian fluids and infer pore size distribution and unsaturated behavior using simple saturated experiments. Specifically, we demonstrate using synthetic porous media composed of different combinations of sizes and numbers of capillary tubes that the use of different non-Newtonian fluids enables the prediction of the pore structure. The results advance the knowledge towards conceptualizing the complexity of porous media and can potentially impact applications in fields like irrigation efficiencies, vadose zone hydrology, soil-root-plant continuum, carbon sequestration into geologic formations, soil remediation, petroleum reservoir engineering, oil exploration and groundwater modeling.
Viscous-elastic dynamics of power-law fluids within an elastic cylinder
NASA Astrophysics Data System (ADS)
Gat, Amir; Boyko, Evgeniy; Bercovici, Moran
2016-11-01
We study the fluid-structure interaction dynamics of non-Newtonian flow through a slender linearly elastic cylinder at the creeping flow regime. Specifically, considering power-law fluids and applying the thin shell approximation for the elastic cylinder, we obtain a non-homogeneous p-Laplacian equation governing the viscous-elastic dynamics. We obtain exact solutions for the pressure and deformation fields for various initial and boundary conditions, for both shear thinning and shear thickening fluids. In particular, impulse or a step in inlet pressure yield self-similar solutions, which exhibit a compactly supported propagation front solely for shear thinning fluids. Applying asymptotic expansions, we provide approximations for weakly non-Newtonian behavior showing good agreement with the exact solutions sufficiently far from the front.
Fingering instability in non-Newtonian fluids during squeeze flow in a Hele-Shaw cell
NASA Astrophysics Data System (ADS)
Dutta Choudhury, M.; Tarafdar, S.
2015-05-01
Instability at the interface separating different fluids, may develop under different conditions, leading to increased roughness of the boundary. A difference in viscosity of the fluids is usually responsible for viscous fingering, this occurs when the pressure on the low viscosity side is higher. We report here a reverse effect when a non-Newtonian fluid is squeezed between two plane surfaces by applying a force. We observe that a wave-like irregularity develops on the interface, though the viscosity of the air surrounding the fluid is negligible compared to the apparent viscosity of the thick potato starch gel under study. Development of the wavelength of the undulations as a function of the fluid composition and other factors is studied. We suggest a qualitative explanation for this effect, which is observed only in non-Newtonian fluids.
Gupta, Renu; Bansal, Ajay
2013-08-01
Axial dispersion is an important parameter in the performance of packed bed reactors. A lot of fluids exhibit non-Newtonian behaviour but the effect of rheological parameters on axial dispersion is not available in literature. The effect of rheology on axial dispersion has been analysed for viscoinelastic and viscoelastic non-Newtonian fluids. Aqueous solutions of carboxymethyl cellulose and polyacrylamide have been chosen to represent viscoinelastic and viscoelastic liquid-phases. Axial dispersion has been measured in terms of BoL number. The single parameter axial dispersion model has been applied to analyse RTD response curve. The BoL numbers were observed to increase with increase in liquid flow rate and consistency index 'K' for viscoinelastic as well as viscoelastic fluids. Bodenstein correlation for Newtonian fluids proposed has been modified to account for the effect of fluid rheology. Further, Weissenberg number is introduced to quantify the effect of viscoelasticity.
Spreading of Non-Newtonian and Newtonian Fluids on a Solid Substrate under Pressure
NASA Astrophysics Data System (ADS)
Dutta Choudhury, Moutushi; Chandra, Subrata; Nag, Soma; Das, Shantanu; Tarafdar, Sujata
2011-09-01
Strongly non-Newtonian fluids namely, aqueous gels of starch, are shown to exhibit visco-elastic behavior, when subjected to a load. We study arrowroot and potato starch gels. When a droplet of the fluid is sandwiched between two glass plates and compressed, the area of contact between the fluid and plates increases in an oscillatory manner. This is unlike Newtonian fluids, where the area increases monotonically in a similar situation. The periphery moreover, develops an instability, which looks similar to Saffman Taylor fingers. This is not normally seen under compression. The loading history is also found to affect the manner of spreading. We attempt to describe the non-Newtonian nature of the fluid through a visco-elastic model incorporating generalized calculus. This is shown to reproduce qualitatively the oscillatory variation in the surface strain.
Etemad, S.G.
1997-11-01
Many important industrial fluids are non-Newtonian in their flow characteristics. These include food materials, soap and detergent slurries, polymer solutions and many others. In the most of the industries such as polymer, foods, petrochemical the heat exchanger is an especially important component of the processing equipment. In the design of heat exchanger, the prediction of the heat transfer coefficient plays a key role as a design factor. Here the Galerkin finite element is used to solve the three dimensional momentum and energy equations for laminar non-Newtonian flow in cross-shaped straight duct. Both flow and heat transfer develop simultaneously from the entrance of the channel. Uniform wall temperature (T) and also constant wall heat flux both axially and peripherally (H2) are used as thermal boundary conditions. The power-law model is chosen to characterize the non-Newtonian behavior of the fluid. The effect of power-law index and geometric parameter on the apparent friction factor as well as Nusselt number are presented and discussed.
Hybrid solution for the laminar flow of power-law fluids inside rectangular ducts
NASA Astrophysics Data System (ADS)
Lima, J. A.; Pereira, L. M.; Macêdo, E. N.; Chaves, C. L.; Quaresma, J. N. N.
The so-called generalized integral transform technique (GITT) is employed in the hybrid numerical-analytical solution of two-dimensional fully-developed laminar flow of non-Newtonian power-law fluids inside rectangular ducts. The characteristic of the automatic and straightforward global error control procedure inherent to this approach, permits the determination of fully converged benchmark results to assess the performance of purely numerical techniques. Therefore, numerical results for the product Fanning friction factor-generalized Reynolds number are computed for different values of power-law index and aspect ratio, which are compared with previously reported results in the literature, providing critical comparisons among them as well as illustrating the powerfulness of the integral transform approach. The resulting velocity profiles computed by using this methodology are also compared with those calculated by approximated methods for power-law fluids, within the range of governing parameters studied.
Vortex rings in non-Newtonian viscoelastic fluids play yo-yo
NASA Astrophysics Data System (ADS)
Albagnac, Julie; Laupsien, David; Anne-Archard, Dominique
2014-11-01
Vortex rings are coherent vortical structures widely presents in geophysical flows and engineering applications. Numerous applications imply industrial processes including food processing, or petrol industry. Those applications are very often confronted with non-Newtonian fluids. Nevertheless, to the best of our knowledge, only few studies dealing with vortex dynamics in non-Newtonian shear-thinning fluids exist, and none with viscoelastic ones. The aim for the present study is to characterize experimentally the dynamics of vortex rings generated thanks to a piston-cylinder apparatus in various viscoelastic fluids as a function of the generalized Reynolds number, the piston stroke and the final piston position relative to the cylinder exit. In particular, the elastic property of the fluid will be highlighted by the furling-unfurling of vortex rings.
Classical XY model with conserved angular momentum is an archetypal non-Newtonian fluid.
Evans, R M L; Hall, Craig A; Simha, R Aditi; Welsh, Tom S
2015-04-03
We find that the classical one-dimensional XY model, with angular-momentum-conserving Langevin dynamics, mimics the non-Newtonian flow regimes characteristic of soft matter when subjected to counterrotating boundaries. An elaborate steady-state phase diagram has continuous and first-order transitions between states of uniform flow, shear-banding, solid-fluid coexistence and slip planes. Results of numerical studies and a concise mean-field constitutive relation offer a paradigm for diverse nonequilibrium complex fluids.
NASA Astrophysics Data System (ADS)
Golykh, R. N.
2016-06-01
Progress of technology and medicine dictates the ever-increasing requirements (heat resistance, corrosion resistance, strength properties, impregnating ability, etc.) for non-Newtonian fluids and materials produced on their basis (epoxy resin, coating materials, liquid crystals, etc.). Materials with improved properties obtaining is possible by modification of their physicochemical structure. One of the most promising approaches to the restructuring of non-Newtonian fluids is cavitation generated by high-frequency acoustic vibrations. The efficiency of cavitation in non-Newtonian fluid is determined by dynamics of gaseous bubble. Today, bubble dynamics in isotropic non-Newtonian fluids, in which cavitation bubble shape remains spherical, is most full investigated, because the problem reduces to ordinary differential equation for spherical bubble radius. However, gaseous bubble in anisotropic fluids which are most wide kind of non-Newtonian fluids (due to orientation of macromolecules) deviates from spherical shape due to viscosity dependence on shear rate direction. Therefore, the paper presents the mathematical model of gaseous bubble dynamics in anisotropic non-Newtonian fluids. The model is based on general equations for anisotropic non-Newtonian fluid flow. The equations are solved by asymptotic decomposition of fluid flow parameters. It allowed evaluating bubble size and shape evolution depending on rheological properties of liquid and acoustic field characteristics.
Transfer of Microparticles across Laminar Streams from Non-Newtonian to Newtonian Fluid.
Ha, Byunghang; Park, Jinsoo; Destgeer, Ghulam; Jung, Jin Ho; Sung, Hyung Jin
2016-04-19
Engineering inertial lift forces and elastic lift forces is explored to transfer microparticles across laminar streams from non-Newtonian to Newtonian fluid. A co-stream of non-Newtonian flow loaded with microparticles (9.9 and 2.0 μm in diameter) and a Newtonian carrier medium flow in a straight rectangular conduit is devised. The elastic lift forces present in the non-Newtonian fluid, undeterred by particle-particle interaction, successfully pass most of the larger (9.9 μm) particles over to the Newtonian fluid. The Newtonian fluid takes over the larger particles and focus them on the equilibrium position, separating the larger particles from the smaller particles. This mechanism enabled processing of densely suspended particle samples. The method offers dilution-free (for number densities up to 10,000 μL(-1)), high throughput (6700 beads/s), and highly efficient (>99% recovery rate, >97% purity) particle separation operated over a wide range of flow rate (2 orders of magnitude).
FDA's nozzle numerical simulation challenge: non-Newtonian fluid effects and blood damage.
Trias, Miquel; Arbona, Antonio; Massó, Joan; Miñano, Borja; Bona, Carles
2014-01-01
Data from FDA's nozzle challenge-a study to assess the suitability of simulating fluid flow in an idealized medical device-is used to validate the simulations obtained from a numerical, finite-differences code. Various physiological indicators are computed and compared with experimental data from three different laboratories, getting a very good agreement. Special care is taken with the derivation of blood damage (hemolysis). The paper is focused on the laminar regime, in order to investigate non-Newtonian effects (non-constant fluid viscosity). The code can deal with these effects with just a small extra computational cost, improving Newtonian estimations up to a ten percent. The relevance of non-Newtonian effects for hemolysis parameters is discussed.
Perrin, Christian L; Tardy, Philippe M J; Sorbie, Ken S; Crawshaw, John C
2006-03-15
The in situ rheology of polymeric solutions has been studied experimentally in etched silicon micromodels which are idealizations of porous media. The rectangular channels in these etched networks have dimensions typical of pore sizes in sandstone rocks. Pressure drop/flow rate relations have been measured for water and non-Newtonian hydrolyzed-polyacrylamide (HPAM) solutions in both individual straight rectangular capillaries and in networks of such capillaries. Results from these experiments have been analyzed using pore-scale network modeling incorporating the non-Newtonian fluid mechanics of a Carreau fluid. Quantitative agreement is seen between the experiments and the network calculations in the Newtonian and shear-thinning flow regions demonstrating that the 'shift factor,'alpha, can be calculated a priori. Shear-thickening behavior was observed at higher flow rates in the micromodel experiments as a result of elastic effects becoming important and this remains to be incorporated in the network model.
Studies on heat transfer to Newtonian and non-Newtonian fluids in agitated vessel
NASA Astrophysics Data System (ADS)
Triveni, B.; Vishwanadham, B.; Venkateshwar, S.
2008-09-01
Heat transfer studies to Newtonian and non-Newtonian fluids are carried out in a stirred vessel fitted with anchor/turbine impeller and a coil for heating/cooling with an objective of determining experimentally the heat transfer coefficient of few industrially important systems namely castor oil and its methyl esters, soap solution, CMC and chalk slurries. The effect of impeller geometry, speed and aeration is investigated. Generalized Reynolds and Prandtl numbers are calculated using an apparent viscosity for non-Newtonian fluids. The data is correlated using a Sieder-Tate type equation. A trend of increase in heat transfer coefficient with RPM in presence and absence of solids has been observed. Relatively high values of Nusselt numbers are obtained for non-Newtonian fluids when aeration is coupled with agitation. The contribution of natural convection to heat transfer has been accounted for by incorporating the Grashof number. The correlations developed based on these studies are applied for design of commercial scale soponification reactor. Power per unit volume resulted in reliable design of a reactor.
Lu, Gui; Wang, Xiao-Dong; Duan, Yuan-Yuan
2016-10-01
Dynamic wetting is an important interfacial phenomenon in many industrial applications. There have been many excellent reviews of dynamic wetting, especially on super-hydrophobic surfaces with physical or chemical coatings, porous layers, hybrid micro/nano structures and biomimetic structures. This review summarizes recent research on dynamic wetting from the viewpoint of the fluids rather than the solid surfaces. The reviewed fluids range from simple Newtonian fluids to non-Newtonian fluids and complex nanofluids. The fundamental physical concepts and principles involved in dynamic wetting phenomena are also reviewed. This review focus on recent investigations of dynamic wetting by non-Newtonian fluids, including the latest experimental studies with a thorough review of the best dynamic wetting models for non-Newtonian fluids, to illustrate their successes and limitations. This paper also reports on new results on the still fledgling field of nanofluid wetting kinetics. The challenges of research on nanofluid dynamic wetting is not only due to the lack of nanoscale experimental techniques to probe the complex nanoparticle random motion, but also the lack of multiscale experimental techniques or theories to describe the effects of nanoparticle motion at the nanometer scale (10(-9) m) on the dynamic wetting taking place at the macroscopic scale (10(-3) m). This paper describes the various types of nanofluid dynamic wetting behaviors. Two nanoparticle dissipation modes, the bulk dissipation mode and the local dissipation mode, are proposed to resolve the uncertainties related to the various types of dynamic wetting mechanisms reported in the literature.
Viscoelastic fluid-structure interaction between a non-Newtonian fluid flow and flexible cylinder
NASA Astrophysics Data System (ADS)
Dey, Anita; Modarres-Sadeghi, Yahya; Rothstein, Jonathan
2016-11-01
It is well known that when a flexible or flexibly-mounted structure is placed perpendicular to the flow of a Newtonian fluid, it can oscillate due to the shedding of separated vortices at high Reynolds numbers. If the same flexible object is placed in non-Newtonian flows, however, the structure's response is still unknown. Unlike Newtonian fluids, the flow of viscoelastic fluids can become unstable at infinitesimal Reynolds numbers due to a purely elastic flow instability. In this talk, we will present a series of experiments investigating the response of a flexible cylinder placed in the cross flow of a viscoelastic fluid. The elastic flow instabilities occurring at high Weissenberg numbers can exert fluctuating forces on the flexible cylinder thus leading to nonlinear periodic oscillations of the flexible structure. These oscillations are found to be coupled to the time-dependent state of viscoelastic stresses in the wake of the flexible cylinder. The static and dynamic responses of the flexible cylinder will be presented over a range of flow velocities, along with measurements of velocity profiles and flow-induced birefringence, in order to quantify the time variation of the flow field and the state of stress in the fluid.
Squeeze film lubrication for non-Newtonian fluids with application to manual medicine.
Chaudhry, Hans; Bukiet, Bruce; Roman, Max; Stecco, Antonio; Findley, Thomas
2013-01-01
In this paper, we computed fluid pressure and force on fascia sheets during manual therapy treatments using Squeeze Film Lubrication theory for non-Newtonian fluids. For this purpose, we developed a model valid for three dimensional fluid flow of a non-Newtonian liquid. Previous models considered only one-dimensional flows in two dimensions. We applied this model to compare the one-dimensional flow of HA, considered as a lubricating fluid, around or within the fascia during sliding, vibration, and back-and-forth sliding manipulation treatment techniques. The fluid pressure of HA increases dramatically as fascia is deformed during manual therapies. The fluid force increases more during vertical vibratory manipulation treatment than in constant sliding, and back and forth motion. The variation of fluid pressure/force causes HA to flow near the edges of the fascial area under manipulation in sliding and back and forth motion which may result in greater lubrication. The fluid pressure generated in manual therapy techniques may improve sliding and permit muscles to work more efficiently.
NASA Astrophysics Data System (ADS)
Di Federico, V.; Longo, S.; Ciriello, V.; Chiapponi, L.
2015-12-01
A theoretical and experimental analysis of non-Newtonian gravity-driven flow in porous media with spatially variable properties is presented. The motivation for our study is the rheological complexity exhibited by several environmental contaminants (wastewater sludge, oil pollutants, waste produced by the minerals and coal industries) and remediation agents (suspensions employed to enhance the efficiency of in-situ remediation). Natural porous media are inherently heterogeneous, and this heterogeneity influences the extent and shape of the porous domain invaded by the contaminant or remediation agent. To grasp the combined effect of rheology and spatial heterogeneity, we consider: a) the release of a thin current of non-Newtonian power-law fluid into a 2-D, semi-infinite and saturated porous medium above a horizontal bed; b) perfectly stratified media, with permeability and porosity varying along the direction transverse (vertical) or parallel (horizontal) to the flow direction. This continuous variation of spatial properties is described by two additional parameters. In order to represent several possible spreading scenarios, we consider: i) instantaneous injection with constant mass; ii) continuous injection with time-variable mass; iii) instantaneous release of a mound of fluid, which can drain freely out of the formation at the origin (dipole flow). Under these assumptions, scalings for current length and thickness are derived in self similar form. An analysis of the conditions on model parameters required to avoid an unphysical or asymptotically invalid result is presented. Theoretical results are validated against multiple sets of experiments, conducted for different combinations of spreading scenarios and types of stratification. Two basic setups are employed for the experiments: I) direct flow simulation in an artificial porous medium constructed superimposing layers of glass beads of different diameter; II) a Hele-Shaw (HS) analogue made of two parallel
Flow non-normality-induced transient growth in superposed Newtonian and non-Newtonian fluid layers.
Camporeale, C; Gatti, F; Ridolfi, L
2009-09-01
In recent years non-normality and transient growths have attracted much interest in fluid mechanics. Here, we investigate these topics with reference to the problem of interfacial instability in superposed Newtonian and non-Newtonian fluid layers. Under the hypothesis of the lubrication theory, we demonstrate the existence of significant transient growths in the parameter space region where the dynamical system is asymptotically stable, and show how they depend on the main physical parameters. In particular, the key role of the density ratio is highlighted.
Learning About Non-Newtonian Fluids in a Student-Driven Classroom
NASA Astrophysics Data System (ADS)
Dounas-Frazer, D. R.; Lynn, J.; Zaniewski, A. M.; Roth, N.
2013-01-01
We describe a simple, low-cost experiment and corresponding pedagogical strategies for studying fluids whose viscosities depend on shear rate, referred to as "non-Newtonian fluids." We developed these materials teaching for the Compass Project, an organization that fosters a creative, diverse, and collaborative community of science students at UC Berkeley. Incoming freshmen worked together in a week-long residential program to explore physical phenomena through a combination of conceptual model-building and hands-on experimentation. During the program, students were exposed to three major aspects of scientific discovery: developing a model, testing the model, and investigating deviations from the model.
Wu, Binxin
2010-12-01
In this paper, 12 turbulence models for single-phase non-newtonian fluid flow in a pipe are evaluated by comparing the frictional pressure drops obtained from computational fluid dynamics (CFD) with those from three friction factor correlations. The turbulence models studied are (1) three high-Reynolds-number k-ε models, (2) six low-Reynolds-number k-ε models, (3) two k-ω models, and (4) the Reynolds stress model. The simulation results indicate that the Chang-Hsieh-Chen version of the low-Reynolds-number k-ε model performs better than the other models in predicting the frictional pressure drops while the standard k-ω model has an acceptable accuracy and a low computing cost. In the model applications, CFD simulation of mixing in a full-scale anaerobic digester with pumped circulation is performed to propose an improvement in the effective mixing standards recommended by the U.S. EPA based on the effect of rheology on the flow fields. Characterization of the velocity gradient is conducted to quantify the growth or breakage of an assumed floc size. Placement of two discharge nozzles in the digester is analyzed to show that spacing two nozzles 180° apart with each one discharging at an angle of 45° off the wall is the most efficient. Moreover, the similarity rules of geometry and mixing energy are checked for scaling up the digester.
NASA Astrophysics Data System (ADS)
Gray, J. D.; Owen, I.; Escudier, M. P.
2007-10-01
Dimensional analysis has been applied to an unsteady pulsatile flow of a shear-thinning power-law non-Newtonian liquid. An experiment was then designed in which both Newtonian and non-Newtonian liquids were used to model blood flow through a large-scale (38.5 mm dia.), simplified, rigid arterial junction (a distal anastomosis of a femorodistal bypass). The flow field within the junction was obtained by Particle Imaging Velocimetry and near-wall velocities were used to calculate the wall shear stresses. Dimensionless wall shear stresses were obtained at different points in the cardiac cycle for two different but dynamically similar non-Newtonian fluids; the good agreement between the measured dimensionless wall shear stresses confirm the validity of the dimensional analysis. However, blood exhibits a constant viscosity at high-shear rates and to obtain complete dynamic similarity between large-scale experiments and life-scale flows, the high-shear viscosity also needs to be included in the analysis. How this might be done is discussed in the paper.
Pullback Asymptotic Behavior of Solutions for a 2D Non-autonomous Non-Newtonian Fluid
NASA Astrophysics Data System (ADS)
Liu, Guowei
2016-10-01
This paper studies the pullback asymptotic behavior of solutions for the non-autonomous incompressible non-Newtonian fluid in 2D bounded domains. Firstly, with a little high regularity of the force, the semigroup method and ɛ -regularity method are used to establish the existence of compact pullback absorbing sets. Then, with a minimal regularity of the force, by verifying the flattening property also known as the "Condition (C)", the author proves the existence of pullback attractors for the universe of fixed bounded sets and for the another universe given by a tempered condition. Furthermore, the regularity of pullback attractors is given.
Acoustic waveform of continuous bubbling in a non-Newtonian fluid.
Vidal, Valérie; Ichihara, Mie; Ripepe, Maurizio; Kurita, Kei
2009-12-01
We study experimentally the acoustic signal associated with a continuous bubble bursting at the free surface of a non-Newtonian fluid. Due to the fluid rheological properties, the bubble shape is elongated, and, when bursting at the free surface, acts as a resonator. For a given fluid concentration, at constant flow rate, repetitive bubble bursting occurs at the surface. We report a modulation pattern of the acoustic waveform through time. Moreover, we point out the existence of a precursor acoustic signal, recorded on the microphone array, previous to each bursting. The time delay between this precursor and the bursting signal is well correlated with the bursting signal frequency content. Their joint modulation through time is driven by the fluid rheology, which strongly depends on the presence of small satellite bubbles trapped in the fluid due to the yield stress.
Non-Newtonian fluid model incorporated into elastohydrodynamic lubrication of rectangular contacts
NASA Technical Reports Server (NTRS)
Jacobson, B. O.; Hamrock, B. J.
1984-01-01
A procedure is outlined for the numerical solution of the complete elastohydrodynamic lubrication of rectangular contacts incorporating a non-Newtonian fluid model. The approach uses a Newtonian model as long as the shear stress is less than a limiting shear stress. If the shear stress exceeds the limiting value, the shear stress is set equal to the limiting value. The numerical solution requires the coupled solution of the pressure, film shape, and fluid rheology equations from the inlet to the outlet. Isothermal and no-side-leakage assumptions were imposed in the analysis. The influence of dimensionless speed, load, materials, and sliding velocity and limiting-shear-strength proportionality constant on dimensionless minimum film thickness was investigated. Fourteen cases were used in obtaining the minimum-film-thickness equation for an elastohydrodynamically lubricated rectangular contact incorporating a non-Newtonian fluid model. Computer plots are also presented that indicate in detail pressure distribution, film shape, shear stress at the surfaces, and flow throughout the conjunction.
CFD simulation of gas and non-Newtonian fluid two-phase flow in anaerobic digesters.
Wu, Binxin
2010-07-01
This paper presents an Eulerian multiphase flow model that characterizes gas mixing in anaerobic digesters. In the model development, liquid manure is assumed to be water or a non-Newtonian fluid that is dependent on total solids (TS) concentration. To establish the appropriate models for different TS levels, twelve turbulence models are evaluated by comparing the frictional pressure drops of gas and non-Newtonian fluid two-phase flow in a horizontal pipe obtained from computational fluid dynamics (CFD) with those from a correlation analysis. The commercial CFD software, Fluent12.0, is employed to simulate the multiphase flow in the digesters. The simulation results in a small-sized digester are validated against the experimental data from literature. Comparison of two gas mixing designs in a medium-sized digester demonstrates that mixing intensity is insensitive to the TS in confined gas mixing, whereas there are significant decreases with increases of TS in unconfined gas mixing. Moreover, comparison of three mixing methods indicates that gas mixing is more efficient than mixing by pumped circulation while it is less efficient than mechanical mixing.
Non-Newtonian Fluid Model Incorporated into Elastohydrodynamic Lubrication of Rectangular Contacts
NASA Technical Reports Server (NTRS)
Jacobson, B. O.; Hamrock, B. J.
1983-01-01
A procedure is outlined for the numerical solution of the complete elastohydrodynamic lubrication of rectangular contacts incorporating a non-Newtonian fluid model. The approach uses a Newtonian model as long as the shear stress is less than a limiting shear stress. If the shear stress exceeds the limiting value, the shear stress is set equal to the limiting value. The numerical solution requires the coupled solution of the pressure, film shape, and fluid rheology equations from the inlet to the outlet. Isothermal and no-side-leakage assumptions were imposed in the analysis. The influence of dimensionless speed, load, materials, and sliding velocity and limiting-shear-strength proportionality constant on dimensionless minimum film thickness was investigated. Fourteen cases were used in obtaining the minimum-film-thickness equation for an elastohydrodynamically lubricated rectangular contact incorporating a non-Newtonian fluid model. Computer plots are also presented that indicate in detail pressure distribution, film shape, shear stress at the surfaces, and flow throughout the conjunction.
Apparao, Siddangouda; Biradar, Trimbak Vaijanath; Naduvinamani, Neminath Bhujappa
2014-01-01
Theoretical study of non-Newtonian effects of second-order fluids on the performance characteristics of inclined slider bearings is presented. An approximate method is used for the solution of the highly nonlinear momentum equations for the second-order fluids. The closed form expressions for the fluid film pressure, load carrying capacity, frictional force, coefficient of friction, and centre of pressure are obtained. The non-Newtonian second order fluid model increases the film pressure, load carrying capacity, and frictional force whereas the center of pressure slightly shifts towards exit region. Further, the frictional coefficient decreases with an increase in the bearing velocity as expected for an ideal fluid.
Apparao, Siddangouda; Biradar, Trimbak Vaijanath; Naduvinamani, Neminath Bhujappa
2014-01-01
Theoretical study of non-Newtonian effects of second-order fluids on the performance characteristics of inclined slider bearings is presented. An approximate method is used for the solution of the highly nonlinear momentum equations for the second-order fluids. The closed form expressions for the fluid film pressure, load carrying capacity, frictional force, coefficient of friction, and centre of pressure are obtained. The non-Newtonian second order fluid model increases the film pressure, load carrying capacity, and frictional force whereas the center of pressure slightly shifts towards exit region. Further, the frictional coefficient decreases with an increase in the bearing velocity as expected for an ideal fluid. PMID:27437446
Coalescence of drops and bubbles rising through a non-Newtonian fluid in a tube.
Al-Matroushi, Eisa; Borhan, Ali
2009-04-01
We conducted an experimental study of the interaction and coalescence of two drops (of the same fluid) or bubbles translating under the action of buoyancy in a cylindrical tube. The close approach of two Newtonian fluid particles of different size in a non-Newtonian continuous phase was examined using image analysis, and measurements of the coalescence time are reported for various particle size ratios, Bond numbers, and particle-to-suspending-fluid viscosity ratios. The flow disturbance behind the leading bubble and the viscoelastic nature of the continuous phase seemed to retard bubble coalescence. The time scale for coalescence of liquid drops in highly elastic continuous phase was influenced by the relative motion of the drops and their coalescence behavior.
Inertial migration of elastic particles in a pressure-driven power-law fluid
NASA Astrophysics Data System (ADS)
Bowie, Samuel; Alexeev, Alexander
2016-11-01
Using three-dimensional computer simulations, we study the cross-stream migration of deformable particles in a channel filled with a non-Newtonian fluid driven by a pressure gradient. Our numerical approach integrates lattice Boltzmann method and lattice spring method in order to model fluid structural interactions of the elastic particle and the surrounding power fluid in the channel. The particles are modeled as elastic shells filled with a viscous fluid that are initially spherical. We focus on the regimes where the inertial effects cannot be neglected and cause cross-stream drift of particles. We probe the flow with different power law indexes including both the shear thickening and thinning fluids. We also examine migration of particles of with different elasticity and relative size. To isolate the non-Newtonian effects on particle migration, we compare the results with the inertial migration results found in the case where the channel is filled with a simple Newtonian fluid. The results can be useful for applications requiring high throughput separation, sorting, and focusing of both synthetic particles and biological cells in microfluidic devices. Financial support provided by National Science Foundation (NSF) Grant No. CMMI1538161.
Validation of computational non-Newtonian fluid model for membrane bioreactor.
Sørensen, Lasse; Bentzen, Thomas Ruby; Skov, Kristian
2015-01-01
Membrane bioreactor (MBR) systems are often considered as the wastewater treatment method of the future due to their high effluent quality. One of the main problems with such systems is a relative large energy consumption, compared to conventional activated sludge (CAS) systems, which has led to further research in this specific area. A powerful tool for optimizing MBR-systems is computational fluid dynamics (CFD) modelling, which gives researchers the ability to describe the flow in the systems. A parameter which is often neglected in such models is the non-Newtonian properties of active sludge, which is of great importance for MBR systems since they operate at sludge concentrations up to a factor of 10 compared to CAS systems, resulting in strongly shear thinning liquids. A CFD-model is validated against measurements conducted in a system with rotating cross-flow membranes submerged in non-Newtonian liquids, where tangential velocities are measured with a Laser Doppler Anemometer (LDA). The CFD model is found to be capable of modelling the correct velocities in a range of setups, making CFD models a powerful tool for optimization of MBR systems.
Generalized multiscale finite element method for non-Newtonian fluid flow in perforated domain
NASA Astrophysics Data System (ADS)
Chung, E. T.; Iliev, O.; Vasilyeva, M. V.
2016-10-01
In this work, we consider a non-Newtonian fluid flow in perforated domains. Fluid flow in perforated domains have a multiscale nature and solution techniques for such problems require high resolution. In particular, the discretization needs to honor the irregular boundaries of perforations. This gives rise to a fine-scale problems with many degrees of freedom which can be very expensive to solve. In this work, we develop a multiscale approach that attempt to solve such problems on a coarse grid by constructing multiscale basis functions. We follow Generalized Multiscale Finite Element Method (GMsFEM) [1, 2] and develop a multiscale procedure where we identify multiscale basis functions in each coarse block using snapshot space and local spectral problems [3, 4]. We show that with a few basis functions in each coarse block, one can accurately approximate the solution, where each coarse block can contain many small inclusions.
Minale, Mario; Caserta, Sergio; Guido, Stefano
2010-01-05
In this work, the microconfined shear deformation of a droplet in an equiviscous non-Newtonian immiscible fluid is investigated by modeling and experiments. A phenomenological model based on the assumption of ellipsoidal shape and taking into account wall effects is proposed for systems made of non-Newtonian second-order fluids. The model, without any adjustable parameters, is tested by comparison with experiments under simple shear flow performed in a sliding plate apparatus, where the ratio between the distance between the confining walls and the droplet radius can be varied. The agreement between model predictions and experimental data is good both in steady state shear and in transient drop retraction upon cessation of flow. The results obtained in this work are relevant for microfluidics applications where non-Newtonian fluids are used.
Deyranlou, Amin; Niazmand, Hamid; Sadeghi, Mahmood-Reza
2015-09-18
Low-density lipoprotein (LDL), which is recognized as bad cholesterol, typically has been regarded as a main cause of atherosclerosis. LDL infiltration across arterial wall and subsequent formation of Ox-LDL could lead to atherogenesis. In the present study, combined effects of non-Newtonian fluid behavior and fluid-structure interaction (FSI) on LDL mass transfer inside an artery and through its multilayer arterial wall are examined numerically. Navier-Stokes equations for the blood flow inside the lumen and modified Darcy's model for the power-law fluid through the porous arterial wall are coupled with the equations of mass transfer to describe LDL distributions in various segments of the artery. In addition, the arterial wall is considered as a heterogeneous permeable elastic medium. Thus, elastodynamics equation is invoked to examine effects of different wall elasticity on LDL distribution in the artery. Findings suggest that non-Newtonian behavior of filtrated plasma within the wall enhances LDL accumulation meaningfully. Moreover, results demonstrate that at high blood pressure and due to the wall elasticity, endothelium pores expand, which cause significant variations on endothelium physiological properties in a way that lead to higher LDL accumulation. Additionally, results describe that under hypertension, by increasing angular strain, endothelial junctions especially at leaky sites expand more dramatic for the high elastic model, which in turn causes higher LDL accumulation across the intima layer and elevates atherogenesis risk.
On the rheology of refractive-index-matched, non-Newtonian blood-analog fluids for PIV experiments
NASA Astrophysics Data System (ADS)
Najjari, Mohammad Reza; Hinke, Jessica A.; Bulusu, Kartik V.; Plesniak, Michael W.
2016-06-01
Four commonly used refractive-index (RI)-matched Newtonian blood-analog fluids are reviewed, and different non-Newtonian blood-analogs, with RI of 1.372-1.495, are investigated. Sodium iodide (NaI), sodium thiocyanate (NaSCN) and potassium thiocyanate are used to adjust the RI of blood-analogs to that of test sections for minimizing optical distortions in particle image velocimetry data, and xanthan gum (XG) is added to the fluids to give them non-Newtonian properties (shear thinning and viscoelasticity). Our results support the general belief that adding NaI to Newtonian fluids matches the RI without changing the kinematic viscosity. However, in contrast to claims made in a few studies that did not measure rheology, our investigation revealed that adding NaI or NaSCN to XG-based non-Newtonian fluids changes the viscosity of the fluids considerably and reduces the shear-thinning property. Therefore, the RI of non-Newtonian blood-analog fluids with XG cannot be adjusted easily by varying the concentration of NaI or NaSCN and needs more careful rheological study.
Finite and Infinite Width Stokes Layers in a Power-Law Fluid
NASA Astrophysics Data System (ADS)
Wilson, Stephen; Pritchard, David; McArdle, Catriona
2011-11-01
Self-similar solutions for the oscillatory boundary layer (the ``Stokes layer'') in a semi-infinite power-law fluid bounded by an oscillating wall (the so-called Stokes problem) are obtained and analysed. These semi-analytical solutions differ qualitatively from the classical solution for a Newtonian fluid, both in the non-sinusoidal form of the velocity oscillations and in the manner at which their amplitude decays with distance from the wall. In particular, for shear-thickening fluids the velocity reaches zero at a finite distance from the wall, and for shear-thinning fluids it decays algebraically with distance, in contrast to the exponential decay for a Newtonian fluid. We demonstrate numerically that these self-similar solutions provide a good approximation to the flow driven by a sinusoidally oscillating wall. Further details can be found in the recent paper by D. Pritchard, C. R. McArdle and S. K. Wilson entitled ``The Stokes boundary layer for a power-law fluid,'' in Journal of Non-Newtonian Fluid Mechanics 166, 745-753 (2011).
Chaube, M. K.; Tripathi, D.; Bég, O. Anwar; Sharma, Shashi; Pandey, V. S.
2015-01-01
A mathematical study on creeping flow of non-Newtonian fluids (power law model) through a nonuniform peristaltic channel, in which amplitude is varying across axial displacement, is presented, with slip effects included. The governing equations are simplified by employing the long wavelength and low Reynolds number approximations. The expressions for axial velocity, stream function, pressure gradient, and pressure difference are obtained. Computational and numerical results for velocity profile, pressure gradient, and trapping under the effects of slip parameter, fluid behavior index, angle between the walls, and wave number are discussed with the help of Mathematica graphs. The present model is applicable to study the behavior of intestinal flow (chyme movement from small intestine to large intestine). It is also relevant to simulations of biomimetic pumps conveying hazardous materials, polymers, and so forth. PMID:27057132
A Numerical Study of Mesh Adaptivity in Multiphase Flows with Non-Newtonian Fluids
NASA Astrophysics Data System (ADS)
Percival, James; Pavlidis, Dimitrios; Xie, Zhihua; Alberini, Federico; Simmons, Mark; Pain, Christopher; Matar, Omar
2014-11-01
We present an investigation into the computational efficiency benefits of dynamic mesh adaptivity in the numerical simulation of transient multiphase fluid flow problems involving Non-Newtonian fluids. Such fluids appear in a range of industrial applications, from printing inks to toothpastes and introduce new challenges for mesh adaptivity due to the additional ``memory'' of viscoelastic fluids. Nevertheless, the multiscale nature of these flows implies huge potential benefits for a successful implementation. The study is performed using the open source package Fluidity, which couples an unstructured mesh control volume finite element solver for the multiphase Navier-Stokes equations to a dynamic anisotropic mesh adaptivity algorithm, based on estimated solution interpolation error criteria, and conservative mesh-to-mesh interpolation routine. The code is applied to problems involving rheologies ranging from simple Newtonian to shear-thinning to viscoelastic materials and verified against experimental data for various industrial and microfluidic flows. This work was undertaken as part of the EPSRC MEMPHIS programme grant EP/K003976/1.
The flow of power law fluids in elastic networks and porous media.
Sochi, Taha
2016-02-01
The flow of power law fluids, which include shear thinning and shear thickening as well as Newtonian as a special case, in networks of interconnected elastic tubes is investigated using a residual-based pore scale network modeling method with the employment of newly derived formulae. Two relations describing the mechanical interaction between the local pressure and local cross-sectional area in distensible tubes of elastic nature are considered in the derivation of these formulae. The model can be used to describe shear dependent flows of mainly viscous nature. The behavior of the proposed model is vindicated by several tests in a number of special and limiting cases where the results can be verified quantitatively or qualitatively. The model, which is the first of its kind, incorporates more than one major nonlinearity corresponding to the fluid rheology and conduit mechanical properties, that is non-Newtonian effects and tube distensibility. The formulation, implementation, and performance indicate that the model enjoys certain advantages over the existing models such as being exact within the restricting assumptions on which the model is based, easy implementation, low computational costs, reliability, and smooth convergence. The proposed model can, therefore, be used as an alternative to the existing Newtonian distensible models; moreover, it stretches the capabilities of the existing modeling approaches to reach non-Newtonian rheologies.
Fast imaging technique to study drop impact dynamics of non-Newtonian fluids.
Xu, Qin; Peters, Ivo; Wilken, Sam; Brown, Eric; Jaeger, Heinrich
2014-03-05
In the field of fluid mechanics, many dynamical processes not only occur over a very short time interval but also require high spatial resolution for detailed observation, scenarios that make it challenging to observe with conventional imaging systems. One of these is the drop impact of liquids, which usually happens within one tenth of millisecond. To tackle this challenge, a fast imaging technique is introduced that combines a high-speed camera (capable of up to one million frames per second) with a macro lens with long working distance to bring the spatial resolution of the image down to 10 µm/pixel. The imaging technique enables precise measurement of relevant fluid dynamic quantities, such as the flow field, the spreading distance and the splashing speed, from analysis of the recorded video. To demonstrate the capabilities of this visualization system, the impact dynamics when droplets of non-Newtonian fluids impinge on a flat hard surface are characterized. Two situations are considered: for oxidized liquid metal droplets we focus on the spreading behavior, and for densely packed suspensions we determine the onset of splashing. More generally, the combination of high temporal and spatial imaging resolution introduced here offers advantages for studying fast dynamics across a wide range of microscale phenomena.
Diagnosis at a glance of biological non-Newtonian fluids with Film Interference Flow Imaging (FIFI)
NASA Astrophysics Data System (ADS)
Hidema, R.; Yamada, N.; Furukawa, H.
2012-04-01
In the human body, full of biological non-Newtonian fluids exist. For example, synovial fluids exist in our joints, which contain full of biopolymers, such as hyaluronan and mucin. It is thought that these polymers play critical roles on the smooth motion of the joint. Indeed, luck of biopolymers in synovial fluid cause joint pain. Here we study the effects of polymer in thin liquid layer by using an original experimental method called Film Interference Flow Imaging (FIFI). A vertically flowing soap film containing polymers is made as two-dimensional flow to observe turbulence. The thickness of water layer is about 4 μm sandwiched between surfactant mono-layers. The interference pattern of the soap film is linearly related to the flow velocity in the water layer through the change in the thickness of the film. Thus the flow velocity is possibly analyzed by the single image analysis of the interference pattern, that is, FIFI. The grid turbulence was made in the flowing soap films containing the long flexible polymer polyethyleneoxide (PEO, Mw=3.5x106), and rigid polymer hydroxypropyl cellulose (HPC, Mw > 1.0 x106). The decaying process of the turbulence is affected by PEO and HPC at several concentrations. The effects of PEO are sharply seen even at low concentrations, while the effects of HPC are gradually occurred at much higher concentration compared to the PEO. It is assumed that such a difference between PEO and HPC is due to the polymer stretching or polymer orientation under turbulence, which is observed and analyzed by FIFI. We believe the FIFI will be applied in the future to examine biological fluids such as synovial fluids quickly and quantitatively.
NASA Astrophysics Data System (ADS)
Rathod, Maureen L.
Initially 3D FEM simulation of a simplified mixer was used to examine the effect of mixer configuration and operating conditions on dispersive mixing of a non-Newtonian fluid. Horizontal and vertical velocity magnitudes increased with increasing mixer speed, while maximum axial velocity and shear rate were greater with staggered paddles. In contrast, parallel paddles produced an area of efficient dispersive mixing between the center of the paddle and the barrel wall. This study was expanded to encompass the complete nine-paddle mixing section using power-law and Bird-Carreau fluid models. In the center of the mixer, simple shear flow was seen, corresponding with high [special character omitted]. Efficient dispersive mixing appeared near the barrel wall at all flow rates and near the barrel center with parallel paddles. Areas of backflow, improving fluid retention time, occurred with staggered paddles. The Bird-Carreau fluid showed greater influence of paddle motion under the same operating conditions due to the inelastic nature of the fluid. Shear-thinning behavior also resulted in greater maximum shear rate as shearing became easier with decreasing fluid viscosity. Shear rate distributions are frequently calculated, but extension rate calculations have not been made in a complex geometry since Debbaut and Crochet (1988) defined extension rate as the ratio of the third to the second invariant of the strain rate tensor. Extension rate was assumed to be negligible in most studies, but here extension rate is shown to be significant. It is possible to calculate maximum stable bubble diameter from capillary number if shear and extension rates in a flow field are known. Extension rate distributions were calculated for Newtonian and non-Newtonian fluids. High extension and shear rates were found in the intermeshing region. Extension is the major influence on critical capillary number and maximum stable bubble diameter, but when extension rate values are low shear rate has
Measurement of viscosity of highly viscous non-Newtonian fluids by means of ultrasonic guided waves.
Kazys, Rymantas; Mazeika, Liudas; Sliteris, Reimondas; Raisutis, Renaldas
2014-04-01
In order to perform monitoring of the polymerisation process, it is necessary to measure viscosity. However, in the case of non-Newtonian highly viscous fluids, viscosity starts to be dependent on the vibration or rotation frequency of the sensing element. Also, the sensing element must possess a sufficient mechanical strength. Some of these problems may be solved applying ultrasonic measurement methods, however until now most of the known investigations were devoted to measurements of relatively low viscosities (up to a few Pas) of Newtonian liquids. The objective of the presented work is to develop ultrasonic method for measurement of viscosity of high viscous substances during manufacturing process in extreme conditions. For this purpose the method based on application of guided Lamb waves possessing the predominant component of in-plane displacements (the S0 and the SH0 modes) and propagating in an aluminium planar waveguide immersed in a viscous liquid has been investigated. The simulations indicated that in the selected modes mainly in-plane displacements are dominating, therefore the attenuation of those modes propagating in a planar waveguide immersed in a viscous liquid is mainly caused by viscosity of the liquid. The simulation results were confirmed by experiments. All measurements were performed in the viscosity standard Cannon N2700000. Measurements with the S0 wave mode were performed at the frequency of 500kHz. The SH0 wave mode was exited and used for measurements at the frequency of 580kHz. It was demonstrated that by selecting the particular mode of guided waves (S0 or SH0), the operation frequency and dimensions of the aluminium waveguide it is possible to get the necessary viscosity measurement range and sensitivity. The experiments also revealed that the measured dynamic viscosity is strongly frequency dependent and as a characteristic feature of non-Newtonian liquids is much lower than indicated by the standards. Therefore, in order to get the
MHD micropumping of power-law fluids: A numerical solution
NASA Astrophysics Data System (ADS)
Moghaddam, Saied
2013-02-01
The performance of MHD micropumps is studied numerically assuming that the viscosity of the fluid is shear-dependent. Using power-law model to represent the fluid of interest, the effect of power-law exponent, N, is investigated on the volumetric flow rate in a rectangular channel. Assuming that the flow is laminar, incompressible, two-dimensional, but (approximately) unidirectional, finite difference method (FDM) is used to solve the governing equations. It is found that shear-thinning fluids provide a larger flow rate as compared to Newtonian fluids provided that the Hartmann number is above a critical value. There exists also an optimum Hartmann number (which is larger than the critical Hartmann number) at which the flow rate is maximum. The power-law exponent, N, strongly affects the optimum geometry depending on the Hartmann number being smaller or larger than the critical Hartmann number.
Mass transport in a porous microchannel for non-Newtonian fluid with electrokinetic effects.
Mondal, Sourav; De, Sirshendu
2013-03-01
Quantification of mass transfer in porous microchannel is of paramount importance in several applications. Transport of neutral solute in presence of convective-diffusive EOF having non-Newtonian rheology, in a porous microchannel was presented in this article. The governing mass transfer equation coupled with velocity field was solved along with associated boundary conditions using a similarity solution method. An analytical solution of mass transfer coefficient and hence, Sherwood number were derived from first principles. The corresponding effects of assisting and opposing pressure-driven flow and EOF were also analyzed. The influence of wall permeation, double-layer thickness, rheology, etc. on the mass transfer was also investigated. Permeation at the wall enhanced the mass transfer coefficient more than five times compared to impervious conduit in case of pressure-driven flow assisting the EOF at higher values of κh. Shear thinning fluid exhibited more enhancement of Sherwood number in presence of permeation compared to shear thickening one. The phenomenon of stagnation was observed at a particular κh (∼2.5) in case of EOF opposing the pressure-driven flow. This study provided a direct quantification of transport of a neutral solute in case of transdermal drug delivery, transport of drugs from blood to target region, etc.
Gravity driven instabilities in miscible non-Newtonian fluid displacements in porous media
NASA Astrophysics Data System (ADS)
Freytes, V. M.; D'Onofrio, A.; Rosen, M.; Allain, C.; Hulin, J. P.
2001-02-01
Gravity driven instabilities in model porous packings of 1 mm diameter spheres are studied by comparing the broadening of the displacement front between fluids of slightly different densities in stable and unstable configurations. Water, water-glycerol and water-polymer solutions are used to vary independently viscosity and molecular diffusion and study the influence of shear-thinning properties. Both injected and displaced solutions are identical but for a different concentration of NaNO 3 salt used as an ionic tracer and to introduce the density contrast. Dispersivity in stable configuration increases with polymer concentration - as already reported for double porosity packings of porous grains. Gravity-induced instabilities are shown to develop below a same threshold Péclet number Pe for water and water-glycerol solutions of different viscosities and result in considerable increases of the dispersivity. Measured threshold Pe values decrease markedly on the contrary with polymer concentration. The quantitative analysis demonstrates that the development of the instabilities is controlled by viscosity through a characteristic gravity number G (ratio between hydrostatic and viscous pressure gradients). A single threshold value of G accounts for results obtained on Newtonian and non-Newtonian solutions.
NASA Astrophysics Data System (ADS)
Tong, Dengke; Wang, Ruihe
2004-08-01
In this paper, fractional order derivative, fractal dimension and spectral dimension are introduced into the seepage flow mechanics to establish the relaxation models of non-Newtonian viscoelastic fluids with the fractional derivative in fractal reservoirs. A new type integral transform is introduced, and the flow characteristics of non-Newtonian viscoelastic fluids with the fractional order derivative through a fractal reservoir are studied by using the integral transform, the discrete Laplace transform of sequential fractional derivatives and the generalized Mittag-Leffler functions. Exact solutions are obtained for arbitrary fractional order derivative. The long-time and short-time asymptotic solutions for an infinite formation are also obtained. The pressure transient behavior of non-Newtonian viscoelastic fluids flow through an infinite fractal reservoir is studied by using the Stehfest's inversion method of the numerical Laplace transform. It is shown that the clearer the viscoelastic characteristics of the fluid, the more the fluid is sensitive to the order of the fractional derivative. The new type integral transform provides a new analytical tool for studying the seepage mechanics of fluid in fractal porous media.
Spreading dynamics and dynamic contact angle of non-Newtonian fluids.
Wang, X D; Lee, D J; Peng, X F; Lai, J Y
2007-07-17
The spreading dynamics of power-law fluids, both shear-thinning and shear-thickening fluids, that completely or partially wet solid substrate was investigated theoretically and experimentally. An evolution equation for liquid-film thickness was derived using a lubrication approximation, from which the dynamic contact angle versus the contact line moving velocity relationship was evaluated. In the capillary spreading regime, film thickness h is proportional to xi3/(n+2) (xi is the distance from the contact line), whereas in the gravitational regime, h is proportional to xi1/(n+2), relating to the rheological power exponent n. The derived model fit the experimental data well for a shear-thinning fluid (0.2% w/w xanthan solution) or a shear-thickening fluid (7.5% w/w 10 nm silica in polypropylene glycol) on a completely wetted substrate. The derived model was extended using Hoffmann's proposal for partially wetting fluids. Good agreement was also attained between model predictions and the shear-thinning fluid (1% w/w cmc solution) and shear-thickening fluid (10% w/w 15 nm silica) on partially wetted surfaces.
Ali, N; Asghar, Z; Anwar Bég, O; Sajid, M
2016-05-21
Gliding bacteria are an assorted group of rod-shaped prokaryotes that adhere to and glide on certain layers of ooze slime attached to a substratum. Due to the absence of organelles of motility, such as flagella, the gliding motion is caused by the waves moving down the outer surface of these rod-shaped cells. In the present study we employ an undulating surface model to investigate the motility of bacteria on a layer of non-Newtonian slime. The rheological behavior of the slime is characterized by an appropriate constitutive equation, namely the Carreau model. Employing the balances of mass and momentum conservation, the hydrodynamic undulating surface model is transformed into a fourth-order nonlinear differential equation in terms of a stream function under the long wavelength assumption. A perturbation approach is adopted to obtain closed form expressions for stream function, pressure rise per wavelength, forces generated by the organism and power required for propulsion. A numerical technique based on an implicit finite difference scheme is also employed to investigate various features of the model for large values of the rheological parameters of the slime. Verification of the numerical solutions is achieved with a variational finite element method (FEM). The computations demonstrate that the speed of the glider decreases as the rheology of the slime changes from shear-thinning (pseudo-plastic) to shear-thickening (dilatant). Moreover, the viscoelastic nature of the slime tends to increase the swimming speed for the shear-thinning case. The fluid flow in the pumping (generated where the organism is not free to move but instead generates a net fluid flow beneath it) is also investigated in detail. The study is relevant to marine anti-bacterial fouling and medical hygiene biophysics.
NASA Astrophysics Data System (ADS)
Ilyasov, A. M.; Bulgakova, G. T.
2016-08-01
This paper describes a mathematical model of the main fracture isolation in porous media by water-based mature gels. While modeling injection, water infiltration from the gel pack through fracture walls is taking into account, due to which the polymer concentration changes and the residual water resistance factor changes as a consequence. The salutation predicts velocity and pressure fields of the non-Newtonian incompressible fluid filtration for conditions of a non-deformable formation as well as a gel front trajectory in the fracture. The mathematical model of agent injection into the main fracture is based on the fundamental laws of continuum mechanics conservation describing the flow of non-Newtonian and Newtonian fluids separated by an interface plane in a flat channel with permeable walls. The mathematical model is based on a one-dimensional isothermal approximation, with dynamic parameters pressure and velocity, averaged over the fracture section.
Data on the mixing of non-Newtonian fluids by a Rushton turbine in a cylindrical tank.
Khapre, Akhilesh; Munshi, Basudeb
2016-09-01
The paper focuses on the data collected from the mixing of shear thinning non-Newtonian fluids in a cylindrical tank by a Rushton turbine. The data presented are obtained by using Computational Fluid Dynamics (CFD) simulation of fluid flow field in the entire tank volume. The CFD validation data for this study is reported in the research article 'Numerical investigation of hydrodynamic behavior of shear thinning fluids in stirred tank' (Khapre and Munshi, 2015) [1]. The tracer injection method is used for the prediction of mixing time and mixing efficiency of a Rushton turbine impeller.
NASA Astrophysics Data System (ADS)
Sahebi, S. A. R.; Pourziaei, H.; Feizi, A. R.; Taheri, M. H.; Rostamiyan, Y.; Ganji, D. D.
2015-12-01
In this paper, natural convection of non-Newtonian bio-nanofluids flow between two vertical flat plates is investigated numerically. Sodium Alginate (SA) and Sodium Carboxymethyl Cellulose (SCMC) are considered as the base non-Newtonian fluid, and nanoparticles such as Titania ( TiO2 and Alumina ( Al2O3 were added to them. The effective thermal conductivity and viscosity of nanofluids are calculated through Maxwell-Garnetts (MG) and Brinkman models, respectively. A fourth-order Runge-Kutta numerical method (NUM) and three Weighted Residual Methods (WRMs), Collocation (CM), Galerkin (GM) and Least-Square Method (LSM) and Finite-Element Method (FEM), are used to solve the present problem. The influence of some physical parameters such as nanofluid volume friction on non-dimensional velocity and temperature profiles are discussed. The results show that SCMC- TiO2 has higher velocity and temperature values than other nanofluid structures.
Mathematical modeling of slope flows with entrainment as flows of non-Newtonian fluids
NASA Astrophysics Data System (ADS)
Zayko, Julia; Eglit, Margarita
2015-04-01
Non-Newtonian fluids in which the shear stresses are nonlinear functions of the shear strain rates are used to model slope flows such as snow avalanches, mudflows, debris flows. The entrainment of bottom material is included into the model basing on the assumption that in entraining flows the bed friction is equal to the shear stress of the bottom material (Issler et al, 2011). Unsteady motion down long homogeneous slopes with constant inclines is studied numerically for different flow rheologies and different slope angles. Variation of the velocity profile, increase of the flow depth and velocity due to entrainment as well as the value of the entrainment rate is calculated. Asymptotic formulae for the entrainment rate are derived for unsteady flows of different rheological properties. REFERENCES Chowdhury M., Testik F., 2011. Laboratory testing of mathematical models for high-concentration fluid mud turbidity currents. Ocean Engineering 38, 256-270. Eglit, M.E., Demidov, K.S., 2005. Mathematical modeling of snow entrainment in avalanche motion. Cold Reg. Sci. Technol. 43 (1-2), 10-23. Eglit M. E., Yakubenko A. E., 2012, Mathematical Modeling of slope flows entraining bottom material. Eglit M. E., Yakubenko A. E., 2014, Numerical modeling of slope flows entraining bottom material. Cold Reg. Sci. Technol. 108, 139-148. Issler D, M. Pastor Peréz. 2011. Interplay of entrainment and rheology in snow avalanches; a numerical study. Annals of Glaciology, 52(58), pp.143-147 Kern M. A., Tiefenbacher F., McElwaine J., N., 2004. The rheology of snow in large chute flows. Cold Regions Science and Technology, 39, 181 -192. Naaim, M., Faug, T., Naaim-Bouvet, F., 2003. Dry granular flow modelling including erosion and deposition. Surv. Geophys. 24, 569-585. Naaim, M., Naaim-Bouvet, F., Faug, T., Bouchet, A., 2004. Dense snow avalanche modeling: flow, erosion, deposition and obstacle effects. Cold Reg. Sci. Technol. 39, 193-204. Rougier, J & Kern, M 2010, 'Predicting snow
Akbarzadeh, Pooria
2016-04-01
In this paper, the unsteady pulsatile magneto-hydrodynamic blood flows through porous arteries concerning the influence of externally imposed periodic body acceleration and a periodic pressure gradient are numerically simulated. Blood is taken into account as the third-grade non-Newtonian fluid. Besides the numerical solution, for small Womersley parameter (such as blood flow through arterioles and capillaries), the analytical perturbation method is used to solve the nonlinear governing equations. Consequently, analytical expressions for the velocity profile, wall shear stress, and blood flow rate are obtained. Excellent agreement between the analytical and numerical predictions is evident. Also, the effects of body acceleration, magnetic field, third-grade non-Newtonian parameter, pressure gradient, and porosity on the flow behaviors are examined. Some important conclusions are that, when the Womersley parameter is low, viscous forces tend to dominate the flow, velocity profiles are parabolic in shape, and the center-line velocity oscillates in phase with the driving pressure gradient. In addition, by increasing the pressure gradient, the mean value of the velocity profile increases and the amplitude of the velocity remains constant. Also, when non-Newtonian effect increases, the amplitude of the velocity profile.
Widmer Soyka, René P; López, Alejandro; Persson, Cecilia; Cristofolini, Luca; Ferguson, Stephen J
2013-11-01
Fluids present or used in biology, medicine and (biomedical) engineering are often significantly non-Newtonian. Furthermore, they are chemically complex and can interact with the porous matrix through which they flow. The porous structures themselves display complex morphological inhomogeneities on a wide range of length scales. In vertebroplasty, a shear-thinning fluid, e.g. poly(methyl methacrylate) (PMMA), is injected into the cavities of vertebral trabecular bone for the stabilization of fractures and metastatic lesions. The main objective of this study was therefore to provide a protocol for numerically investigating the rheological properties of PMMA-based bone cements to predict its spreading behavior while flowing through vertebral trabecular bone. A numerical upscaling scheme based on a dimensionless formulation of the Navier-Stokes equation is proposed in order to relate the pore-scale rheological properties of the PMMA that were experimentally estimated using a plate rheometer, to the continuum-scale. On the pore length scale, a viscosity change on the order of one magnitude was observed whilst the shear-thinning properties caused a viscosity change on the order of only 10% on the continuum length scale and in a flow regime that is relevant for vertebroplasty. An experimental validation, performed on human cadaveric vertebrae (n=9), showed a significant improvement of the cement spreading prediction accuracy with a non-Newtonian formulation. A root mean square cement surface prediction error of 1.53mm (assuming a Newtonian fluid) and 1.37mm (assuming a shear-thinning fluid) was found. Our findings highlight the importance of incorporating the non-Newtonian fluids properties in computational models of porous media at the appropriate length scale.
Nam, Jeonghun; Lim, Hyunjung; Kim, Dookon; Jung, Hyunwook; Shin, Sehyun
2012-04-07
Pure separation and sorting of microparticles from complex fluids are essential for biochemical analyses and clinical diagnostics. However, conventional techniques require highly complex and expensive labeling processes for high purity separation. In this study, we present a simple and label-free method for separating microparticles with high purity using the elasto-inertial characteristic of a non-Newtonian fluid in microchannel flow. At the inlet, particle-containing sample flow was pushed toward the side walls by introducing sheath fluid from the center inlet. Particles of 1 μm and 5 μm in diameter, which were suspended in viscoelastic fluid, were successfully separated in the outlet channels: larger particles were notably focused on the centerline of the channel at the outlet, while smaller particles continued flowing along the side walls with minimal lateral migration towards the centerline. The same technique was further applied to separate platelets from diluted whole blood. Through cytometric analysis, we obtained a purity of collected platelets of close to 99.9%. Conclusively, our microparticle separation technique using elasto-inertial forces in non-Newtonian fluid is an effective method for separating and collecting microparticles on the basis of size differences with high purity.
Accelerated Sedimentation Velocity Assessment for Nanowires Stabilized in a Non-Newtonian Fluid.
Chang, Chia-Wei; Liao, Ying-Chih
2016-12-27
In this work, the long-term stability of titanium oxide nanowire suspensions was accessed by an accelerated sedimentation with centrifugal forces. Titanium oxide (TiO2) nanoparticle (NP) and nanowire (NW) dispersions were prepared, and their sizes were carefully characterized. To replace the time-consuming visual observation, sedimentation velocities of the TiO2 NP and NW suspensions were measured using an analytical centrifuge. For an aqueous TiO2 NP suspension, the measured sedimentation velocities were linearly dependent on the relative centrifugal forces (RCF), as predicted by the classical Stokes law. A similar linear relationship was also found in the case of TiO2 NW aqueous suspensions. However, NWs preferred to settle parallel to the centrifugal direction under high RCF because of the lower flow resistance along the long axis. Thus, the extrapolated sedimentation velocity under regular gravity can be overestimated. Finally, a stable TiO2 NW suspension was formulated with a shear thinning fluid and showed great stability for weeks using visual observation. A theoretical analysis was deduced with rheological shear-thinning parameters to describe the nonlinear power-law dependence between the measured sedimentation velocities and RCF. The good agreement between the theoretical predictions and measurements suggested that the sedimentation velocity can be properly extrapolated to regular gravity. In summary, this accelerated assessment on a theoretical basis can yield quantitative information about long-term stability within a short time (a few hours) and can be further extended to other suspension systems.
Power-law rheology and flow behavior of low-invasion coring fluids
McGuire, P.L.
1981-08-01
An improved pressure coring system has been developed in which an extremely viscous polymer mud is extruded by the core and is used to seal and protect the core from flushing by drilling fluids. The polymer mud must be extremely viscous to minimize invasion, yet must be extruded through a long, narrow annular gap with a minimum of pressure buildup. A highly non-Newtonian shear-thinning polymer is utilized in the low invasion coring fluid. This paper describes the measurement and modeling of non-Newtonian rheology from rotary viscometer data in detail since the simplified equations which are generally used with these instruments can be grossly in error. The development of both an approximate analytical solution and an exact numerical solution of the non-Newtonian extrusion process is presented. These solutions were used to optimize the non-Newtonian rheology of the low-invasion fluid which will be used in actual coring operations.
Coalescence of Drops of a Power-law Fluid
NASA Astrophysics Data System (ADS)
Kamat, Pritish; Thete, Sumeet; Basaran, Osman
2014-11-01
Drop coalescence is crucial in a host of industrial, household, and natural processes that involve dispersions. Coalescence is a rate-controlling process in breaking emulsions and strongly influences drop-size-distributions in sprays. In a continuum approach, coalescence begins by the formation of a microscopic, non-slender bridge connecting the two drops. Indefinitely large axial curvature at the neck results in local lowering of pressure that drives fluid from the bulk of the drops toward the neck, thereby causing the bridge radius r (t) and height z (t) to increase in time t. The coalescence of Newtonian drops in air has heretofore been thoroughly studied. Here, we extend these earlier studies by analyzing the coalescence of drops of power-law fluids because many fluids encountered in real applications, including cosmetic creams, shampoos, grease, and paint, exhibit power-law (deformation-rate thinning) rheology. On account of the non-slender geometry of the liquid bridge connecting the two drops (z << r) , we analyze the resulting free surface flow problem by numerical simulation. Among other results, we present and discuss the nature of flows and scaling behaviors for r and z as functions of the initial viscosity and power-law index (0 < n <= 1) .
Hayat, Tasawar; Awais, Muhammad; Imtiaz, Amna
2016-01-01
This communication deals with the properties of heat source/sink in a magneto-hydrodynamic flow of a non-Newtonian fluid immersed in a porous medium. Shrinking phenomenon along with the permeability of the wall is considered. Mathematical modelling is performed to convert the considered physical process into set of coupled nonlinear mathematical equations. Suitable transformations are invoked to convert the set of partial differential equations into nonlinear ordinary differential equations which are tackled numerically for the solution computations. It is noted that dual solutions for various physical parameters exist which are analyzed in detail.
NASA Astrophysics Data System (ADS)
M. El-Hawary, H.; Mostafa, A. A. Mahmoud; Reda, G. Abdel-Rahman; Abeer, S. Elfeshawey
2014-09-01
The theoretic transformation group approach is applied to address the problem of unsteady boundary layer flow of a non-Newtonian fluid near a stagnation point with variable viscosity and thermal conductivity. The application of a two-parameter group method reduces the number of independent variables by two, and consequently the governing partial differential equations with the boundary conditions transformed into a system of ordinary differential equations with the appropriate corresponding conditions. Two systems of ordinary differential equations have been solved numerically using a fourth-order Runge—Kutta algorithm with a shooting technique. The effects of various parameters governing the problem are investigated.
Hayat, Tasawar; Awais, Muhammad; Imtiaz, Amna
2016-01-01
This communication deals with the properties of heat source/sink in a magneto-hydrodynamic flow of a non-Newtonian fluid immersed in a porous medium. Shrinking phenomenon along with the permeability of the wall is considered. Mathematical modelling is performed to convert the considered physical process into set of coupled nonlinear mathematical equations. Suitable transformations are invoked to convert the set of partial differential equations into nonlinear ordinary differential equations which are tackled numerically for the solution computations. It is noted that dual solutions for various physical parameters exist which are analyzed in detail. PMID:27598314
Janečka, Adam Průša, Vít
2015-04-28
We discuss the benefits of using the so-called implicit type constitutive relations introduced by K. R. Rajagopal, J. Fluid Mech. 550, 243-249 (2006) and K. R. Rajagopal, Appl. Math. 48, 279-319 (2003) in the description of the behaviour of non-Newtonian fluids. In particular, we focus on the benefits of using the implicit type constitutive relations in the mathematical modelling of fluids in which the shear stress/shear rate dependence is given by an S-shaped curve, and in modelling of fluids that exhibit nonzero normal stress differences. We also discuss a thermodynamical framework that allows one to cope with the implicit type constitutive relations.
Accuracy of non-Newtonian Lattice Boltzmann simulations
NASA Astrophysics Data System (ADS)
Conrad, Daniel; Schneider, Andreas; Böhle, Martin
2015-11-01
This work deals with the accuracy of non-Newtonian Lattice Boltzmann simulations. Previous work for Newtonian fluids indicate that, depending on the numerical value of the dimensionless collision frequency Ω, additional artificial viscosity is introduced, which negatively influences the accuracy. Since the non-Newtonian fluid behavior is incorporated through appropriate modeling of the dimensionless collision frequency, a Ω dependent error EΩ is introduced and its influence on the overall error is investigated. Here, simulations with the SRT and the MRT model are carried out for power-law fluids in order to numerically investigate the accuracy of non-Newtonian Lattice Boltzmann simulations. A goal of this accuracy analysis is to derive a recommendation for an optimal choice of the time step size and the simulation Mach number, respectively. For the non-Newtonian case, an error estimate for EΩ in the form of a functional is derived on the basis of a series expansion of the Lattice Boltzmann equation. This functional can be solved analytically for the case of the Hagen-Poiseuille channel flow of non-Newtonian fluids. With the help of the error functional, the prediction of the global error minimum of the velocity field is excellent in regions where the EΩ error is the dominant source of error. With an optimal simulation Mach number, the simulation is about one order of magnitude more accurate. Additionally, for both collision models a detailed study of the convergence behavior of the method in the non-Newtonian case is conducted. The results show that the simulation Mach number has a major impact on the convergence rate and second order accuracy is not preserved for every choice of the simulation Mach number.
Secondary flow in a curved artery model with Newtonian and non-Newtonian blood-analog fluids
NASA Astrophysics Data System (ADS)
Najjari, Mohammad Reza; Plesniak, Michael W.
2016-11-01
Steady and pulsatile flows of Newtonian and non-Newtonian fluids through a 180°-curved pipe were investigated using particle image velocimetry (PIV). The experiment was inspired by physiological pulsatile flow through large curved arteries, with a carotid artery flow rate imposed. Sodium iodide (NaI) and sodium thiocyanate (NaSCN) were added to the working fluids to match the refractive index (RI) of the test section to eliminate optical distortion. Rheological measurements revealed that adding NaI or NaSCN changes the viscoelastic properties of non-Newtonian solutions and reduces their shear-thinning property. Measured centerline velocity profiles in the upstream straight pipe agreed well with an analytical solution. In the pulsatile case, secondary flow structures, i.e. deformed-Dean, Dean, Wall and Lyne vortices, were observed in various cross sections along the curved pipe. Vortical structures at each cross section were detected using the d2 vortex identification method. Circulation analysis was performed on each vortex separately during the systolic deceleration phase, and showed that vortices split and rejoin. Secondary flow structures in steady flows were found to be morphologically similar to those in pulsatile flows for sufficiently high Dean number. supported by the George Washington University Center for Biomimetics and Bioinspired Engineering.
Aspects of non-Newtonian flow and displacement in porous media
Shah, C.; Yortsos, Y.C.
1993-02-01
The rheology of many heavy oils has been shown to be non-Newtonian, Bingham plastics being one manifestation of heavy oil flow. In EOR applications, non-Newtonian fluids such as low concentration polymer solutions, emulsions, gels etc. are simultaneously injected to increase the viscosity of driving agents that displace oil. Such rheologically complex fluids are used to improve sweep efficiencies, divert displacing fluids and block swept zones. The present study has been undertaken to understand the flow of non-Newtonian fluids through porous media. The work considered involves the numerical (pore network) modeling of both single and multiphase flow of power-law and Bingham plastic fluids in network-like porous media. We consider aspects of both single- and multi-phase flow and displacement. Section 2 describes elementary aspects of non-Newtonian flow and some simple models for porous media. Viscoelastic effects in the flow of non-Newtonian fluids are also discussed. The section includes a brief literature review on non-Newtonian flow in porous media. Section 3 describes single-phase flow.
Analysis of the formation and evolution of vortex rings in non Newtonian fluids using 3D PTV
NASA Astrophysics Data System (ADS)
Bajpayee, Abhishek; Techet, Alexandra
2013-11-01
Formation and evolution of vortex rings have been studied for a long time but mostly only in Newtonian fluids. However, many fluids in nature and in the industry such as blood, crude oil, etc., exhibit non Newtonian characteristics. Palacios-Morales and Zenit recently studied the formation of vortex rings in shear thinning liquids for the first time using 2D PIV and compared experimental findings with theoretical predictions. The authors recently demonstrated the applicability of Light Field (LF) imaging to conduct 3D Particle Tracking Velocimetry (PTV) to study densely seeded flow fields and their evolution over time using synthetic data. LF based 3D PTV is now used to quantitatively study vortex rings created in Glycerin based on multiple parameters and the results are compared with previous findings. ONR (Grant #N00014-12-1-0787, Dr. Steven Russell), Naval Engineering Education Center.
Hu, Bin; Kieweg, Sarah L
2012-07-15
Gravity-driven thin film flow is of importance in many fields, as well as for the design of polymeric drug delivery vehicles, such as anti-HIV topical microbicides. There have been many prior works on gravity-driven thin films. However, the incorporation of surface tension effect has not been well studied for non-Newtonian fluids. After surface tension effect was incorporated into our 2D (i.e. 1D spreading) power-law model, we found that surface tension effect not only impacted the spreading speed of the microbicide gel, but also had an influence on the shape of the 2D spreading profile. We observed a capillary ridge at the front of the fluid bolus. Previous literature shows that the emergence of a capillary ridge is strongly related to the contact line fingering instability. Fingering instabilities during epithelial coating may change the microbicide gel distribution and therefore impact how well it can protect the epithelium. In this study, we focused on the capillary ridge in 2D flow and performed a series of simulations and showed how the capillary ridge height varies with other parameters, such as surface tension coefficient, inclination angle, initial thickness, and power-law parameters. As shown in our results, we found that capillary ridge height increased with higher surface tension, steeper inclination angle, bigger initial thickness, and more Newtonian fluids. This study provides the initial insights of how to optimize the flow and prevent the appearance of a capillary ridge and fingering instability.
A constitutive framework for the non-Newtonian pressure tensor of a simple fluid under planar flows.
Hartkamp, Remco; Todd, B D; Luding, Stefan
2013-06-28
Non-equilibrium molecular dynamics simulations of an atomic fluid under shear flow, planar elongational flow, and a combination of shear and elongational flow are unified consistently with a tensorial model over a wide range of strain rates. A model is presented that predicts the pressure tensor for a non-Newtonian bulk fluid under a homogeneous planar flow field. The model provides a quantitative description of the strain-thinning viscosity, pressure dilatancy, deviatoric viscoelastic lagging, and out-of-flow-plane pressure anisotropy. The non-equilibrium pressure tensor is completely described through these four quantities and can be calculated as a function of the equilibrium material constants and the velocity gradient. This constitutive framework in terms of invariants of the pressure tensor departs from the conventional description that deals with an orientation-dependent description of shear stresses and normal stresses. The present model makes it possible to predict the full pressure tensor for a simple fluid under various types of flows without having to produce these flow types explicitly in a simulation or experiment.
MASS TRANSFER COEFFICIENTS FOR A NON-NEWTONIAN FLUID AND WATER WITH AND WITHOUT ANTI-FOAM AGENTS
Leishear, R.
2009-09-09
Mass transfer rates were measured in a large scale system, which consisted of an 8.4 meter tall by 0.76 meter diameter column containing one of three fluids: water with an anti-foam agent, water without an anti-foam agent, and AZ101 simulant, which simulated a non-Newtonian nuclear waste. The testing contributed to the evaluation of large scale mass transfer of hydrogen in nuclear waste tanks. Due to its radioactivity, the waste was chemically simulated, and due to flammability concerns oxygen was used in lieu of hydrogen. Different liquids were used to better understand the mass transfer processes, where each of the fluids was saturated with oxygen, and the oxygen was then removed from solution as air bubbled up, or sparged, through the solution from the bottom of the column. Air sparging was supplied by a single tube which was co-axial to the column, the decrease in oxygen concentration was recorded, and oxygen measurements were then used to determine the mass transfer coefficients to describe the rate of oxygen transfer from solution. Superficial, average, sparging velocities of 2, 5, and 10 mm/second were applied to each of the liquids at three different column fill levels, and mass transfer coefficient test results are presented here for combinations of superficial velocities and fluid levels.
Flow instabilities during annular displacement of one non-Newtonian fluid by another
NASA Astrophysics Data System (ADS)
Tehrani, M. A.; Bittleston, S. H.; Long, P. J. G.
1993-02-01
This paper describes an experimental setup for axial laminar flow of liquids in the annulus between two eccentered cylinders. The design uses a conductivity method for measuring peak axial velocities around the annulus, and for the determination of displacement efficiency when displacing one fluid by another (displacement efficiency being defined as the ratio of volume of displaced fluid removed from the annulus, to the volume of the annulus, after a given number of annular volumes have been pumped). In an eccentric annulus, lower axial velocity in the narrow side produces “channeling” of the displacing fluid in the wide side and reduces the displacement efficiency. A positive density contrast between the two fluids can increase the efficiency by promoting azimuthal flow of the (denser) displacing fluid towards the narrow side. In this paper we report that gravity driven azimuthal flow is prone to severe instabilities which accelerate the displacement process but may leave behind an immobile strip of the displaced fluid in the narrow side.
Analysis of non-Newtonian effects on Low-Density Lipoprotein accumulation in an artery.
Iasiello, Marcello; Vafai, Kambiz; Andreozzi, Assunta; Bianco, Nicola
2016-06-14
In this work, non-Newtonian effects on Low-Density Lipoprotein (LDL) transport across an artery are analyzed with a multi-layer model. Four rheological models (Carreau, Carreau-Yasuda, power-law and Newtonian) are used for the blood flow through the lumen. For the non-Newtonian cases, the arterial wall is modeled with a generalized momentum equation. Convection-diffusion equation is used for the LDL transport through the lumen, while Staverman-Kedem-Katchalsky, combined with porous media equations, are used for the LDL transport through the wall. Results are presented in terms of filtration velocity, Wall Shear Stresses (WSS) and concentration profiles. It is shown that non-Newtonian effects on mass transport are negligible for a healthy intramural pressure value. Non-Newtonian effects increase slightly with intramural pressure, but Newtonian assumption can still be considered reliable. Effects of arterial size are also analyzed, showing that Newtonian assumption can be considered valid for both medium and large arteries, in predicting LDL deposition. Finally, non-Newtonian effects are also analyzed for an aorta-common iliac bifurcation, showing that Newtonian assumption is valid for mass transport at low Reynolds numbers. At a high Reynolds number, it has been shown that a non-Newtonian fluid model can have more impact due to the presence of flow recirculation.
Nandy, S; Tarbell, J M
1987-01-01
Wall shear stress has been measured by flush-mounted hot film anemometry distal to an Ionescu-Shiley tri-leaflet valve under pulsatile flow conditions. Both Newtonian (aqueous glycerol) and non-Newtonian (aqueous polyacrylamide) blood analog fluids were investigated. Significant differences in the axial distribution of wall shear stress between the two fluids are apparent in flows having nearly identical Reynolds numbers. The Newtonian fluid exhibits a (peak) wall shear rate which is maximized near the valve seat (30 mm) and then decays to a fully developed flow value (by 106 mm). In contrast, the shear rate of the non-Newtonian fluid at 30 mm is less than half that of the Newtonian fluid and at 106 mm is more than twice that of the Newtonian fluid. It is suggested that non-Newtonian rheology influences valve flow patterns either through alterations in valve opening associated with low shear separation zones behind valve leaflets, or because of variations in the rate of jet spreading. More detailed studies are required to clarify the mechanisms. The Newtonian wall shear stresses for this valve are low. The highest value observed anywhere in the aortic chamber was 2.85 N/m2 at a peak Reynolds number of 3694.
Study of blades inclination influence of gate impeller with a non-Newtonian fluid of Bingham
NASA Astrophysics Data System (ADS)
Rahmani, Lakhdar; Seghier, O.; Draoui, B.; Benachour, E.
2016-03-01
A large number of chemical operations, biochemical or petrochemical industry is very depending on the rheological fluids nature. In this work, we study the case of highly viscous of viscoplastic fluids in a classical system of agitation: a cylindrical tank with plate bottom without obstacles agitated by gate impeller agitator. We are interested to the laminar, incompressible and isothermal flows. We devote to a numerical approach carried out using an industrial code CFD Fluent 6.3.26 based on the method of finites volumes discretization of Navier - Stokes equations formulated in variables (U.V.P). The threshold of flow related to the viscoplastic behavior is modeled by a theoretical law of Bingham. The results obtained are used to compare between the five configurations suggested of power consumption. We study the influence of inertia by the variation of Reynolds number.
Shaw, Sachin; Murthy, P V S N
2010-09-01
The present investigation deals with finding the trajectories of the drug dosed magnetic carrier particle in a microvessel with two-phase fluid model which is subjected to the external magnetic field. The radius of the microvessel is divided into the endothelial glycocalyx layer in which the blood is assumed to obey Newtonian character and a core and plug regions where the blood obeys the non-Newtonian Herschel-Bulkley character which is suitable for the microvessel of radius 50 microm. The carrier particles, bound with nanoparticles and drug molecules are injected into the vascular system upstream from malignant tissue, and captured at the tumor site using a local applied magnetic field. The applied magnetic field is produced by a cylindrical magnet positioned outside the body and near the tumor position. The expressions for the fluidic force for the carrier particle traversing in the two-phase fluid in the microvessel and the magnetic force due to the external magnetic field are obtained. Several factors that influence the magnetic targeting of the carrier particles in the microvasculature, such as the size of the carrier particle, the volume fraction of embedded magnetic nanoparticles, and the distance of separation of the magnet from the axis of the microvessel are considered in the present problem. An algorithm is given to solve the system of coupled equations for trajectories of the carrier particle in the invasive case. The trajectories of the carrier particle are found for both invasive and noninvasive targeting systems. A comparison is made between the trajectories in these cases. Also, the present results are compared with the data available for the impermeable microvessel with single-phase fluid flow. Also, a prediction of the capture of therapeutic magnetic nanoparticle in the impermeable microvasculature is made for different radii, distances and volume fractions in both the invasive and noninvasive cases.
PFG NMR and Bayesian analysis to characterise non-Newtonian fluids
NASA Astrophysics Data System (ADS)
Blythe, Thomas W.; Sederman, Andrew J.; Stitt, E. Hugh; York, Andrew P. E.; Gladden, Lynn F.
2017-01-01
Many industrial flow processes are sensitive to changes in the rheological behaviour of process fluids, and there therefore exists a need for methods that provide online, or inline, rheological characterisation necessary for process control and optimisation over timescales of minutes or less. Nuclear magnetic resonance (NMR) offers a non-invasive technique for this application, without limitation on optical opacity. We present a Bayesian analysis approach using pulsed field gradient (PFG) NMR to enable estimation of the rheological parameters of Herschel-Bulkley fluids in a pipe flow geometry, characterised by a flow behaviour index n , yield stress τ0 , and consistency factor k , by analysis of the signal in q -space. This approach eliminates the need for velocity image acquisition and expensive gradient hardware. We investigate the robustness of the proposed Bayesian NMR approach to noisy data and reduced sampling using simulated NMR data and show that even with a signal-to-noise ratio (SNR) of 100, only 16 points are required to be sampled to provide rheological parameters accurate to within 2% of the ground truth. Experimental validation is provided through an experimental case study on Carbopol 940 solutions (model Herschel-Bulkley fluids) using PFG NMR at a 1H resonance frequency of 85.2 MHz; for SNR > 1000, only 8 points are required to be sampled. This corresponds to a total acquisition time of <60 s and represents an 88% reduction in acquisition time when compared to MR flow imaging. Comparison of the shear stress-shear rate relationship, quantified using Bayesian NMR, with non-Bayesian NMR methods demonstrates that the Bayesian NMR approach is in agreement with MR flow imaging to within the accuracy of the measurement. Furthermore, as we increase the concentration of Carbopol 940 we observe a change in rheological characteristics, probably due to shear history-dependent behaviour and the different geometries used. This behaviour highlights the need for
Deformation of a Capsule in a Power-Law Shear Flow.
Tian, Fang-Bao
2016-01-01
An immersed boundary-lattice Boltzmann method is developed for fluid-structure interactions involving non-Newtonian fluids (e.g., power-law fluid). In this method, the flexible structure (e.g., capsule) dynamics and the fluid dynamics are coupled by using the immersed boundary method. The incompressible viscous power-law fluid motion is obtained by solving the lattice Boltzmann equation. The non-Newtonian rheology is achieved by using a shear rate-dependant relaxation time in the lattice Boltzmann method. The non-Newtonian flow solver is then validated by considering a power-law flow in a straight channel which is one of the benchmark problems to validate an in-house solver. The numerical results present a good agreement with the analytical solutions for various values of power-law index. Finally, we apply this method to study the deformation of a capsule in a power-law shear flow by varying the Reynolds number from 0.025 to 0.1, dimensionless shear rate from 0.004 to 0.1, and power-law index from 0.2 to 1.8. It is found that the deformation of the capsule increases with the power-law index for different Reynolds numbers and nondimensional shear rates. In addition, the Reynolds number does not have significant effect on the capsule deformation in the flow regime considered. Moreover, the power-law index effect is stronger for larger dimensionless shear rate compared to smaller values.
Chen, Kaihui; Wang, Yu; Xuan, Shouhu; Gong, Xinglong
2017-07-01
To investigate the microstructural evolution dependency on the apparent viscosity in shear-thickening fluids (STFs), a hybrid mesoscale model combined with stochastic rotation dynamics (SRD) and molecular dynamics (MD) is used. Muller-Plathe reverse perturbation method is adopted to analyze the viscosities of STFs in a two-dimensional model. The characteristic of microstructural evolution of the colloidal suspensions under different shear rate is studied. The effect of diameter of colloidal particles and the phase volume fraction on the shear thickening behavior is investigated. Under low shear rate, the two-atom structure is formed, because of the strong particle attractions in adjacent layers. At higher shear rate, the synergetic pair structure extends to layered structure along flow direction because of the increasing hydrodynamics action. As the shear rate rises continuously, the layered structure rotates and collides with other particles, then turned to be individual particles under extension or curve string structure under compression. Finally, at the highest shear rate, the strings curve more severely and get into two-dimensional cluster. The apparent viscosity of the system changes from shear-thinning behavior to the shear-thickening behavior. This work presents valuable information for further understanding the shear thickening mechanism.
Nonlinear drainage of some non-Newtonian free films
NASA Astrophysics Data System (ADS)
Tabakova, S.
2015-10-01
In the present work we apply the generalized lubrication approach (including inertial, viscous, capillary and van-der-Waals forces) to study the dynamics of a free thin film of a non-Newtonian fluid, whose viscosity is described by the Power law and Carreau models. For planar films with fully mobile surfaces, this approach leads to a system of two nonlinear PDE for the film thickness and lateral velocity. This system is solved numerically in the case of laterally bounded free films. The calculations of the film shape and velocity are presented using data of some real liquids: blood and aqueous solution of 0.5% hydroxyethylcellulose. It is shown that the Power law model predicts a very different viscosity to the Carreau model viscosity, although that the film profiles are not very different for all film wetting angles.
Weak solutions for a non-Newtonian diffuse interface model with different densities
NASA Astrophysics Data System (ADS)
Abels, Helmut; Breit, Dominic
2016-11-01
We consider weak solutions for a diffuse interface model of two non-Newtonian viscous, incompressible fluids of power-law type in the case of different densities in a bounded, sufficiently smooth domain. This leads to a coupled system of a nonhomogenouos generalized Navier-Stokes system and a Cahn-Hilliard equation. For the Cahn-Hilliard part a smooth free energy density and a constant, positive mobility is assumed. Using the {{L}∞} -truncation method we prove existence of weak solutions for a power-law exponent p>\\frac{2d+2}{d+2} , d = 2, 3.
Hydrodynamics of Newtonian and power-law fluids in microchannel with superhydrophobic wall
NASA Astrophysics Data System (ADS)
Vagner, S. A.; Patlazhan, S. A.
2016-11-01
The flow peculiarities of the Newtonian and Carreau-Yasuda power-law fluids in a microchannel with the striped superhydrophobic wall is studied numerically. The driving forces leading to deviation of streamlines from the channel axis are analyzed.
NASA Astrophysics Data System (ADS)
Boyko, Evgeniy; Bercovici, Moran; Gat, Amir
2016-11-01
We analyze flow of a non-Newtonian fluid in a Hele-Shaw cell, subjected to spatially non-uniform electroosmotic flow. We specifically focus on power-law fluids with wall depletion properties and derive a p-Poisson equation governing the pressure field, as well as a set of linearized equations representing its asymptotic approximation for weakly non-Newtonian behavior. To investigate the effect of non-Newtonian properties on the resulting fluidic pressure and velocity, we consider several configurations in one and two dimensions, and calculate both exact and approximate solutions. We show that the asymptotic approximation is in good agreement with exact solutions even for fluids with significant non-Newtonian behavior. The asymptotic model thus enables prediction of the flow and pressure fields for non-Newtonian fluids, and may be particularly useful for the analysis and design of microfluidic systems involving electro-kinetic transport of such fluids.
Yang, Chun; Tang, Dalin; Yuan, Chun; Hatsukami, Thomas S; Zheng, Jie; Woodard, Pamela K
2007-01-01
It has been recognized that fluid-structure interactions (FSI) play an important role in cardiovascular disease initiation and development. However, in vivo MRI multi-component FSI models for human carotid atherosclerotic plaques with bifurcation and quantitative comparisons of FSI models with fluid-only or structure-only models are currently lacking in the literature. A 3D non-Newtonian multi-component FSI model based on in vivo/ex vivo MRI images for human atherosclerotic plaques was introduced to investigate flow and plaque stress/strain behaviors which may be related to plaque progression and rupture. Both artery wall and plaque components were assumed to be hyperelastic, isotropic, incompressible and homogeneous. Blood flow was assumed to be laminar, non-Newtonian, viscous and incompressible. In vivo/ex vivo MRI images were acquired using histologically-validated multi-spectral MRI protocols. The 3D FSI models were solved and results were compared with those from a Newtonian FSI model and wall-only/fluid-only models. A 145% difference in maximum principal stresses (Stress-P(1)) between the FSI and wall-only models and 40% difference in flow maximum shear stress (MSS) between the FSI and fluid-only models were found at the throat of the plaque using a severe plaque sample (70% severity by diameter). Flow maximum shear stress (MSS) from the rigid wall model is much higher (20-40% in maximum MSS values, 100-150% in stagnation region) than those from FSI models.
NASA Astrophysics Data System (ADS)
Başağaoğlu, Hakan; Harwell, John R.; Nguyen, Hoa; Succi, Sauro
2017-04-01
Significant improvements in the computational performance of the lattice-Boltzmann (LB) model, coded in FORTRAN90, were achieved through application of enhancement techniques. Applied techniques include optimization of array memory layouts, data structure simplification, random number generation outside the simulation thread(s), code parallelization via OpenMP, and intra- and inter-timestep task pipelining. Effectiveness of these optimization techniques was measured on three benchmark problems: (i) transient flow of multiple particles in a Newtonian fluid in a heterogeneous fractured porous domain, (ii) thermal fluctuation of the fluid at the sub-micron scale and the resultant Brownian motion of a particle, and (iii) non-Newtonian fluid flow in a smooth-walled channel. Application of the aforementioned optimization techniques resulted in an average 21 × performance improvement, which could significantly enhance practical uses of the LB models in diverse applications, focusing on the fate and transport of nano-size or micron-size particles in non-Newtonian fluids.
Analysis of electroosmotic flow of power-law fluids in a slit microchannel.
Zhao, Cunlu; Zholkovskij, Emilijk; Masliyah, Jacob H; Yang, Chun
2008-10-15
Electroosmotic flow of power-law fluids in a slit channel is analyzed. The governing equations including the linearized Poisson-Boltzmann equation, the Cauchy momentum equation, and the continuity equation are solved to seek analytical expressions for the shear stress, dynamic viscosity, and velocity distribution. Specifically, exact solutions of the velocity distributions are explicitly found for several special values of the flow behavior index. Furthermore, with the implementation of an approximate scheme for the hyperbolic cosine function, approximate solutions of the velocity distributions are obtained. In addition, a generalized Smoluchowski velocity is introduced by taking into account contributions due to the finite thickness of the electric double layer and the flow behavior index of power-law fluids. Calculations are performed to examine the effects of kappaH, flow behavior index, double layer thickness, and applied electric field on the shear stress, dynamic viscosity, velocity distribution, and average velocity/flow rate of the electroosmotic flow of power-law fluids.
Interception efficiency in flow of power-law fluids past confined porous bodies
NASA Astrophysics Data System (ADS)
Shahsavari, Setareh; McKinley, Gareth
2014-11-01
Understanding the flow of power-law fluids through porous media is important for a wide range of filtration and sedimentation processes. In this study, the mobility of power-law fluids through porous media is investigated numerically and we use parametric studies to systematically understand the individual roles of geometrical characteristics, rheological properties as well as flow conditions. In addition, an analytical solution is presented that can be used as a modified Darcy law for generalized Newtonian fluids. Building on this modified Darcy law, the incompressible laminar flow of power-law and Carreau fluids past a confined porous body is modeled numerically. From the simulations we calculate the flow interception efficiency, which provides a measure of the fraction of streamlines that intercept a porous collector. Finally, the interception efficiency of power-law fluids are compared with the case of a Newtonian fluid. The focus of this work is principally for flow of inelastic fluids in fibrous media; however, the methodology can also be extended to other porous media.
NASA Astrophysics Data System (ADS)
Hu, Bin; Kieweg, Sarah
2010-11-01
Gravity-driven thin film flow down an incline is studied for optimal design of polymeric drug delivery vehicles, such as anti-HIV topical microbicides. We develop a 3D FEM model using non-Newtonian mechanics to model the flow of gels in response to gravity, surface tension and shear-thinning. Constant volume setup is applied within the lubrication approximation scope. The lengthwise profiles of the 3D model agree with our previous 2D finite difference model, while the transverse contact line patterns of the 3D model are compared to the experiments. With incorporation of surface tension, capillary ridges are observed at the leading front in both 2D and 3D models. Previously published studies show that capillary ridge can amplify the fingering instabilities in transverse direction. Sensitivity studies (2D & 3D) and experiments are carried out to describe the influence of surface tension and shear-thinning on capillary ridge and fingering instabilities.
NASA Astrophysics Data System (ADS)
Ramachandra Prasad, V.; Gaffar, S. Abdul; Keshava Reddy, E.; Bég, O. Anwar
2014-07-01
Polymeric enrobing flows are important in industrial manufacturing technology and process systems. Such flows are non-Newtonian. Motivated by such applications, in this article we investigate the nonlinear steady state boundary layer flow, heat, and mass transfer of an incompressible Jefferys non-Newtonian fluid past a vertical porous plate in a non-Darcy porous medium. The transformed conservation equations are solved numerically subject to physically appropriate boundary conditions using a versatile, implicit, Keller-box finite-difference technique. The numerical code is validated with previous studies. The influence of a number of emerging non-dimensional parameters, namely Deborah number (De), Darcy number (Da), Prandtl number (Pr), ratio of relaxation to retardation times (λ), Schmidt number (Sc), Forchheimer parameter (Λ), and dimensionless tangential coordinate (ξ) on velocity, temperature, and concentration evolution in the boundary layer regime are examined in detail. Furthermore, the effects of these parameters on surface heat transfer rate, mass transfer rate, and local skin friction are also investigated. It is found that the boundary layer flow is decelerated with increasing De and Forchheimer parameter, whereas temperature and concentration are elevated. Increasing λ and Da enhances the velocity but reduces the temperature and concentration. The heat transfer rate and mass transfer rates are found to be depressed with increasing De and enhanced with increasing λ. Local skin friction is found to be decreased with a rise in De, whereas it is elevated with increasing λ. An increasing Sc decreases the velocity and concentration but increases temperature.
Walker, Andrew M; Johnston, Clifton R; Rival, David E
2012-11-01
Although deployed in the vasculature to expand vessel diameter and improve blood flow, protruding stent struts can create complex flow environments associated with flow separation and oscillating shear gradients. Given the association between magnitude and direction of wall shear stress (WSS) and endothelial phenotype expression, accurate representation of stent-induced flow patterns is critical if we are to predict sites susceptible to intimal hyperplasia. Despite the number of stents approved for clinical use, quantification on the alteration of hemodynamic flow parameters associated with the Gianturco Z-stent is limited in the literature. In using experimental and computational models to quantify strut-induced flow, the majority of past work has assumed blood or representative analogs to behave as Newtonian fluids. However, recent studies have challenged the validity of this assumption. We present here the experimental quantification of flow through a Gianturco Z-stent wire in representative Newtonian and non-Newtonian blood analog environments using particle image velocimetry (PIV). Fluid analogs were circulated through a closed flow loop at physiologically appropriate flow rates whereupon PIV snapshots were acquired downstream of the wire housed in an acrylic tube with a diameter characteristic of the carotid artery. Hemodynamic parameters including WSS, oscillatory shear index (OSI), and Reynolds shear stresses (RSS) were measured. Our findings show that the introduction of the stent wire altered downstream hemodynamic parameters through a reduction in WSS and increases in OSI and RSS from nonstented flow. The Newtonian analog solution of glycerol and water underestimated WSS while increasing the spatial coverage of flow reversal and oscillatory shear compared to a non-Newtonian fluid of glycerol, water, and xanthan gum. Peak RSS were increased with the Newtonian fluid, although peak values were similar upon a doubling of flow rate. The introduction of the
NASA Astrophysics Data System (ADS)
Najjari, Mohammad Reza; Plesniak, Michael W.
2016-06-01
Steady flow and physiological pulsatile flow in a rigid 180° curved tube are investigated using particle image velocimetry. A non-Newtonian blood-analog fluid is used, and in-plane primary and secondary velocity fields are measured. A vortex detection scheme ( d 2-method) is applied to distinguish vortical structures. In the pulsatile flow case, four different vortex types are observed in secondary flow: deformed-Dean, Dean, Wall and Lyne vortices. Investigation of secondary flow in multiple cross sections suggests the existence of vortex tubes. These structures split and merge over time during the deceleration phase and in space as flow progresses along the 180° curved tube. The primary velocity data for steady flow conditions reveal additional vortices rotating in a direction opposite to Dean vortices—similar to structures observed in pulsatile flow—if the Dean number is sufficiently high.
Contact Line Instability of Gravity-Driven Flow of Power-Law Fluids.
Hu, Bin; Kieweg, Sarah L
2015-11-01
The moving contact line of a thin fluid film can often corrugate into fingers, which is also known as a fingering instability. Although the fingering instability of Newtonian fluids has been studied extensively, there are few studies published on contact line fingering instability of non-Newtonian fluids. In particular, it is still unknown how shear-thinning rheological properties can affect the formation, growth, and shape of a contact line instability. Our previous study (Hu and Kieweg, 2012) showed a decreased capillary ridge formation for more shear-thinning fluids in a 2D model (i.e. 1D thin film spreading within the scope of lubrication theory). Those results motivated this study's hypothesis: more shear-thinning fluids should have suppressed finger growth and longer finger wavelength, and this should be evident in linear stability analysis (LSA) and 3D (i.e. 2D spreading) numerical simulations. In this study, we developed a LSA model for the gravity-driven flow of shear-thinning films, and carried out a parametric study to investigate the impact of shear-thinning on the growth rate of the emerging fingering pattern. A fully 3D model was also developed to compare and verify the LSA results using single perturbations, and to explore the result of multiple-mode, randomly imposed perturbations. Both the LSA and 3D numerical results confirmed that the contact line fingers grow faster for Newtonian fluids than the shear-thinning fluids on both vertical and inclined planes. In addition, both the LSA and 3D model indicated that the Newtonian fluids form fingers with shorter wavelengths than the shear-thinning fluids when the plane is inclined; no difference in the most unstable (i.e. emerging) wavelength was observed at vertical. This study also showed that the distance between emerging fingers was smaller on a vertical plane than on a less-inclined plane for shear-thinning fluids, as previously shown for Newtonian fluids. For the first time for shear
NASA Astrophysics Data System (ADS)
Shit, G. C.; Mondal, A.; Sinha, A.; Kundu, P. K.
2016-11-01
A mathematical model has been developed for studying the electro-osmotic flow and heat transfer of bio-fluids in a micro-channel in the presence of Joule heating effects. The flow of bio-fluid is governed by the non-Newtonian power-law fluid model. The effects of thermal radiation and velocity slip condition have been examined in the case of hydrophobic channel. The Poisson-Boltzmann equation governing the electrical double layer field and a body force generated by the applied electric potential field are taken into consideration. The results presented here pertain to the case where the height of the channel is much greater than the thickness of electrical double layer comprising the Stern and diffuse layers. The expressions for flow characteristics such as velocity, temperature, shear stress and Nusselt number have been derived analytically under the purview of the present model. The results estimated on the basis of the data available in the existing scientific literatures are presented graphically. The effects of thermal radiation have an important bearing on the therapeutic procedure of hyperthermia, particularly in understanding the heat transfer in micro-channel in the presence of electric potential. The dimensionless Joule heating parameter has a reducing impact on Nusselt number for both pseudo-plastic and dilatant fluids, nevertheless its impact on Nusselt number is more pronounced for dilatant fluid. Furthermore, the effect of viscous dissipation has a significant role in controlling heat transfer and should not be neglected.
Deformation of a Capsule in a Power-Law Shear Flow
2016-01-01
An immersed boundary-lattice Boltzmann method is developed for fluid-structure interactions involving non-Newtonian fluids (e.g., power-law fluid). In this method, the flexible structure (e.g., capsule) dynamics and the fluid dynamics are coupled by using the immersed boundary method. The incompressible viscous power-law fluid motion is obtained by solving the lattice Boltzmann equation. The non-Newtonian rheology is achieved by using a shear rate-dependant relaxation time in the lattice Boltzmann method. The non-Newtonian flow solver is then validated by considering a power-law flow in a straight channel which is one of the benchmark problems to validate an in-house solver. The numerical results present a good agreement with the analytical solutions for various values of power-law index. Finally, we apply this method to study the deformation of a capsule in a power-law shear flow by varying the Reynolds number from 0.025 to 0.1, dimensionless shear rate from 0.004 to 0.1, and power-law index from 0.2 to 1.8. It is found that the deformation of the capsule increases with the power-law index for different Reynolds numbers and nondimensional shear rates. In addition, the Reynolds number does not have significant effect on the capsule deformation in the flow regime considered. Moreover, the power-law index effect is stronger for larger dimensionless shear rate compared to smaller values. PMID:27840656
Mobility of power-law and Carreau fluids through fibrous media.
Shahsavari, Setareh; McKinley, Gareth H
2015-12-01
The flow of generalized Newtonian fluids with a rate-dependent viscosity through fibrous media is studied, with a focus on developing relationships for evaluating the effective fluid mobility. Three methods are used here: (i) a numerical solution of the Cauchy momentum equation with the Carreau or power-law constitutive equations for pressure-driven flow in a fiber bed consisting of a periodic array of cylindrical fibers, (ii) an analytical solution for a unit cell model representing the flow characteristics of a periodic fibrous medium, and (iii) a scaling analysis of characteristic bulk parameters such as the effective shear rate, the effective viscosity, geometrical parameters of the system, and the fluid rheology. Our scaling analysis yields simple expressions for evaluating the transverse mobility functions for each model, which can be used for a wide range of medium porosity and fluid rheological parameters. While the dimensionless mobility is, in general, a function of the Carreau number and the medium porosity, our results show that for porosities less than ɛ≃0.65, the dimensionless mobility becomes independent of the Carreau number and the mobility function exhibits power-law characteristics as a result of the high shear rates at the pore scale. We derive a suitable criterion for determining the flow regime and the transition from a constant viscosity Newtonian response to a power-law regime in terms of a new Carreau number rescaled with a dimensionless function which incorporates the medium porosity and the arrangement of fibers.
NASA Astrophysics Data System (ADS)
Goloshevsky, A. G.; Walton, J. H.; Shutov, M. V.; de Ropp, J. S.; Collins, S. D.; McCarthy, M. J.
2005-02-01
This work reports on applications of a miniaturized RF coil combined with a capillary tube for the design of a portable on-line/in-line magnetic resonance imaging (MRI) based viscometer. A microfabricated Helmholtz RF coil with the average diameter of 7 mm and a Teflon tube with ID = 1.02 mm were utilized. Tube flows of two aqueous CMC polymer solutions (2% with MW = 250k and 1% with MW = 700k) of different viscosities at 1.99 µL s-1 volumetric flow rate were monitored. It was shown that the RF coil and the capillary permit measurement of shear thinning phenomena during flow. A constitutive power law model was used to analyse the tube flows. Viscosity was successfully measured for both the CMC solutions. The less viscous CMC solution was found to have the power index n = 0.77 ± 0.06 and the flow consistency coefficient K = 1.68, whereas the more viscous CMC solution exhibited n = 0.5 ± 0.03 and K = 7.23. The MRI measurements compared well with measurements of the same samples performed on a conventional rotational rheometer. The range of shear rates covered by the obtained MRI viscosity data was 3-20 s-1.
Exact solutions for the flow of non-Newtonian fluid with fractional derivative in an annular pipe
NASA Astrophysics Data System (ADS)
Tong, Dengke; Wang, Ruihe; Yang, Heshan
2005-08-01
This paper deals with some unsteady unidirectional transient flows of Oldroyd-B fluid in an annular pipe. The fractional calculus approach in the constitutive relationship model Oldroyd-B fluid is introduced and a generalized Jeffreys model with the fractional calculus has been built. Exact solutions of some unsteady flows of Oldroyd-B fluid in an annular pipe are obtained by using Hankel transform and Laplace transform for fractional calculus. The following four problems have been studied: (1) Poiseuille flow due to a constant pressure gradient; (2) axial Couette flow in an annulus; (3) axial Couette flow in an annulus due to a longitudinal constant shear; (4) Poiseuille flow due to a constant pressure gradient and a longitudinal constant shear. The well-known solutions for Navier-Stokes fluid, as well as those corresponding to a Maxwell fluid and a second grade one, appear as limited cases of our solutions.
Theory of creeping gravity currents of a non-Newtonian liquid
Gratton, Julio; Minotti, Fernando; Mahajan, Swadesh M.
1999-12-01
Recently several experiments on creeping gravity currents have been performed, using highly viscous silicone oils and putties. The interpretation of the experiments relies on the available theoretical results that were obtained by means of the lubrication approximation with the assumption of a Newtonian rheology. Since very viscous fluids are usually non-Newtonian, an extension of the theory to include non-Newtonian effects is needed. We derive the governing equations for unidirectional and axisymmetric creeping gravity currents of a non-Newtonian liquid with a power-law rheology, generalizing the usual lubrication approximation. The equations differ from those for Newtonian liquids, being nonlinear in the spatial derivative of the thickness of the current. Similarity solutions for currents whose volume varies as a power of time are obtained. For the spread of a constant volume of liquid, analytic solutions are found that are in good agreement with experiment. We also derive solutions of the waiting-time type, as well as those describing steady flows from a constant source to a sink. General traveling-wave solutions are given, and analytic formulas for a simple case are derived. A phase plane formalism that allows the systematic derivation of self-similar solutions is introduced. The application of the Boltzmann transform is briefly discussed. All the self-similar solutions obtained here have their counterparts in Newtonian flows, as should be expected because the power-law rheology involves a single-dimensional parameter as the Newtonian constitutive relation. Thus one finds similarity solutions whenever the analogous Newtonian problem is self-similar, but now the spreading relations are rheology-dependent. In most cases this dependence is weak but leads to significant differences easily detected in experiments. The present results may also be of interest for geophysics since the lithosphere deforms according to an average power-law rheology. (c) 1999 The American
NASA Astrophysics Data System (ADS)
Aranda, Alfredo; Amigo, Nicolás; Ihle, Christian; Tamburrino, Aldo
2016-06-01
A method based on digital image correlation (DIC) is implemented for measuring the height of the roll waves developed in a non-Newtonian fluid flowing on an inclined channel. A projector and a high-resolution digital camera, placed vertically above the fluid surface, are used to project and record a random speckle pattern located on the free liquid surface, where the pattern is deformed due to the developed roll waves. According to the experimental geometry, the height of the roll waves associated to the out-of-plane deformation of the dots is obtained through a quantitative relationship between the experimental parameters and the in-plane displacement field in the flow direction. In terms of this, the out-of-plane deformation is found using a DIC criterion based on the speckle comparison between a reference image without the deformed pattern and an image with a deformed pattern. The maximum height of the roll waves computed with this technique is compared with the height measured using a lateral camera, with both results differing by <10% over the set of experimental instances.
Slip-flow and heat transfer of a non-newtonian nanofluid in a microtube.
Niu, Jun; Fu, Ceji; Tan, Wenchang
2012-01-01
The slip-flow and heat transfer of a non-Newtonian nanofluid in a microtube is theoretically studied. The power-law rheology is adopted to describe the non-Newtonian characteristics of the flow, in which the fluid consistency coefficient and the flow behavior index depend on the nanoparticle volume fraction. The velocity profile, volumetric flow rate and local Nusselt number are calculated for different values of nanoparticle volume fraction and slip length. The results show that the influence of nanoparticle volume fraction on the flow of the nanofluid depends on the pressure gradient, which is quite different from that of the Newtonian nanofluid. Increase of the nanoparticle volume fraction has the effect to impede the flow at a small pressure gradient, but it changes to facilitate the flow when the pressure gradient is large enough. This remarkable phenomenon is observed when the tube radius shrinks to micrometer scale. On the other hand, we find that increase of the slip length always results in larger flow rate of the nanofluid. Furthermore, the heat transfer rate of the nanofluid in the microtube can be enhanced due to the non-Newtonian rheology and slip boundary effects. The thermally fully developed heat transfer rate under constant wall temperature and constant heat flux boundary conditions is also compared.
Jin, L.; Chenevert, M.E. . Dept. of Petroleum Engineering)
1994-03-01
Aqueous solutions of different concentrations of three polymers: a synthetic high molecular weight polymer, partially hydrolyzed polyacrylamide (PHPA), a xanthan-type biopolymer (Xanvis), and a cellulose-type polymer (HEC) were investigated in this study. It was found that the steric arrangement of molecules or interactions between molecules can be detected by a systematically designed strain and frequency sweep measurement, and is reflected by the different relaxation times of the solutions. The degree of elasticity can be quantified by G[prime]/[vert bar]G*[vert bar] in linear viscoelastic range. The responses of the fluids to frequency sweeps are displayed in a normalized moduli versus normalized frequency pattern derived from the Maxwell model. Results show that within the tested concentration ranges, PHPA solutions are highly elastic with moderate relaxation times that are strain and concentration insensitive. Xanvis solutions are also highly elastic, but with high relaxation times that are both strain and concentration sensitive, indicating a different mechanism of elasticity compared to PHPA solutions. HEC (cellulose derivatives) are mostly viscous shear thinning fluids with weak elasticity and short relaxation times that are insensitive to strain, but sensitive to concentration.
Forces acting on a stationary sphere in power-law fluid flow near the wall
NASA Astrophysics Data System (ADS)
Bocharov, O. B.; Kushnir, D. Yu.
2016-01-01
The analysis and evaluation of the forces acting on the particle in a linear shear flow of power-law fluid (PLF) in the presence of the wall were performed. Using the results of a series of computations for a model problem with a spherical particle near a flat wall in the Reynolds number range of 0-200 and the distance to the wall from 0 to 20 particle diameters, the correlation formulas for calculating the coefficients of drag force and lift force were obtained. Special attention was paid to the behavior of the forces acting on the particle approaching the wall.
Spin-coating process evolution and reproducibility for power-law fluids.
Jardim, P L G; Michels, A F; Horowitz, F
2014-03-20
A distinct development of an exact analytical solution for power-law fluids during the spin-coating process is presented for temporal and spatial thickness evolution, after steady state conditions are attained. This solution leads to the definition of a characteristic time, related to the memory of the initial thickness profile. Previously obtained experimental data, for several rotation speeds and carboxymetilcellulose concentrations in water, are quantitatively analyzed through the evaluation of their characteristic times and compared with theoretical predictions, thus allowing better understanding of thickness profile evolution and of process reproducibility.
Inelastic non-Newtonian flow over heterogeneously slippery surfaces.
Haase, A Sander; Wood, Jeffery A; Sprakel, Lisette M J; Lammertink, Rob G H
2017-02-01
In this study, we investigated inelastic non-Newtonian fluid flow over heterogeneously slippery surfaces. First, we simulated the flow of aqueous xanthan gum solutions over a bubble mattress, which is a superhydrophobic surface consisting of transversely positioned no-slip walls and no-shear gas bubbles. The results reveal that for shear-thinning fluids wall slip can be increased significantly, provided that the system is operated in the shear-thinning regime. For a 0.2 wt% xanthan gum solution with a power-law index of n=0.4, the numerical results indicate that wall slip can be enhanced 3.2 times when compared to a Newtonian liquid. This enhancement factor was also predicted from a theoretical analysis, which gave an expression for the maximum slip length that can be attained over flat, heterogeneously slippery surfaces. Although this equation was derived for a no-slip/no-shear unit length that is much larger than the typical size of the system, we found that it can also be used to predict the enhancement in the regime where the slip length is proportional to the size of the no-shear region or the bubble width. The results could be coupled to the hydrodynamic development or entrance length of the system, as maximum wall slip is only reached when the fluid flow can fully adapt to the no-slip and no-shear conditions at the wall.
Inelastic non-Newtonian flow over heterogeneously slippery surfaces
NASA Astrophysics Data System (ADS)
Haase, A. Sander; Wood, Jeffery A.; Sprakel, Lisette M. J.; Lammertink, Rob G. H.
2017-02-01
In this study, we investigated inelastic non-Newtonian fluid flow over heterogeneously slippery surfaces. First, we simulated the flow of aqueous xanthan gum solutions over a bubble mattress, which is a superhydrophobic surface consisting of transversely positioned no-slip walls and no-shear gas bubbles. The results reveal that for shear-thinning fluids wall slip can be increased significantly, provided that the system is operated in the shear-thinning regime. For a 0.2 wt% xanthan gum solution with a power-law index of n =0.4 , the numerical results indicate that wall slip can be enhanced 3.2 times when compared to a Newtonian liquid. This enhancement factor was also predicted from a theoretical analysis, which gave an expression for the maximum slip length that can be attained over flat, heterogeneously slippery surfaces. Although this equation was derived for a no-slip/no-shear unit length that is much larger than the typical size of the system, we found that it can also be used to predict the enhancement in the regime where the slip length is proportional to the size of the no-shear region or the bubble width. The results could be coupled to the hydrodynamic development or entrance length of the system, as maximum wall slip is only reached when the fluid flow can fully adapt to the no-slip and no-shear conditions at the wall.
Vertical-channel free convection with a power-law fluid
Irvine, T.F. Jr.; Wu, K.C.; Schneider, W.J.
1982-01-01
A finite-difference solution is presented of the velocity and temperature fields for the flow of an Ostwald-de-Waele (power law) fluid between two vertical isothermal parallel plates under the influence of free convection. Two quantities are of particular interest: the total heat transferred from the plates and the average velocity between the plates. Although these quantities can be presented in a dimensionless manner as related to the generalized Grashof and Prandtl numbers, there is an important difference compared to the similar problem involving Newtonian fluids. In the present case, the generalized Prandtl number is not a fluid property but contains a geometric factor and thus the geometry of the system must be specified before the Prandtl number is fixed. The results and the manner in which they can be used are illustrated by a numerical example.
Sinking of spherical slablets through a non-Newtonian mantle
NASA Astrophysics Data System (ADS)
Stegman, D. R.; Crameri, F.; Petersen, R. I.; Tackley, P. J.
2013-12-01
The dominant driving force for plate tectonics is slab pull, in which sinking slabs pull the trailing plate. Forward plate velocities are typically similar in magnitude (7 cm/yr) as estimates for sinking velocities of slabs through the upper mantle. However, these estimates are based on data for slabs that are coherent into the transition zone as well as models that considered the upper mantle to be entirely Newtonian. Dislocation creep in the upper mantle can strongly influence mantle flow, and is likely activated for flow around vertically sinking slabs in the uppermost mantle. Thus, it is possible that in some scenarios, a non-Newtonian mantle will have an influence on plate motions but it is unclear to what degree. To address this question, we investigate how the non-Newtonian rheology modifies the sinking velocities of slablets (spherical, negatively buoyant and highly viscous blobs). The model set-up is similar to a Stokes sphere sinking, but is in 2-D cartesian with temperature-and stress-dependent rheology. For these numerical models, we use the StagYY code and also includes a pseudo-free surface (';sticky air') with a thin surface thermal boundary. The sinking blob is both highly viscous and compositionally dense, but is the same temperature as the background fluid which eliminates thermal diffusion and associated variations in thermal buoyancy. The model domain is 2x1 and allows enough distance to the sidewalls so that sinking velocites are not influenced by the boundary conditions. We compare our results with those previously obtained for salt diapirs rising through a power-law rheology mantle/crust (Weinberg, 1993; Weinberg and Podladchikov, 1994) which provided both numerical and analytic results. Previous results indicate a speed-up of an order of magnitude is possible. We then extend the models and analysis to mantle convection systems that include for single-sided subduction. Surface plate motions are driven by the subducting slabs to which they are
NASA Astrophysics Data System (ADS)
Jiao, Chengru; Zheng, Liancun; Ma, Lianxi
2015-08-01
This paper studies the magnetohydrodynamic (MHD) thermosolutal Marangoni convection heat and mass transfer of power-law fluids driven by a power law temperature and a power law concentration which is assumed that the surface tension varies linearly with both the temperature and concentration. Heat and mass transfer constitutive equation is proposed based on N-diffusion proposed by Philip and the abnormal convection-diffusion model proposed by Pascal in which we assume that the heat diffusion depends non-linearly on both the temperature and the temperature gradient and the mass diffusion depends non-linearly on both the concentration and the concentration gradient with modified Fourier heat conduction for power law fluid. The governing equations are reduced to nonlinear ordinary differential equations by using suitable similarity transformations. Approximate analytical solution is obtained using homotopy analytical method (HAM). The transport characteristics of velocity, temperature and concentration fields are analyzed in detail.
Contracting bubbles in Hele-Shaw cells with a power-law fluid
NASA Astrophysics Data System (ADS)
McCue, Scott W.; King, John R.
2011-02-01
The problem of bubble contraction in a Hele-Shaw cell is studied for the case in which the surrounding fluid is of power-law type. A small perturbation of the radially symmetric problem is first considered, focussing on the behaviour just before the bubble vanishes, it being found that for shear-thinning fluids the radially symmetric solution is stable, while for shear-thickening fluids the aspect ratio of the bubble boundary increases. The borderline (Newtonian) case considered previously is neutrally stable, the bubble boundary becoming elliptic in shape with the eccentricity of the ellipse depending on the initial data. Further light is shed on the bubble contraction problem by considering a long thin Hele-Shaw cell: for early times the leading-order behaviour is one-dimensional in this limit; however, as the bubble contracts its evolution is ultimately determined by the solution of a Wiener-Hopf problem, the transition between the long thin limit and the extinction limit in which the bubble vanishes being described by what is in effect a similarity solution of the second kind. This same solution describes the generic (slit-like) extinction behaviour for shear-thickening fluids, the interface profiles that generalize the ellipses that characterize the Newtonian case being constructed by the Wiener-Hopf calculation.
NASA Astrophysics Data System (ADS)
Afify, Ahmed A.; El-Aziz, Mohamed Abd
2017-02-01
The steady two-dimensional flow and heat transfer of a non-Newtonian power-law nanofluid over a stretching surface under convective boundary conditions and temperature-dependent fluid viscosity has been numerically investigated. The power-law rheology is adopted to describe non-Newtonian characteristics of the flow. Four different types of nanoparticles, namely copper (Cu), silver (Ag), alumina (Al 2 O 3) and titanium oxide (TiO 2) are considered by using sodium alginate (SA) as the base non-Newtonian fluid. Lie symmetry group transformations are used to convert the boundary layer equations into non-linear ordinary differential equations. The transformed equations are solved numerically by using a shooting method with fourth-order Runge-Kutta integration scheme. The results show that the effect of viscosity on the heat transfer rate is remarkable only for relatively strong convective heating. Moreover, the skin friction coefficient and the rate of heat transfer increase with an increase in Biot number.
Particle capture in axial magnetic filters with power law flow model
NASA Astrophysics Data System (ADS)
Abbasov, T.; Herdem, S.; Köksal, M.
1999-05-01
A theory of capture of magnetic particle carried by laminar flow of viscous non-Newtonian (power law) fluid in axially ordered filters is presented. The velocity profile of the fluid flow is determined by the Kuwabara-Happel cell model. For the trajectory of the particle, the capture area and the filter performance simple analytical expressions are obtained. These expressions are valid for particle capture processes from both Newtonian and non-Newtonian fluids. For this reason the obtained theoretical results make it possible to widen the application of high-gradient magnetic filtration (HGMF) to other industrial areas. For Newtonian fluids the theoretical results are shown to be in good agreement with the experimental ones reported in the literature.
Edited by Guenther, Chris; Garg, Rahul
2013-08-19
The Department of Energy’s (DOE) National Energy Technology Laboratory (NETL) sponsored a workshop on non-Newtonian multiphase slurry at NETL’s Morgantown campus August 19 and 20, 2013. The objective of this special two-day meeting of 20-30 invited experts from industry, National Labs and academia was to identify and address technical issues associated with handling non-Newtonian multiphase slurries across various facilities managed by DOE. Particular emphasis during this workshop was placed on applications managed by the Office of Environmental Management (EM). The workshop was preceded by two webinars wherein personnel from ORP and NETL provided background information on the Hanford WTP project and discussed the critical design challenges facing this project. In non-Newtonian fluids, viscosity is not constant and exhibits a complex dependence on applied shear stress or deformation. Many applications under EM’s tank farm mission involve non-Newtonian slurries that are multiphase in nature; tank farm storage and handling, slurry transport, and mixing all involve multiphase flow dynamics, which require an improved understanding of the mechanisms responsible for rheological changes in non-Newtonian multiphase slurries (NNMS). To discuss the issues in predicting the behavior of NNMS, the workshop focused on two topic areas: (1) State-of-the-art in non-Newtonian Multiphase Slurry Flow, and (2) Scaling up with Confidence and Ensuring Safe and Reliable Long-Term Operation.
Experiments on densely-loaded non-Newtonian slurries in laminar and turbulent pipe flows
NASA Astrophysics Data System (ADS)
Mannheimer, R. J.; Grimley, T. A.; Park, J. T.; Morrow, T. B.
1987-04-01
The structure of non-Newtonian slurries in laminar, transitional, and turbulent flow regimes in pipes is studied. Experiments are conducted in a large-scale pipe slurry flow facility with an inside pipe diameter of 51 mm. Flow measurements including turbulence quantities such as Reynolds stress are taken with a two-component laser-Doppler velocimeter in a transparent test section with a transparent model slurry. Two transparent model slurries have been developed with non-Newtonian rheological properties. Silica gel particles with diameters on the order of one micron are suspended in two different hydrocarbon liquid mixtures with viscosities of 1.19 and 6.39 cS. In rheological measurements with a concentric cylinder viscometer, slurries from both liquid mixtures exhibited slip. From a linear regression analysis with a power-law model, slurries with the higher viscosity fluid had yield values of 80 and 30 dyn/sq cm for silica gel concentrations of 5.6 and 4.0% by weight, respectively, and the exponents were 0.584 and 0.763. The measured refractive index for the transparent slurries is 1.454 where the difference in refractive index between the fluid and silica gel is estimated to be less than 0.001. Bench scale tests with large diameter silica gel particles on the order of 100 microns have produced slurries with excessive turbidity. A silica gel manufactured by a different process which may form a less turbid slurry is currently under investigation.
Soulis, Johannes V; Giannoglou, George D; Chatzizisis, Yiannis S; Seralidou, Kypriani V; Parcharidis, George E; Louridas, George E
2008-01-01
The capabilities and limitations of various molecular viscosity models, in the left coronary arterial tree, were analyzed via: molecular viscosity, local and global non-Newtonian importance factors, wall shear stress (WSS) and wall shear stress gradient (WSSG). The vessel geometry was acquired using geometrically correct 3D intravascular ultrasound (3D IVUS). Seven non-Newtonian molecular viscosity models, plus the Newtonian one, were compared. The WSS distribution yielded a consistent LCA pattern for nearly all non-Newtonian models. High molecular viscosity, low WSS and low WSSG values occurred at the outer walls of the major bifurcation in proximal LCA regions. The Newtonian blood flow was found to be a good approximation at mid- and high-strain rates. The non-Newtonian Power Law, Generalized Power Law, Carreau and Casson and Modified Cross blood viscosity models gave comparable molecular viscosity, WSS and WSSG values. The Power Law and Walburn-Schneck models over-estimated the non-Newtonian global importance factor I(G) and under-estimated the area averaged WSS and WSSG values. The non-Newtonian Power Law and the Generalized Power Law blood viscosity models were found to approximate the molecular viscosity and WSS calculations in a more satisfactory way.
Turbulence modeling based on non-Newtonian constitutive laws
NASA Astrophysics Data System (ADS)
Mompean, G.; Qiu, X.; Schmitt, F. G.; Thompson, R.
2011-12-01
This work revisits the analogy between Newtonian turbulence and non-Newtonian laminar flows. Several direct numerical simulations (DNS) data of a plane channel flow, for a large range of Reynolds numbers (180 <= Reτ <= 2000) were explored. The profiles of mean velocity and second moment quantities were used to extract viscometric functions in the non-Newtonian modeling framework. The Reynolds stress tensor is expressed in terms of a set of basis kinematic tensors based on a projection of a nonlinear framework. The coefficients of the model are given as functions of the intensity of the mean strain tensor. The apparent eddy turbulent viscosity, the first and second normal stress differences are presented as function of the shear rate. One of the advantages of the new algebraic nonlinear power law constitutive equation derived in the paper, is that is only dependent on the mean velocity gradient and can be integrated up to the wall.
Reduced viscosity interpreted for fluid/gas mixtures
NASA Technical Reports Server (NTRS)
Lewis, D. H.
1981-01-01
Analysis predicts decrease in fluid viscosity by comparing pressure profile of fluid/gas mixture with that of power-law fluid. Fluid is taken to be viscous, non-Newtonian, and incompressible; the gas to be ideal; the flow to be inertia-free, isothermal, and one dimensional. Analysis assists in design of flow systems for petroleum, coal, polymers, and other materials.
Soulis, Johannes V.; Fytanidis, Dimitrios K.; Lampri, Olga P.; Giannoglou, George D.
2016-01-01
Background The temporal variation of the hemodynamic mechanical parameters during cardiac pulse wave is considered as an important atherogenic factor. Applying non-Newtonian blood molecular viscosity simulation is crucial for hemodynamic analysis. Understanding low density lipoprotein (LDL) distribution in relation to flow parameters will possibly spot the prone to atherosclerosis aorta regions. Methods The biomechanical parameters tested were averaged wall shear stress (AWSS), oscillatory shear index (OSI) and relative residence time (RRT) in relation to the LDL concentration. Four non-Newtonian molecular viscosity models and the Newtonian one were tested for the normal human aorta under oscillating flow. The analysis was performed via computational fluid dynamic. Results Tested viscosity blood flow models for the biomechanical parameters yield a consistent aorta pattern. High OSI and low AWSS develop at the concave aorta regions. This is most noticeable in downstream flow region of the left subclavian artery and at concave ascending aorta. Concave aorta regions exhibit high RRT and elevated LDL. For the concave aorta site, the peak LDL value is 35.0% higher than its entrance value. For the convex site, it is 18.0%. High LDL endothelium regions located at the aorta concave site are well predicted with high RRT. Conclusions We are in favor of using the non-Newtonian power law model for analysis. It satisfactorily approximates the molecular viscosity, WSS, OSI, RRT and LDL distribution. Concave regions are mostly prone to atherosclerosis. The flow biomechanical factor RRT is a relatively useful tool for identifying the localization of the atheromatic plaques of the normal human aorta. PMID:28197271
Physiological non-Newtonian blood flow through single stenosed artery
NASA Astrophysics Data System (ADS)
Mamun, Khairuzzaman; Rahman, Mohammad Matiur; Akhter, Most. Nasrin; Ali, Mohammad
2016-07-01
A numerical simulation to investigate the Non-Newtonian modelling effects on physiological flows in a three dimensional idealized artery with a single stenosis of 85% severity. The wall vessel is considered to be rigid. Oscillatory physiological and parabolic velocity profile has been imposed for inlet boundary condition. Where the physiological waveform is performed using a Fourier series with sixteen harmonics. The investigation has a Reynolds number range of 96 to 800. Low Reynolds number k - ω model is used as governing equation. The investigation has been carried out to characterize two Non-Newtonian constitutive equations of blood, namely, (i) Carreau and (ii) Cross models. The Newtonian model has also been investigated to study the physics of fluid. The results of Newtonian model are compared with the Non-Newtonian models. The numerical results are presented in terms of pressure, wall shear stress distributions and the streamlines contours. At early systole pressure differences between Newtonian and Non-Newtonian models are observed at pre-stenotic, throat and immediately after throat regions. In the case of wall shear stress, some differences between Newtonian and Non-Newtonian models are observed when the flows are minimum such as at early systole or diastole.
Muehlhausen, M-P; Janoske, U; Oertel, H
2015-03-01
Although image-based methods like MRI are well-developed, numerical simulation can help to understand human heart function. This function results from a complex interplay of biochemistry, structural mechanics, and blood flow. The complexity of the entire system often causes one of the three parts to be neglected, which limits the truth to reality of the reduced model. This paper focuses on the interaction of myocardial stress distribution and ventricular blood flow during diastole and systole in comparison to a simulation of the same patient-specific geometry with a given wall movement (Spiegel, Strömungsmechanischer Beitrag zur Planung von Herzoperationen, 2009). The orthotropic constitutive law proposed by Holzapfel et al. (Philos. Trans. R. Soc. Lond. Ser. A, 367:3445-3475, 2009) was implemented in a finite element package to model the passive behavior of the myocardium. Then, this law was modified for contraction. Via the ALE method, the structural model was coupled to a flow model which incorporates blood rheology and the circulatory system (Oertel, Prandtl-Essentials of Fluid Mechanics, 3rd edn, Springer Science + Business Media, 2010; Oertel et al., Modelling the Human Cardiac Fluid Mechanics, 3rd edn, Universitätsverlag Karlsruhe, 2009). Comparison reveals a good quantitative and qualitative agreement with respect to fluid flow. The motion of the myocardium is consistent with physiological observations. The calculated stresses and the distribution are within the physiological range and appear to be reasonable. The coupled model presented contains many features essential to cardiac function. It is possible to calculate wall stresses as well as the characteristic ventricular fluid flow. Based on the simulations we derive two characteristics to assess the health state quantitatively including solid and fluid mechanical aspects.
Amiri Delouei, A; Nazari, M; Kayhani, M H; Succi, S
2014-05-01
In this study, the immersed boundary-thermal lattice Boltzmann method has been used to simulate non-Newtonian fluid flow over a heated circular cylinder. The direct-forcing algorithm has been employed to couple the off-lattice obstacles and on-lattice fluid nodes. To investigate the effect of boundary sharpness, two different diffuse interface schemes are considered to interpolate the velocity and temperature between the boundary and computational grid points. The lattice Boltzmann equation with split-forcing term is applied to consider the effects of the discrete lattice and the body force to the momentum flux, simultaneously. A method for calculating the Nusselt number based on diffuse interface schemes is developed. The rheological and thermal properties of non-Newtonian fluids are investigated under the different power-law indices and Reynolds numbers. The effect of numerical parameters on the accuracy of the proposed method has been investigated in detail. Results show that the rheological and thermal properties of non-Newtonian fluids in the presence of a heated immersed body can be suitably captured using the immersed boundary thermal lattice Boltzmann method.
Bleyer, J; Coussot, P
2014-06-01
We study the flow, through a model two-dimensional porous medium, of Newtonian fluids, power-law fluids, and viscoplastic fluids in the laminar regime and with moderate or dominant effects of the yielding term. A numerical technique able to take properly into account yielding effects in viscoplastic flows without any regularization is used to determine the detailed flow characteristics. We show that as soon as the distance between the disks forming the porous medium is sufficiently small, the velocity field and in particular the distribution function of the velocity of these different fluids in a wide range of flow regimes are similar. Moreover, the volume fraction of fluid at rest is negligible even at low flow rate. Thus the non-Newtonian character of a fluid flowing through such a complex geometry tends to be broken. We suggest that this is due to the fact that in a flow through a channel of rapidly varying cross section, the deformation, and thus the flow field, is imposed on the fluid, a situation that is encountered almost everywhere in a porous medium. These results make it possible to deduce a general expression for Darcy's law of these fluid types and estimate the parameters appearing in this expression.
Fluid physics phenomena of resistojet thrusters
NASA Technical Reports Server (NTRS)
DeWitt, Kenneth J. (Principal Investigator)
1996-01-01
This final report includes a list of publications and part of an M.S. thesis titled 'Analyses in Theoretical and Experimental Fluid Flow', by Tony G. Howell. The thesis discusses analyses of momentum and heat transfer occurring in a laminar boundary layer of a non-Newtonian power-law fluid, and experiments completed in a simulated space thruster's plume for prediction comparison.
Brey, J Javier; Ruiz-Montero, M J
2015-01-01
The hydrodynamic part of the velocity autocorrelation function of a granular fluid in the homogeneous cooling state has been calculated by using mode-coupling theory for a finite system with periodic boundary conditions. The existence of the shearing instability, leading to a divergent behavior of the velocity flow fluctuations, is taken into account. A time region in which the velocity autocorrelation function exhibits a power-law decay, when time is measured by the number of collisions per particle, has been been identified. Also the explicit form of the exponential asymptotic long time decay has been obtained. The theoretical prediction for the power-law decay is compared with molecular dynamics simulation results, and a good agreement is found, after taking into account finite size corrections. The effects of approaching the shearing instability are also explored.
NASA Astrophysics Data System (ADS)
Mezzasalma, Stefano A.
2000-08-01
A theory is presented to describe the apparent viscosity of thixotropic fluids as a function of the rate of shear. It represents the extension of a semiclassical approach that was previously formulated to deal with matter densification phenomena in solids starting from the state equation of the medium. In this context, the Debye expression for the Helmholtz free energy has been provided with a density of vibrational modes that accounts for atomic and microstructural changes occurring at the frequency scale of momentum transport (see diffusion). Working out the steady-state condition with respect to time gives an equation relating reduced apparent viscosity (η˜) and shear rate (γ˜) through the temperature value (θ*) that is energetically equivalent to the medium vibrations implied. Viscosity also turns out to depend on the Debye temperature θD (see φ˜θ*/θD) and an equivalent Gruneisen parameter (μ), defined with respect to viscosity variations. Increasing φ in pseudoplastic and dilatant media, respectively, increases and decreases η˜, which always increases with increasing μ. The analogy between dilatancy/sintering and pseudoplasticity/desintering is suggested, and a correspondence between matter and momentum transports is traced on the basis of the phononic spectrum properties. Application to experimental measurements are presented and discussed for aqueous monodispersions of polystyrene (PS) latex particles, aqueous glycerol solutions of partially hydrolyzed polyacrylamide (PHPAA) at different sodium chloride (NaCl) concentrations, polymethylmethacrylate (PMMA) suspensions in dioctylphthalate (DOP), and for a molecularly thin liquid film of octamethylciclotetrasiloxane (OMCTS). Best fit coefficients for φ and μ have been constrained to the Debye temperature and the effective low-shear viscosity (η0) according to their dependences upon the suspended volume fraction (φ), θD=θD(φ), and η0=η0(φ), and the agreement with experimental data is
Sliding friction in the hydrodynamic lubrication regime for a power-law fluid
NASA Astrophysics Data System (ADS)
Warren, P. B.
2017-02-01
A scaling analysis is undertaken for the load balance in sliding friction in the hydrodynamic lubrication regime, with a particular emphasis on power-law shear-thinning typical of a structured liquid. It is argued that the shear-thinning regime is mechanically unstable if the power-law index n < 1/2, where n is the exponent that relates the shear stress to the shear rate. Consequently the Stribeck (friction) curve should be discontinuous, with possible hysteresis. Further analysis suggests that normal stress and flow transience (stress overshoot) do not destroy this basic picture, although they may provide stabilising mechanisms at higher shear rates. Extensional viscosity is also expected to be insignificant unless the Trouton ratio is large. A possible application to shear thickening in non-Brownian particulate suspensions is indicated.
Numerical simulation of the non-Newtonian mixing layer
NASA Technical Reports Server (NTRS)
Azaiez, Jalel; Homsy, G. M.
1993-01-01
This work is a continuing effort to advance our understanding of the effects of polymer additives on the structures of the mixing layer. In anticipation of full nonlinear simulations of the non-Newtonian mixing layer, we examined in a first stage the linear stability of the non-Newtonian mixing layer. The results of this study show that, for a fluid described by the Oldroyd-B model, viscoelasticity reduces the instability of the inviscid mixing layer in a special limit where the ratio (We/Re) is of order 1 where We is the Weissenberg number, a measure of the elasticity of the flow, and Re is the Reynolds number. In the present study, we pursue this project with numerical simulations of the non-Newtonian mixing layer. Our primary objective is to determine the effects of viscoelasticity on the roll-up structure. We also examine the origin of the numerical instabilities usually encountered in the simulations of non-Newtonian fluids.
Numerical simulation of non-Newtonian blood flow dynamics in human thoracic aorta.
Caballero, A D; Laín, S
2015-08-01
Three non-Newtonian blood viscosity models plus the Newtonian one are analysed for a patient-specific thoracic aorta anatomical model under steady-state flow conditions via wall shear stress (WSS) distribution, non-Newtonian importance factors, blood viscosity and shear rate. All blood viscosity models yield a consistent WSS distribution pattern. The WSS magnitude, however, is influenced by the model used. WSS is found to be the lowest in the vicinity of the three arch branches and along the distal walls of the branches themselves. In this region, the local non-Newtonian importance factor and the blood viscosity are elevated, and the shear rate is low. The present study revealed that the Newtonian assumption is a good approximation at mid-and-high flow velocities, as the greater the blood flow, the higher the shear rate near the arterial wall. Furthermore, the capabilities of the applied non-Newtonian models appeared at low-flow velocities. It is concluded that, while the non-Newtonian power-law model approximates the blood viscosity and WSS calculations in a more satisfactory way than the other non-Newtonian models at low shear rates, a cautious approach is given in the use of this blood viscosity model. Finally, some preliminary transient results are presented.
NASA Astrophysics Data System (ADS)
Deyranlou, Amin; Niazmand, Hamid; Sadeghi, Mahmood-Reza; Mesri, Yaser
2016-06-01
Blood non-Newtonian behavior on low-density lipoproteins (LDL) accumulation is analyzed numerically, while fluid-multilayered arteries are adopted for nonstenotic and 30%-60% symmetrical stenosed models. Present model considers non-Newtonian effects inside the lumen and within arterial layers simultaneously, which has not been examined in previous studies. Navier-Stokes equations are solved along with the mass transport convection-diffusion equations and Darcy’s model for species transport inside the luminal flow and across wall layers, respectively. Carreau model for the luminal flow and the modified Darcy equation for the power-law fluid within arterial layers are employed to model blood rheological characteristics, appropriately. Results indicate that in large arteries with relatively high Reynolds number Newtonian model estimates LDL concentration patterns well enough, however, this model seriously incompetent for regions with low WSS. Moreover, Newtonian model for plasma underestimates LDL concentration especially on luminal surface and across arterial wall. Therefore, applying non-Newtonian model seems essential for reaching to a more accurate estimation of LDL distribution in the artery. Finally, blood flow inside constricted arteries demonstrates that LDL concentration patterns along the stenoses inside the luminal flow and across arterial layers are strongly influenced as compared to the nonstenotic arteries. Additionally, among four stenosis severity grades, 40% stenosis is prone to more LDL accumulation along the post-stenotic regions.
NASA Technical Reports Server (NTRS)
Yuen, D. A.; Schubert, G.
1976-01-01
Stress is placed on the temperature dependence of both a linear Newtonian rheology and a nonlinear olivine rheology in accounting for narrow mantle flow structures. The boundary-layer theory developed incorporates an arbitrary temperature-dependent power-law rheology for the medium, in order to facilitate the study of mantle plume dynamics under real conditions. Thermal, kinematic, and dynamic structures of mantle plumes are modelled by a two-dimensional natural-convection boundary layer rising in a fluid with a temperature-dependent power-law relationship between shear stress and strain rate. An analytic similarity solution is arrived at for upwelling adjacent to a vertical isothermal stress-free plane. Newtonian creep as a deformation mechanism, thermal anomalies resulting from chemical heterogeneity, the behavior of plumes in non-Newtonian (olivine) mantles, and differences in the dynamics of wet and dry olivine are discussed.
Trejo-Soto, C; Costa-Miracle, E; Rodriguez-Villarreal, I; Cid, J; Castro, M; Alarcon, T; Hernandez-Machado, A
2017-04-04
We introduce a new framework to study the non-Newtonian behaviour of fluids at the microscale based on the analysis of front advancement. We apply this methodology to study the non-linear rheology of blood in microchannels. We carry out experiments in which the non-linear viscosity of blood samples is quantified at different haematocrits and ages. Under these conditions, blood exhibits a power-law dependence on the shear rate. In order to analyse our experimental data, we put forward a scaling theory which allows us to define an adhesion scaling number. This theory yields a scaling behaviour of the viscosity expressed as a function of the adhesion capillary number. By applying this scaling theory to samples of different ages, we are able to quantify how the characteristic adhesion energy varies as time progresses. This connection between microscopic and mesoscopic properties allows us to estimate quantitatively the change in the cell-cell adhesion energies as the sample ages.
NASA Astrophysics Data System (ADS)
Amiri Delouei, A.; Nazari, M.; Kayhani, M. H.; Kang, S. K.; Succi, S.
2016-04-01
In the current study, a direct-forcing immersed boundary-non-Newtonian lattice Boltzmann method (IB-NLBM) is developed to investigate the sedimentation and interaction of particles in shear-thinning and shear-thickening fluids. In the proposed IB-NLBM, the non-linear mechanics of non-Newtonian particulate flows is detected by combination of the most desirable features of immersed boundary and lattice Boltzmann methods. The noticeable roles of non-Newtonian behavior on particle motion, settling velocity and generalized Reynolds number are investigated by simulating benchmark problem of one-particle sedimentation under the same generalized Archimedes number. The effects of extra force due to added accelerated mass are analyzed on the particle motion which have a significant impact on shear-thinning fluids. For the first time, the phenomena of interaction among the particles, such as Drafting, Kissing, and Tumbling in non-Newtonian fluids are investigated by simulation of two-particle sedimentation and twelve-particle sedimentation. The results show that increasing the shear-thickening behavior of fluid leads to a significant increase in the kissing time. Moreover, the transverse position of particles for shear-thinning fluids during the tumbling interval is different from Newtonian and the shear-thickening fluids. The present non-Newtonian particulate study can be applied in several industrial and scientific applications, like the non-Newtonian sedimentation behavior of particles in food industrial and biological fluids.
Sinking of spherical slablets through a non-Newtonian mantle
NASA Astrophysics Data System (ADS)
Crameri, Fabio; Stegman, Dave; Petersen, Robert; Tackley, Paul
2014-05-01
The dominant driving force for plate tectonics is slab pull, in which sinking slabs pull the trailing plate. Forward plate velocities are typically similar in magnitude (7 cm/yr) as estimates for sinking velocities of slabs through the upper mantle. However, these estimates are based on data for slabs that are coherent into the transition zone as well as models that considered the upper mantle to be entirely Newtonian. Dislocation creep in the upper mantle can strongly influence mantle flow, and is likely activated for flow around vertically sinking slabs in the uppermost mantle. Thus, it is possible that in some scenarios, a non-Newtonian mantle will have an influence on plate motions but it is unclear to what degree. To address this question, we investigate how the non-Newtonian rheology modifies the sinking velocities of slablets (spherical, negatively buoyant and highly viscous blobs). The model set-up is similar to a Stokes sphere sinking, but is in 2-D cartesian with temperature-and stress-dependent rheology. For these numerical models, we use the Stag-YY code (e.g., Tackley 2008) and apply a pseudo-free surface using the 'sticky-air' approach (Matsumoto and Tomoda 1983; Schmeling et al, 2008, Crameri et al., 2012). The sinking blob is both highly viscous and compositionally dense, but is the same temperature as the background fluid which eliminates thermal diffusion and associated variations in thermal buoyancy. The model domain is 2x1 or 4x1 and allows enough distance to the sidewalls so that sinking velocities are not influenced by the boundary conditions. We compare our results with those previously obtained for salt diapirs rising through a power-law rheology mantle/crust (Weinberg, 1993; Weinberg and Podladchikov, 1994), which provided both numerical and analytic results. Previous results indicate a speed-up of an order of magnitude is possible. Finally, we then extend the models and analysis to mantle convection systems that include for single
NASA Astrophysics Data System (ADS)
Bouteraa, Mondher; Nouar, Chérif
2015-12-01
Finite-amplitude thermal convection in a shear-thinning fluid layer between two horizontal plates of finite thermal conductivity is considered. Weakly nonlinear analysis is adopted as a first approach to investigate nonlinear effects. The rheological behavior of the fluid is described by the Carreau model. As a first step, the critical conditions for the onset of convection are computed as a function of the ratio ξ of the thermal conductivity of the plates to the thermal conductivity of the fluid. In agreement with the literature, the critical Rayleigh number Rac and the critical wave number kc decrease from 1708 to 720 and from 3.11 to 0, when ξ decreases from infinity to zero. In the second step, the critical value αc of the shear-thinning degree above which the bifurcation becomes subcritical is determined. It is shown that αc increases with decreasing ξ . The stability of rolls and squares is then investigated as a function of ξ and the rheological parameters. The limit value ξc, below which squares are stable, decreases with increasing shear-thinning effects. This is related to the fact that shear-thinning effects increase the nonlinear interactions between sets of rolls that constitute the square patterns [M. Bouteraa et al., J. Fluid Mech. 767, 696 (2015), 10.1017/jfm.2015.64]. For a significant deviation from the critical conditions, nonlinear convection terms and nonlinear viscous terms become stronger, leading to a further diminution of ξc. The dependency of the heat transfer on ξ and the rheological parameters is reported. It is consistent with the maximum heat transfer principle. Finally, the flow structure and the viscosity field are represented for weakly and highly conducting plates.
Bouteraa, Mondher; Nouar, Chérif
2015-12-01
Finite-amplitude thermal convection in a shear-thinning fluid layer between two horizontal plates of finite thermal conductivity is considered. Weakly nonlinear analysis is adopted as a first approach to investigate nonlinear effects. The rheological behavior of the fluid is described by the Carreau model. As a first step, the critical conditions for the onset of convection are computed as a function of the ratio ξ of the thermal conductivity of the plates to the thermal conductivity of the fluid. In agreement with the literature, the critical Rayleigh number Ra(c) and the critical wave number k(c) decrease from 1708 to 720 and from 3.11 to 0, when ξ decreases from infinity to zero. In the second step, the critical value α(c) of the shear-thinning degree above which the bifurcation becomes subcritical is determined. It is shown that α(c) increases with decreasing ξ. The stability of rolls and squares is then investigated as a function of ξ and the rheological parameters. The limit value ξ(c), below which squares are stable, decreases with increasing shear-thinning effects. This is related to the fact that shear-thinning effects increase the nonlinear interactions between sets of rolls that constitute the square patterns [M. Bouteraa et al., J. Fluid Mech. 767, 696 (2015)]. For a significant deviation from the critical conditions, nonlinear convection terms and nonlinear viscous terms become stronger, leading to a further diminution of ξ(c). The dependency of the heat transfer on ξ and the rheological parameters is reported. It is consistent with the maximum heat transfer principle. Finally, the flow structure and the viscosity field are represented for weakly and highly conducting plates.
Allouche, M H; Millet, S; Botton, V; Henry, D; Ben Hadid, H; Rousset, F
2015-12-01
Squire's theorem, which states that the two-dimensional instabilities are more dangerous than the three-dimensional instabilities, is revisited here for a flow down an incline, making use of numerical stability analysis and Squire relationships when available. For flows down inclined planes, one of these Squire relationships involves the slopes of the inclines. This means that the Reynolds number associated with a two-dimensional wave can be shown to be smaller than that for an oblique wave, but this oblique wave being obtained for a larger slope. Physically speaking, this prevents the possibility to directly compare the thresholds at a given slope. The goal of the paper is then to reach a conclusion about the predominance or not of two-dimensional instabilities at a given slope, which is of practical interest for industrial or environmental applications. For a Newtonian fluid, it is shown that, for a given slope, oblique wave instabilities are never the dominant instabilities. Both the Squire relationships and the particular variations of the two-dimensional wave critical curve with regard to the inclination angle are involved in the proof of this result. For a generalized Newtonian fluid, a similar result can only be obtained for a reduced stability problem where some term connected to the perturbation of viscosity is neglected. For the general stability problem, however, no Squire relationships can be derived and the numerical stability results show that the thresholds for oblique waves can be smaller than the thresholds for two-dimensional waves at a given slope, particularly for large obliquity angles and strong shear-thinning behaviors. The conclusion is then completely different in that case: the dominant instability for a generalized Newtonian fluid flowing down an inclined plane with a given slope can be three dimensional.
NASA Astrophysics Data System (ADS)
Allouche, M. H.; Millet, S.; Botton, V.; Henry, D.; Ben Hadid, H.; Rousset, F.
2015-12-01
Squire's theorem, which states that the two-dimensional instabilities are more dangerous than the three-dimensional instabilities, is revisited here for a flow down an incline, making use of numerical stability analysis and Squire relationships when available. For flows down inclined planes, one of these Squire relationships involves the slopes of the inclines. This means that the Reynolds number associated with a two-dimensional wave can be shown to be smaller than that for an oblique wave, but this oblique wave being obtained for a larger slope. Physically speaking, this prevents the possibility to directly compare the thresholds at a given slope. The goal of the paper is then to reach a conclusion about the predominance or not of two-dimensional instabilities at a given slope, which is of practical interest for industrial or environmental applications. For a Newtonian fluid, it is shown that, for a given slope, oblique wave instabilities are never the dominant instabilities. Both the Squire relationships and the particular variations of the two-dimensional wave critical curve with regard to the inclination angle are involved in the proof of this result. For a generalized Newtonian fluid, a similar result can only be obtained for a reduced stability problem where some term connected to the perturbation of viscosity is neglected. For the general stability problem, however, no Squire relationships can be derived and the numerical stability results show that the thresholds for oblique waves can be smaller than the thresholds for two-dimensional waves at a given slope, particularly for large obliquity angles and strong shear-thinning behaviors. The conclusion is then completely different in that case: the dominant instability for a generalized Newtonian fluid flowing down an inclined plane with a given slope can be three dimensional.
Mathematical analysis of non-Newtonian blood flow in stenosis narrow arteries.
Sriyab, Somchai
2014-01-01
The flow of blood in narrow arteries with bell-shaped mild stenosis is investigated that treats blood as non-Newtonian fluid by using the K-L model. When skin friction and resistance of blood flow are normalized with respect to non-Newtonian blood in normal artery, the results present the effect of stenosis length. When skin friction and resistance of blood flow are normalized with respect to Newtonian blood in stenosis artery, the results present the effect of non-Newtonian blood. The effect of stenosis length and effect of non-Newtonian fluid on skin friction are consistent with the Casson model in which the skin friction increases with the increase of either stenosis length or the yield stress but the skin friction decreases with the increase of plasma viscosity coefficient. The effect of stenosis length and effect of non-Newtonian fluid on resistance of blood flow are contradictory. The resistance of blood flow (when normalized by non-Newtonian blood in normal artery) increases when either the plasma viscosity coefficient or the yield stress increases, but it decreases with the increase of stenosis length. The resistance of blood flow (when normalized by Newtonian blood in stenosis artery) decreases when either the plasma viscosity coefficient or the yield stress increases, but it decreases with the increase of stenosis length.
The extensional rheology of non-Newtonian materials
NASA Technical Reports Server (NTRS)
Spiegelberg, Stephen H.; Gaudet, Samuel; Mckinley, Gareth H.
1994-01-01
It has been proposed to measure the extensional viscosity function of a non-Newtonian polymer solution in a reduced gravity environment as part of the Advanced Fluid Module. In ground-based extensional measurements, the no-sip boundary condition at solid-fluid interfaces always result in appreciable shear gradients in the test fluid; however the removal of gravitational body forces permits controlled extensional deformation of containerless test samples and the first unambiguous measurements of this kind. Imperative to successful implementation of this experiment is the generation and subsequent deformation of a stable cylindrical column of test fluid. A study of the generation and deformation of liquid bridges demonstrates that Newtonian liquid bridges undergo capillary breakup as anticipated when stretched beyond a critical aspect ratio; non-Newtonian liquid bridges, however, are stabilized by the strain-hardening phenomenon exhibited by these materials. Numerical simulations of Newtonian breakup are compared with experimental results, and show that previous ground-based attempts at measuring the extensional viscosity of Newtonian fluids are of limited accuracy.
NASA Astrophysics Data System (ADS)
De Vita, F.; de Tullio, M. D.; Verzicco, R.
2016-04-01
This work focuses on the comparison between Newtonian and non-Newtonian blood flows through a bileaflet mechanical heart valve in the aortic root. The blood, in fact, is a concentrated suspension of cells, mainly red blood cells, in a Newtonian matrix, the plasma, and consequently its overall behavior is that of a non-Newtonian fluid owing to the action of the cells' membrane on the fluid part. The common practice, however, assumes the blood in large vessels as a Newtonian fluid since the shear rate is generally high and the effective viscosity becomes independent of the former. In this paper, we show that this is not always the case even in the aorta, the largest artery of the systemic circulation, owing to the pulsatile and transitional nature of the flow. Unexpectedly, for most of the pulsating cycle and in a large part of the fluid volume, the shear rate is smaller than the threshold level for the blood to display a constant effective viscosity and its shear thinning character might affect the system dynamics. A direct inspection of the various flow features has shown that the valve dynamics, the transvalvular pressure drop and the large-scale features of the flow are very similar for the Newtonian and non-Newtonian fluid models. On the other hand, the mechanical damage of the red blood cells (hemolysis), induced by the altered stress values in the flow, is larger for the non-Newtonian fluid model than for the Newtonian one.
Choi, Hyo Won; Barakat, Abdul I
2005-01-01
Endothelial cell (EC) responsiveness to shear stress is essential for vasoregulation and plays a role in atherogenesis. Although blood is a non-Newtonian fluid, EC flow studies in vitro are typically performed using Newtonian fluids. The goal of the present study was to determine the impact of non-Newtonian behavior on the flow field within a model flow chamber capable of producing flow disturbance and whose dimensions permit Reynolds and Womersley numbers comparable to those present in vivo. We performed two-dimensional computational fluid dynamic simulations of steady and pulsatile laminar flow of Newtonian and non-Newtonian fluids over a backward facing step. In the non-Newtonian simulations, the fluid was modeled as a shear-thinning Carreau fluid. Steady flow results demonstrate that for Re in the range 50-400, the flow recirculation zone downstream of the step is 22-63% larger for the Newtonian fluid than for the non-Newtonian fluid, while spatial gradients of shear stress are larger for the non-Newtonian fluid. In pulsatile flow, the temporal gradients of shear stress within the flow recirculation zone are significantly larger for the Newtonian fluid than for the non-Newtonian fluid. These findings raise the possibility that in regions of flow disturbance, EC mechanotransduction pathways stimulated by Newtonian and non-Newtonian fluids may be different.
Non-Newtonian effects of blood flow on hemodynamics in distal vascular graft anastomoses.
Chen, Jie; Lu, Xi-Yun; Wang, Wen
2006-01-01
Non-Newtonian fluid flow in a stenosed coronary bypass is investigated numerically using the Carreau-Yasuda model for the shear thinning behavior of the blood. End-to-side coronary bypass anastomosis is considered in a simplified model geometry where the host coronary artery has a 75% severity stenosis. Different locations of the bypass graft to the stenosis and different flow rates in the graft and in the host artery are studied. Particular attention is given to the non-Newtonian effect of the blood on the primary and secondary flow patterns in the host coronary artery and the wall shear stress (WSS) distribution there. Interaction between the jet flow from the stenosed artery and the flow from the graft is simulated by solving the three-dimensional Navier-Stokes equation coupled with the non-Newtonian constitutive model. Results for the non-Newtonian flow, the Newtonian flow and the rescaled Newtonian flow are presented. Significant differences in axial velocity profiles, secondary flow streamlines and WSS between the non-Newtonian and Newtonian fluid flows are revealed. However, reasonable agreement between the non-Newtonian and the rescaled Newtonian flows is found. Results from this study support the view that the residual flow in a partially occluded coronary artery interacts with flow in the bypass graft and may have significant hemodynamic effects in the host vessel downstream of the graft. Non-Newtonian property of the blood alters the flow pattern and WSS distribution and is an important factor to be considered in simulating hemodynamic effects of blood flow in arterial bypass grafts.
Dynamics of Non-Newtonian Liquid Droplet Collision
NASA Astrophysics Data System (ADS)
Chen, Xiaodong; Yang, Vigor
2012-11-01
Collision of Newtonian liquid droplets has been extensively investigated both experimentally and numerically for decades. Limited information, however, is available about non-Newtonian droplet collision dynamics. In the present work, high-fidelity numerical simulations were performed to study the situation associated with shear-thinning non-Newtonian liquids. The formulation is based on a complete set of conservation equations for the liquid and the surrounding gas phases. An improved volume-of-fluid (VOF) method, combined with an innovative topology-oriented adaptive mesh refinement (TOAMR) technique, was developed and implemented to track the interfacial dynamics. The complex evolution of the droplet surface over a broad range of length scales was treated accurately and efficiently. In particular, the thin gas film between two approaching droplets and subsequent breakup of liquid threads were well-resolved. Various types of droplet collision were obtained, including coalescence, bouncing, and reflexive and stretching separations. A regime diagram was developed and compared with that for Newtonian liquids. Fundamental mechanisms and key parameters that dictate droplet behaviors were identified. In addition, collision-induced atomization was addressed. This work was sponsored by the U.S. Army Research Office under the Multi-University Research Initiative under contract No. W911NF-08-1-0124. The support and encouragement provided by Dr. Ralph Anthenien are gratefully acknowledged.
Homogenization of an incompressible non-Newtonian flow through a thin porous medium
NASA Astrophysics Data System (ADS)
Anguiano, María; Suárez-Grau, Francisco Javier
2017-04-01
In this paper, we consider a non-Newtonian flow in a thin porous medium Ω _{ɛ} of thickness ɛ which is perforated by periodically solid cylinders of size a_{ɛ}. The flow is described by the 3D incompressible Stokes system with a nonlinear viscosity, being a power of the shear rate (power law) of flow index 1
Process averaging in a granular medium with non-Newtonian interlayers
NASA Astrophysics Data System (ADS)
Karakin, A. V.; Shklover, V. E.
1992-08-01
The paper is concerned with the problem of process averaging in three-component media consisting of solid grains, a non-Newtonian viscously deformable material filling the gaps between the grains, and a nonviscous liquid or a gas within the pores. The basic equations are derived in general form for an arbitrary rheological law and then further specified for a power-law rheological behavior. Macrorelations are obtained analytically and in quadratures for shear and tension/compression. A full solution is obtained for a specific type of microstructure. Some particular cases are examined.
Non-Newtonian bile flow in elastic cystic duct: one- and three-dimensional modeling.
Li, W G; Luo, X Y; Chin, S B; Hill, N A; Johnson, A G; Bird, N C
2008-11-01
Bile flow is thought to play an essential role in the pathophysiological genesis of cholelithiasis (gallstone formation) and in gallbladder pain. In this paper, we extend our previous study of the human biliary system (Li et al., 2007, J. Biomech. Eng., 129:164-173) to include two important factors: the non-Newtonian properties of bile, and elastic deformation of the cystic duct. A one-dimensional (1D) model is analyzed and compared with three-dimensional (3D) fluid-structure interaction simulations. It is found that non-Newtonian bile raises resistance to the flow of bile, which can be augmented significantly by the elastic deformation (collapse) of the cystic duct. We also show that the 1D model predicts the pressure drop of the cystic duct flow well for all cases considered (Newtonian or non-Newtonian flow, rigid or elastic ducts), when compared with the full 3D simulations.
NASA Astrophysics Data System (ADS)
Di Federico, V.; Ciriello, V.
2011-12-01
Non-Newtonian fluid flow in porous media is of considerable interest in hydrology, chemical and petroleum engineering, and biofluid mechanics. We consider an infinite porous domain of plane (d=1), cylindrical (d=2) or semi-spherical geometry (d=3), having uniform permeability k and porosity Φ, initially at uniform pressure and saturated by a weakly compressible non-Newtonian fluid, and analyze the dynamics of the pressure variation generated within the domain by an instantaneous mass injection m0 in its origin. The fluid is described by a rheological power-law model of given consistency index H and flow behavior index n; the flow law is a modified Darcy's law depending on H, Φ, n. Coupling flow law and mass balance equations yields the nonlinear partial differential equation governing the pressure field; an analytical solution is derived in space r and time t as a function of a self-similar variable η=r/tβ(n). We revisit and expand the work in previous papers by providing a dimensionless general formulation and solution to the problem for d=1,2,3. When a shear-thinning fluid (n<1) is considered, the analytical solution exhibits traveling wave characteristics, in variance with Newtonian fluids; the front velocity is proportional to t(n-2)/2 in plane geometry, t(2n-3)/(3-n) in cylindrical geometry, and t(3n-4)/(4-2n) in semi-spherical geometry. The front position is a markedly increasing function of n and is inversely dependent on d; the pressure front advances at a slower rate for larger values of compressibility, higher injected mass and lower porosity. When pressure is considered, it is seen that an increase in d from 1 to 3 brings about an order of magnitude reduction. An increase in compressibility implies a significant decrease in pressure, especially at early times. To reflect the uncertainty inherent in values of the problem parameters, we then consider selected properties of fluid (flow behavior index n) and porous domain (permeability k, porosity
A Colorful Mixing Experiment in a Stirred Tank Using Non-Newtonian Blue Maize Flour Suspensions
ERIC Educational Resources Information Center
Trujilo-de Santiago, Grissel; Rojas-de Gante, Cecillia; García-Lara, Silverio; Ballesca´-Estrada, Adriana; Alvarez, Marion Moise´s
2014-01-01
A simple experiment designed to study mixing of a material of complex rheology in a stirred tank is described. Non-Newtonian suspensions of blue maize flour that naturally contain anthocyanins have been chosen as a model fluid. These anthocyanins act as a native, wide spectrum pH indicator exhibiting greenish colors in alkaline environments, blue…
Inline Ultrasonic Rheometry of a Non-Newtonian Waste Simulant
Pfund, David M.; Pappas, Richard A.
2004-03-31
This is a discussion of non-invasive determination of the viscosity of a non-Newtonian fluid in laminar pipe flow over the range of shear rates present in the pipe. The procedure requires knowledge of the flow profile in and the pressure drop along the long straight run of pipe. The profile is determined by using a pulsed ultrasonic Doppler velocimeter. This approach is ideal for making non-invasive, real-time measurements for monitoring and control. Rheograms of a shear thinning, thixotropic gel which is often used as a Hanford waste simulant are presented. The operating parameters and limitations of the ultrasound based instrument will be discussed. The component parts of the instrument have been packaged into a unit for field use. The presentation also discusses the features and engineering optimizations done to enhance field usability of the instrument.
Effects of non Newtonian spiral blood flow through arterial stenosis
NASA Astrophysics Data System (ADS)
Hasan, Md. Mahmudul; Maruf, Mahbub Alam; Ali, Mohammad
2016-07-01
The spiral component of blood flow has both beneficial and detrimental effects in human circulatory system. A numerical investigation is carried out to analyze the effect of spiral blood flow through an axisymmetric three dimensional artery having 75% stenosis at the center. Blood is assumed as a Non-Newtonian fluid. Standard k-ω model is used for the simulation with the Reynolds number of 1000. A parabolic velocity profile with spiral flow is used as inlet boundary condition. The peak values of all velocity components are found just after stenosis. But total pressure gradually decreases at downstream. Spiral flow of blood has significant effects on tangential component of velocity. However, the effect is mild for radial and axial velocity components. The peak value of wall shear stress is at the stenosis zone and decreases rapidly in downstream. The effect of spiral flow is significant for turbulent kinetic energy. Detailed investigation and relevant pathological issues are delineated throughout the paper.
Impinging jet spray formation using non-Newtonian liquids
NASA Astrophysics Data System (ADS)
Rodrigues, Neil S.
Over the past two decades there has been a heightened interest in implementing gelled propellants for rocket propulsion, especially for hypergolic bi-propellants such as monomethylhydrazine (MMH) and nitrogen tetroxide oxidizer (NTO). Due to the very high level of toxicity of hypergolic liquid rocket propellants, increasing safety is an important area of need for continued space exploration and defense operations. Gelled propellants provide an attractive solution to meeting the requirements for safety, while also potentially improving performance. A gelling agent can be added to liquid propellants exhibiting Newtonian behavior to transform the liquid into a non-Newtonian fluid with some solid-like behavior, i.e. a gel. Non-Newtonian jet impingement is very different from its Newtonian counterpart in terms of fluid flow, atomization, and combustion. This is due to the added agents changing physical properties such as the bulk rheology (viscosity) and interfacial rheology (surface tension). Spray characterization of jet impingement with Newtonian liquids has been studied extensively in existing literature. However, there is a scarcity in literature of studies that consider the spray characterization of jet impingement with gelled propellants. This is a rather critical void since a major tradeoff of utilizing gelled propellants is the difficulty with atomization due to the increased effective viscosity. However, this difficulty can be overcome by using gels that exhibit shear-thinning behavior---viscosity decreases with increasing strain rate. Shear-thinning fluids are ideal because they have the distinct advantage of only flowing easily upon pressure. Thereby, greatly reducing the amount of propellant that could be accidentally leaked during both critical functions such as liftoff or engagement in the battlefield and regular tasks like refilling propellant tanks. This experimental work seeks to help resolve the scarcity in existing literature by providing drop size
Chen, Jie; Lu, Xi-Yun
2004-12-01
The non-Newtonian fluid flow in a bifurcation model with a non-planar daughter branch is investigated by using finite element method to solve the three-dimensional Navier-Stokes equations coupled with a non-Newtonian constitutive model, in which the shear thinning behavior of the blood fluid is incorporated by the Carreau-Yasuda model. The objective of this study is to investigate the influence of the non-Newtonian property of fluid as well as of curvature and out-of-plane geometry in the non-planar daughter vessel on wall shear stress (WSS) and flow phenomena. In the non-planar daughter vessel, the flows are typified by the skewing of the velocity profile towards the outer wall, creating a relatively low WSS at the inner wall. In the downstream of the bifurcation, the velocity profiles are shifted towards the flow divider. The low WSS is found at the inner walls of the curvature and the lateral walls of the bifurcation. Secondary flow patterns that swirl fluid from the inner wall of curvature to the outer wall in the middle of the vessel are also well documented for the curved and bifurcating vessels. The numerical results for the non-Newtonian fluid and the Newtonian fluid with original Reynolds number and the corresponding rescaled Reynolds number are presented. Significant difference between the non-Newtonian flow and the Newtonian flow is revealed; however, reasonable agreement between the non-Newtonian flow and the rescaled Newtonian flow is found. Results of this study support the view that the non-planarity of blood vessels and the non-Newtonian properties of blood are an important factor in hemodynamics and may play a significant role in vascular biology and pathophysiology.
Numerical study of purely viscous non-Newtonian flow in an abdominal aortic aneurysm.
Marrero, Victor L; Tichy, John A; Sahni, Onkar; Jansen, Kenneth E
2014-10-01
It is well known that blood has non-Newtonian properties, but it is generally accepted that blood behaves as a Newtonian fluid at shear rates above 100 s-1. However, in transient conditions, there are times and locations where the shear rate is well below 100 s-1, and it is reasonable to infer that non-Newtonian effects could become important. In this study, purely viscous non-Newtonian (generalized Newtonian) properties of blood are incorporated into the simulation-based framework for cardiovascular surgery planning developed by Taylor et al. (1999, "Predictive Medicine: Computational Techniques in Therapeutic Decision Making," Comput. Aided Surg., 4, pp. 231-247; 1998, "Finite Element Modeling of Blood Flow in Arteries," Comput. Methods Appl. Mech. Eng., 158, pp. 155-196). Equations describing blood flow are solved in a patient-based abdominal aortic aneurysm model under steady and physiological flow conditions. Direct numerical simulation (DNS) is used, and the complex flow is found to be constantly transitioning between laminar and turbulent in both the spatial and temporal sense. It is found for the case simulated that using the non-Newtonian viscosity modifies the solution in subtle ways that yield a mesh-independent solution with fewer degrees of freedom than the Newtonian counterpart. It appears that in regions of separated flow, the lower shear rate produces higher viscosity with the non-Newtonian model, which reduces the associated resolution needs. When considering the real case of pulsatile flow, high shear layers lead to greater unsteadiness in the Newtonian case relative to the non-Newtonian case. This, in turn, results in a tendency for the non-Newtonian model to need fewer computational resources even though it has to perform additional calculations for the viscosity. It is also shown that both viscosity models predict comparable wall shear stress distribution. This work suggests that the use of a non-Newtonian viscosity models may be attractive
Studying Mixing in Non-Newtonian Blue Maize Flour Suspensions Using Color Analysis
Trujillo-de Santiago, Grissel; Rojas-de Gante, Cecilia; García-Lara, Silverio; Ballescá-Estrada, Adriana; Alvarez, Mario Moisés
2014-01-01
Background Non-Newtonian fluids occur in many relevant flow and mixing scenarios at the lab and industrial scale. The addition of acid or basic solutions to a non-Newtonian fluid is not an infrequent operation, particularly in Biotechnology applications where the pH of Non-Newtonian culture broths is usually regulated using this strategy. Methodology and Findings We conducted mixing experiments in agitated vessels using Non-Newtonian blue maize flour suspensions. Acid or basic pulses were injected to reveal mixing patterns and flow structures and to follow their time evolution. No foreign pH indicator was used as blue maize flours naturally contain anthocyanins that act as a native, wide spectrum, pH indicator. We describe a novel method to quantitate mixedness and mixing evolution through Dynamic Color Analysis (DCA) in this system. Color readings corresponding to different times and locations within the mixing vessel were taken with a digital camera (or a colorimeter) and translated to the CIELab scale of colors. We use distances in the Lab space, a 3D color space, between a particular mixing state and the final mixing point to characterize segregation/mixing in the system. Conclusion and Relevance Blue maize suspensions represent an adequate and flexible model to study mixing (and fluid mechanics in general) in Non-Newtonian suspensions using acid/base tracer injections. Simple strategies based on the evaluation of color distances in the CIELab space (or other scales such as HSB) can be adapted to characterize mixedness and mixing evolution in experiments using blue maize suspensions. PMID:25401332
Dynamic viscosity measurement in non-Newtonian graphite nanofluids.
Duan, Fei; Wong, Ting Foong; Crivoi, Alexandru
2012-07-02
: The effective dynamic viscosity was measured in the graphite water-based nanofluids. The shear thinning non-Newtonian behavior is observed in the measurement. On the basis of the best fitting of the experimental data, the viscosity at zero shear rate or at infinite shear rate is determined for each of the fluids. It is found that increases of the particle volume concentration and the holding time period of the nanofluids result in an enhancement of the effective dynamic viscosity. The maximum enhancement of the effective dynamic viscosity at infinite rate of shear is more than 24 times in the nanofluids held for 3 days with the volume concentration of 4% in comparison with the base fluid. A transmission electron microscope is applied to reveal the morphology of aggregated nanoparticles qualitatively. The large and irregular aggregation of the particles is found in the 3-day fluids in the drying samples. The Raman spectra are extended to characterize the D and G peaks of the graphite structure in the nanofluids. The increasing intensity of the D peak indicates the nanoparticle aggregation growing with the higher concentration and the longer holding time of the nanofluids. The experimental results suggest that the increase on effective dynamic viscosity of nanofluids is related to the graphite nanoparticle aggregation in the fluids.
Dhar, Jayabrata; Ghosh, Uddipta; Chakraborty, Suman
2014-03-01
We study the coupled effect of electrokinetic phenomena and fluid rheology in altering the induced streaming potential in narrow fluidic confinements, which is manifested by establishing a time periodic pressure-driven flow in presence of electrical double layer phenomenon. However, in sharp contrast with reported literature, we take into account nonelectrostatic ion-ion interactions toward estimating the same in addition to electrostatic interactions and steric effects. We employ power law based rheological model for estimating the induced streaming potential. We bring out an intricate interaction between nonelectrostatic interactions and fluid rheology on the concerned electrokinetic phenomena, bearing immense consequences toward designing of integrated lab-on-a-chip-based microdevices and nanodevices.
Non-Newtonian Viscosity Modeling of Crude Oils—Comparison Among Models
NASA Astrophysics Data System (ADS)
Ramírez-González, Patsy V.; Aguayo, Juan Pablo; Quiñones-Cisneros, Sergio E.; Deiters, Ulrich K.
2009-04-01
The presence of precipitated wax or even just low temperatures may induce non-Newtonian rheological behavior in crude oils. Such behavior can be found at operating conditions, for instance, in reservoirs at deep-water conditions. Therefore, reliable rheological models for crude oils applicable over the wide range of conditions the fluid may encounter are essential for a large number of oil technology applications. Such models must also be composition dependent, as many applications require predicting the rheological behavior of the fluid under strong compositional changes, e.g., recovery applications such as vapor extraction (VAPEX) processes or blending of fluids for improved rheological characteristics for piping, among many other applications. In this study, a comparative analysis between some published models applicable to the description of the non-Newtonian behavior of crude oils is carried out. Emphasis is placed on the stability of the model predictions within the wide range of conditions that may be encountered.
Non-Newtonian Aspects of Artificial Intelligence
NASA Astrophysics Data System (ADS)
Zak, Michail
2016-05-01
The challenge of this work is to connect physics with the concept of intelligence. By intelligence we understand a capability to move from disorder to order without external resources, i.e., in violation of the second law of thermodynamics. The objective is to find such a mathematical object described by ODE that possesses such a capability. The proposed approach is based upon modification of the Madelung version of the Schrodinger equation by replacing the force following from quantum potential with non-conservative forces that link to the concept of information. A mathematical formalism suggests that a hypothetical intelligent particle, besides the capability to move against the second law of thermodynamics, acquires such properties like self-image, self-awareness, self-supervision, etc. that are typical for Livings. However since this particle being a quantum-classical hybrid acquires non-Newtonian and non-quantum properties, it does not belong to the physics matter as we know it: the modern physics should be complemented with the concept of the information force that represents a bridge to intelligent particle. As a follow-up of the proposed concept, the following question is addressed: can artificial intelligence (AI) system composed only of physical components compete with a human? The answer is proven to be negative if the AI system is based only on simulations, and positive if digital devices are included. It has been demonstrated that there exists such a quantum neural net that performs simulations combined with digital punctuations. The universality of this quantum-classical hybrid is in capability to violate the second law of thermodynamics by moving from disorder to order without external resources. This advanced capability is illustrated by examples. In conclusion, a mathematical machinery of the perception that is the fundamental part of a cognition process as well as intelligence is introduced and discussed.
Non-Newtonian Rheology of Calc-Alkaline Obsidian at High Stresses and Strain Rates
NASA Astrophysics Data System (ADS)
Dingwell, D. B.; Hess, K.; Lavallee, Y.; Cordonnier, B.; Mueller, S.
2005-12-01
The importance of the Non-Newtonian regime at high stress and strain rates has been reported for a variety of silicate melts subject to different tests but never for natural samples bearing their original contents of magmatic water and microlite content. Here, we used a unique high-load (<500 MPa), high-temperature (<1300°C) deformation apparatus for studying in situ the Non-Newtonian flow behaviour of magmas. A series of experiments were performed on calc-alkaline obsidian lavas from Lipari (Italy), Iceland, and Cougar Creek Dome, Yellowstone (USA), and compared to depolymerized melt (NIST 710). The samples were heated to relevant magmatic effusive temperatures that yielded similar relaxation timescales and were deformed under constant stress in the range of 100 to 200 MPa. The onset of the Non-Newtonian flow regime, registered by a decreasing viscosity with time (at fixed strain rate), occurred at 120 MPa for the depolymerized melt. The Non-Newtonian flow behavior was observed up to pressures as high as approx. 180 MPa, where the samples fragmented readily (hot cracking). In contrast, all three calc-alkaline rhyolitic melt remained in a Newtonian regime up to approx. 160 MPa. The window of Non-Newtonian behavior was, however, very narrow and most samples fragmented instantaneously in the attempt of pursuing the deformation. If this is not an experimental artefact, we conclude that modeling of the flow behaviour of a ascending crystal- and bubble-free calc-alkaline rhyolitic dome magma can be performed using a simple Newtonian fluid approximation. Thus the Non-Arrhenian model of Hess and Dingwell (1996) for the compositional and temperature dependence of viscosity could be applied.
Convective Instability in Ice I with Non-Newtonian Rheology: Application to the Galilean Satellites
NASA Technical Reports Server (NTRS)
Barr, A. C.; Zhong, S.; Pappalardo, R. T.
2004-01-01
At the temperatures and stresses associated with the onset of convection in an ice I shell of the Galilean satellites, ice behaves as a non-Newtonian fluid with a viscosity that depends on both temperature and strain rate. The convective stability of a non-Newtonian ice shell can be judged by comparing the Rayleigh number of the shell to a critical value. Previous studies suggest that the critical Rayleigh number for a non-Newtonian fluid depends on the initial conditions in the fluid layer, in addition to the thermal, rheological, and physical properties of the fluid. We seek to extend the existing definition of the critical Rayleigh number for a non-Newtonian, basally heated fluid by quantifying the conditions required to initiate convection in an ice I layer initially in conductive equilibrium. We find that the critical Rayleigh number for the onset of convection in ice I varies as a power (-0.6 to -0.5) of the amplitude of the initial temperature perturbation issued to the layer, when the amplitude of perturbation is less than the rheological temperature scale. For larger-amplitude perturbations, the critical Rayleigh number achieves a constant value. We characterize the critical Rayleigh number as a function of surface temperature of the satellite, melting temperature of ice, and rheological parameters so that our results may be extrapolated for use with other rheologies and for a generic large icy satellite. The values of critical Rayleigh number imply that triggering convection from a conductive equilibrium in a pure ice shell less than 100 km thick in Europa, Ganymede, or Callisto requires a large, localized temperature perturbation of a few kelvins to tens of kelvins to soften the ice and therefore may require tidal dissipation in the ice shell.
Collision Dynamics and Internal Mixing of Droplets of Non-Newtonian Liquids
NASA Astrophysics Data System (ADS)
Sun, Kai; Zhang, Peng; Law, Chung K.; Wang, Tianyou
2015-11-01
The efficient internal mixing of colliding droplets upon coalescence is critical to various technological processes such as color manipulation in ink-jet printing and the initiation of the liquid-phase reaction of gelled hypergolic propellants in rocket engines. Recognizing that such processes can be optimized by varying the impact inertia as well as employing fluids of non-Newtonian rheology, the head-on collision, coalescence, and internal mixing pattern between two impacting equal-sized droplets of non-Newtonian fluids is computationally investigated by using the lattice Boltzmann method. Results show that, with increasing non-Newtonian effects, droplet deformation and separation following coalescence is promoted for shear-thinning fluids, while permanent coalescence allowing an extended duration for mixing is promoted for shear-thickening fluids. Furthermore, large-scale internal mixing is promoted for the colliding droplets with larger shear-thinning disparity, while coalescence and mixing is synergistically facilitated for the collision between a shear-thinning droplet and a shear-thickening droplet. The individual and coupled influences of viscosity on the droplet deformation and impact inertia, internal motion, viscous loss, and merging of the colliding interfaces leading to the observed outcomes are mechanistically identified and described.
NASA Astrophysics Data System (ADS)
Babu, D. Harish; Narayana, P. V. Satya
2016-08-01
An analysis has been carried out to study the Joule heating effect on MHD heat transfer of an incompressible Jeffrey fluid due to a stretching porous sheet with power law heat flux and heat source. A constant magnetic field is applied normal to the stretching surface. The basic governing equations are reduced into the coupled nonlinear ordinary differential equations by using similarity transformations. The resulting equations are then solved numerically by shooting method with fourth order Runge-Kutta scheme. The effects of various physical parameters entering into the problem on dimensionless velocity and temperature distribution are discussed through graphs and tables. The results reveal that the momentum and thermal boundary layer thickness are significantly influenced by Deborah number (β), ratio of relaxation and retardation times parameter (λ), heat generation parameter (β*), Eckert number (Ec) and magnetic field parameter (M). A comparison with the previously published works shows excellent agreement.
Experiments on densely-loaded non-Newtonian slurries in laminar and turbulent pipe flows
NASA Astrophysics Data System (ADS)
Park, J. T.; Mannheimer, R. J.; Grimley, T. A.; Morrow, T. B.
1988-02-01
An experimental description of the flow structure of non-Newtonian slurries in the laminar, transitional, and full turbulent pipe flow regimes is the primary objective of this research. Measurements include rheological characterization of the fluid and local fluid velocity measurements with a laser Doppler velocimeter (LDV). Optical access to the flow is gained through a test section and model slurry which are both transparent. The model slurry is formulated from silica gel particles and hydrocarbon liquid mixture whose indices of refraction are matched so that light is not scattered from the particles. Experiments are being conducted in a large-scale pipe slurry flow facility with an inside pipe diameter of 51 mm (2 inches). Detailed flow measurements including turbulence quantities such as Reynolds stress were measured with a two-component two-color LDV. The present research indicates that non-Newtonian slurries are possible with concentrations of a few percent by weight of small particles whose sizes are one micron or less. A non-Newtonian slurry from small particles could maintain large particles (100 micron size) at high concentrations in suspension almost indefinitely. Such a slurry would prevent particle fallout and its associated problems. Velocity profiles were acquired by the LDV in the laminar, transitional, and turbulent flow regimes. The velocity profile for laminar flow was in agreement with theory. The range of the transition region was 21 percent of the transition velocity in comparison to 50 percent for a Newtonian fluid.
Smoothed particle hydrodynamics non-Newtonian model for ice-sheet and ice-shelf dynamics
Pan, W.; Tartakovsky, A. M.; Monaghan, J. J.
2013-06-01
Mathematical modeling of ice sheets is complicated by the non-linearity of the governing equations and boundary conditions. Standard grid-based methods require complex front tracking techniques and have limited capability to handle large material deformations and abrupt changes in bottom topography. As a consequence, numerical methods are usually restricted to shallow ice sheet and ice shelf approximations. We propose a new smoothed particle hydrodynamics (SPH) non-Newtonian model for coupled ice sheet and ice shelf dynamics. SPH, a fully Lagrangian particle method, is highly scalable and its Lagrangian nature and meshless discretization are well suited to the simulation of free surface flows, large material deformation, and material fragmentation. In this paper, SPH is used to study 3D ice sheet/ice shelf behavior, and the dynamics of the grounding line. The steady state position of the grounding line obtained from SPH simulations is in good agreement with laboratory observations for a wide range of simulated bedrock slopes, and density ratios, similar to those of ice and sea water. The numerical accuracy of the SPH algorithm is verif;ed by simulating Poiseuille flow, plane shear flow with free surface and the propagation of a blob of ice along a horizontal surface. In the laboratory experiment, the ice was represented with a viscous Newtonian fluid. In the present work, however, the ice is modeled as both viscous Newtonian fluid and non-Newtonian fluid, such that the effect of non-Newtonian rheology on the dynamics of grounding line was examined. The non-Newtonian constitutive relation is prescribed to be Glen’s law for the creep of polycrystalline ice. A V-shaped bedrock ramp is further introduced to model the real geometry of bedrock slope.
Chen, Jie; Lu, Xi-Yun
2006-01-01
The pulsatile flow of non-Newtonian fluid in a bifurcation model with a non-planar daughter branch is investigated numerically by using the Carreau-Yasuda model to take into account the shear thinning behavior of the analog blood fluid. The objective of this study is to deal with the influence of the non-Newtonian property of fluid and of out-of-plane curvature in the non-planar daughter vessel on wall shear stress (WSS), oscillatory shear index (OSI), and flow phenomena during the pulse cycle. The non-Newtonian property in the daughter vessels induces a flattened axial velocity profile due to its shear thinning behavior. The non-planarity deflects flow from the inner wall of the vessel to the outer wall and changes the distribution of WSS along the vessel, in particular in systole phase. Downstream of the bifurcation, the velocity profiles are shifted toward the flow divider, and low WSS and high shear stress temporal oscillations characterized by OSI occur on the outer wall region of the daughter vessels close to the bifurcation. Secondary motions become stronger with the addition of the out-of-plane curvature induced by the bending of the vessel, and the secondary flow patterns swirl along the non-planar daughter vessel. A significant difference between the non-Newtonian and the Newtonian pulsatile flow is revealed during the pulse cycle; however, reasonable agreement between the non-Newtonian and the rescaled Newtonian flow is found. Calculated results for the pulsatile flow support the view that the non-planarity of blood vessels and the non-Newtonian properties of blood are an important factor in hemodynamics and may play a significant role in vascular biology and pathophysiology.
NASA Technical Reports Server (NTRS)
Van Den Berg, Arie P.; Yuen, David A.; Van Keken, Peter E.
1995-01-01
Numerical simulations of mantle convection with a composite temperature-dependent, Newtonian and non-Newtonian creep law have revealed a transition in the dominant creep mechanism with the increasing vigour of convection. Newtonian creep is found to dominate in the low Rayleigh number regime. With sufficiently high effective Rayleigh number, the overall creep mechanism in the convective flow becomes non-Newtonian. The transitional Rayleigh number increases strongly with the activation energy. These results would suggest a scenario that in the early epochs of Earth the flow in the mantle would have been governed by non-Newtonian rheology and would have exhibited both strong spatial and temporal fluctuations. With time the flow mechanism would behave like a Newtonian fluid and would have a different time-dependent character. In time-dependent Newtonian-dominated flows there are still localized features with distinctly non-Newtonian character. Our analysis of the relative contributions to the lateral viscosity field supports the idea that the inference of the nature of lateral viscosity heterogeneities by seismic tomography may be strongly contaminated by the dominant non-Newtonian contributions to the total lateral viscosity field.
Experiments on densely-loaded non-Newtonian slurries in laminar and turbulent pipe flows
NASA Astrophysics Data System (ADS)
Park, J. T.; Mannheimer, R. J.; Grimley, T. A.; Morrow, T. B.
1988-05-01
An experimental description of the flow structure of non-Newtonian slurries in the laminar, transitional, and full turbulent pipe flow regimes is the primary objective of this research. Measurements include rheological characterization of the fluid and local fluid velocity measurements with a Laser Doppler Velocimeter (LDV). Optical access to the flow is gained through a test section and model slurry which are both transparent. The model slurry is formulated from silica gel particles and hydrocarbon liquid mixture whose indices of refraction are matched so that light is not scattered from the particles. Experiments are being conducted in a large-scale pipe slurry. Flow measurements including turbulence quantities such as Reynolds stress were measured with a two-component two-color LDV. The present research indicates that non-Newtonian slurries are possible with concentrations of a few percent by weight of small particles whose sizes are two microns or less. A non-Newtonian slurry from small particles could maintain large particles (one millimeter size) at high concentrations in suspension almost indefinitely. Such a slurry would prevent particle fallout and its associated problems.
Experiments on densely-loaded non-Newtonian slurries in laminar and turbulent pipe flows
NASA Astrophysics Data System (ADS)
Park, J. T.; Mannheimer, R. J.; Grimley, T. A.; Morrow, T. B.
1987-10-01
An experimental description of the flow structure of non-Newtonian slurries in the laminar, transitional, and full turbulent pipe flow regimes is the primary objective of this research. Measurements include rheological characterization of the fluid and local fluid velocity measurements with a laser Doppler velocimeter (LDV). Optical access to the flow is gained through a test section and model slurry which are both transparent. The model slurry is formulated from silica gel particles and hydrocarbon liquid mixture whose indices of refraction are matched so that light is not scattered from the particles. Experiments are being conducted in a large-scale pipe slurry flow facility with an inside pipe diameter of 51 mm (2 inches). Detailed flow measurements including turbulence quantities such as Reynolds stress will be taken with a two-component two-color LDV. The present research indicates that non-Newtonian slurries are possible with concentrations of a few percent by weight of small particles whose sizes are one micron or less. A non-Newtonian slurry from small particles could maintain large particles (100 micron size) at high concentrations in suspension almost indefinitely. Such a slurry would prevent particle fallout and its associated problems.
Minimal model for zero-inertia instabilities in shear-dominated non-Newtonian flows.
Boi, S; Mazzino, A; Pralits, J O
2013-09-01
The emergence of fluid instabilities in the relevant limit of vanishing fluid inertia (i.e., arbitrarily close to zero Reynolds number) has been investigated for the well-known Kolmogorov flow. The finite-time shear-induced order-disorder transition of the non-Newtonian microstructure and the corresponding viscosity change from lower to higher values are the crucial ingredients for the instabilities to emerge. The finite-time low-to-high viscosity change for increasing shear characterizes the rheopectic fluids. The instability does not emerge in shear-thinning or -thickening fluids where viscosity adjustment to local shear occurs instantaneously. The lack of instabilities arbitrarily close to zero Reynolds number is also observed for thixotropic fluids, in spite of the fact that the viscosity adjustment time to shear is finite as in rheopectic fluids. Renormalized perturbative expansions (multiple-scale expansions), energy-based arguments (on the linearized equations of motion), and numerical results (of suitable eigenvalue problems from the linear stability analysis) are the main tools leading to our conclusions. Our findings may have important consequences in all situations where purely hydrodynamic fluid instabilities or mixing are inhibited due to negligible inertia, as in microfluidic applications. To trigger mixing in these situations, suitable (not necessarily viscoelastic) non-Newtonian fluid solutions appear as a valid answer. Our results open interesting questions and challenges in the field of smart (fluid) materials.
NASA Astrophysics Data System (ADS)
Khojasteh, Danial; Mousavi, Seyed Mahmood; Kamali, Reza
2016-11-01
In the present study, the behaviors of Newtonian and shear-thinning non-Newtonian droplets impinging on heated hydrophilic and hydrophobic surfaces have been investigated numerically using Ansys-Fluent. In this context, the volume-of-fluid technique is applied to track the free-surface of the liquid, and variable time-step is also utilized to control the Courant number. Furthermore, we have considered the dependence of viscosity, density and surface tension on temperature during the simulation. The results are compared to available experimental data at the same conditions, such as boundary conditions. The results demonstrate that there is a good agreement between the obtained results and the experimental trends, concerning normalized diameter profiles at various Weber numbers. Therefore, the focus of the present study is an assessment of the effects of variations in Weber number, contact angle and surface temperature for Newtonian and non-Newtonian liquids on dynamics behavior of droplet in collision with hydrophobic and hydrophilic surfaces. The results represent that the behaviors of Newtonian and non-Newtonian droplets are totally different, indicating the droplet sensitivity to the working parameters.
Are Non-Newtonian Effects Important in Hemodynamic Simulations of Patients With Autogenous Fistula?
Javid Mahmoudzadeh Akherat, S M; Cassel, Kevin; Boghosian, Michael; Dhar, Promila; Hammes, Mary
2017-04-01
Given the current emphasis on accurate computational fluid dynamics (CFD) modeling of cardiovascular flows, which incorporates realistic blood vessel geometries and cardiac waveforms, it is necessary to revisit the conventional wisdom regarding the influences of non-Newtonian effects. In this study, patient-specific reconstructed 3D geometries, whole blood viscosity data, and venous pulses postdialysis access surgery are used as the basis for the hemodynamic simulations of renal failure patients with native fistula access. Rheological analysis of the viscometry data initially suggested that the correct choice of constitutive relations to capture the non-Newtonian behavior of blood is important because the end-stage renal disease (ESRD) patient cohort under observation experience drastic variations in hematocrit (Hct) levels and whole blood viscosity throughout the hemodialysis treatment. For this purpose, various constitutive relations have been tested and implemented in CFD practice, namely Quemada and Casson. Because of the specific interest in neointimal hyperplasia and the onset of stenosis in this study, particular attention is placed on differences in nonhomeostatic wall shear stress (WSS) as that drives the venous adaptation process that leads to venous geometric evolution over time in ESRD patients. Surprisingly, the CFD results exhibit no major differences in the flow field and general flow characteristics of a non-Newtonian simulation and a corresponding identical Newtonian counterpart. It is found that the vein's geometric features and the dialysis-induced flow rate have far greater influence on the WSS distribution within the numerical domain.
Microsphere interaction with non-Newtonian solid-supported films to model respiratory therapies
NASA Astrophysics Data System (ADS)
Lee, Nathan; Ally, Javed; Kappl, Michael; Butt, Hans-Jürgen
2012-10-01
Films used as lubricants and particle filters interact with microspheres. One example of a biological particle filter is the mucus lining the human respiratory system. In the conducting airways of the respiratory tract, a 10 μm thick layer of mucus sits on top of a periciliary layer. These cilia sweep the mucus towards the nose and mouth whereby debris, such as dust and bacteria that are trapped by the mucus layer, may be expelled from the body. Mucus, like other biofluids, can be modeled after a non-Newtonian fluid due to their viscoelastic properties. Interactions between particles and non-Newtonian thin films have not been widely characterized. Atomic force microscopy (AFM) is an ideal technique due to its ability to measure in the microNewtown and micrometer scale. The AFM setup also allows for calculation of the force from direct contact of the particle with the film. Data from these experiments may further the development aerosol-based respiratory therapies. Factors such as particle size and approach speed are necessary to determine improved parameters for drug deposition and retention. It is the goal of this study to analyze interaction forces between particles and non-Newtonian solid-supported films.
Mantle flow pressure and the angle of subduction - Non-Newtonian corner flows
NASA Technical Reports Server (NTRS)
Tovish, A.; Schubert, G.; Luyendyk, B. P.
1978-01-01
Corner flows of Newtonian and non-Newtonian fluids are used to model the flow in a subduction zone which is viscously driven by the motions of the converging plates and the descending slab. The pressures induced by the flow tend to lift the slab up beneath the overriding plate thereby offsetting the tendency of gravity to align the slab with the vertical. The low angles of subduction observed in Peru and Central Chile may be the result of strong dynamic pressures forcing the slab up against the overriding plate. Viscous coupling between the overriding plate and the downgoing slab is essential if the nonvertical dips of slabs are a consequence of the balance between gravitational and pressure torques. For a Newtonian mantle, shear stresses and pressures on the top of the slab are comparable. If the mantle is non-Newtonian, however, the pressures greatly exceed the shear stresses, for most acute dip angles. Thus frictional forces on the top and bottom surfaces of slabs are less important in resisting slab descent into a non-Newtonian mantle than they are in resisting penetration into a Newtonian mantle.
Investigating the impact of non-Newtonian blood models within a heart pump.
Al-Azawy, Mohammed G; Turan, A; Revell, A
2017-01-01
A detailed computational fluid dynamics (CFD) study of transient, turbulent blood flow through a positive displacement left ventricular assist device is performed. Two common models for non-Newtonian blood flow are compared to the Newtonian model to investigate their impact on predicted levels of shear rate and wall shear stress. Given that both parameters are directly relevant to the evaluation of risk from thrombus and haemolysis, there is a need to assess the sensitivity to modelling non-Newtonian flow effects within a pulsatile turbulent flow, in order to identify levels of uncertainly in CFD. To capture the effects of turbulence, the elliptic blending Reynolds stress model is used in the present study, on account of superior performance of second moment closure schemes previously identified by the present authors. The CFD configuration includes two cyclically rotating valves and a moving pusher plate to periodically vary the chamber volume. An overset mesh algorithm is used for each instance of mesh motion, and a zero gap technique was employed to ensure full valve closure. The left ventricular assist device was operated at a pumping rate of 86 BPM (beats per minute) and a systolic duration of 40% of the pumping cycle, in line with existing experimental data to which comparisons are made. The sensitivity of the variable viscosity models is investigated in terms of mean flow field, levels of turbulence and global shear rate, and a non-dimensional index is used to directly evaluate the impact of non-Newtonian effects. The clinical relevance of the results is reported along with a discussion of modelling uncertainties, observing that the turbulent kinetic energy is generally predicted to be higher in non-Newtonian flow than that observed in Newtonian flow. Copyright © 2016 John Wiley & Sons, Ltd.
NASA Astrophysics Data System (ADS)
Miklosovic, David Scott
Significant work has been done in the last 10 years to advance the technology of long-term mechanical circulatory assistance, particularly the left ventricular assist device (LVAD). Traditionally, rotary LVADs have been developed using conventional fluid dynamic design methods and Newtonian scaling laws, since non-Newtonian effects were previously assumed to be of second-order importance. To evaluate centrifugal pump performance scaling and flow patterns in a non-Newtonian fluid, the Large-Scale Rotor Testbed (LSRT) at The Ohio State University was developed to test two 9X-scale blood pump impellers in a baseline volute housing of the Innovative Ventricular Assist System (IVAS) designed by the Cleveland Clinic Foundation. Non-Newtonian fluids yielded pump performance deficits of first-order importance, or up to 11% of the Newtonian performance. Thus, the non-Newtonian effects were of the same magnitude as substantial variations in the impeller geometry. Moreover, the dimensionless pressure- and flow-coefficients showed that the non-Newtonian performance deviated from the similarity laws at critical Reynolds numbers that were 2.4--2.7 times higher than the Newtonian value of 71,000. Above the critical Reynolds number, the non-Newtonian fluids followed a similarity behavior, but it was different from the Newtonian case. The deviation increased with the magnitude of shear-thinning behavior as measured by the Weissenberg number. Shear-thinning xanthan gum solutions were used as non-Newtonian test fluids in concentrations from 0 to 1,200 ppm. Fluid samples were characterized in a Couette rheometer to determine viscosity behavior, biological degradation, and shear-induced polymer chain breakdown. The solutions proved to be stable and useful for a duration of up to two weeks of routine LSRT testing. Because the LSRT pump operates in a low-specific speed, low-flow regime, flow visualizations revealed a strong adverse pressure gradient and a prominent inverse Ekman layer in
Patil, A.G.
2000-02-01
Results of an experimental investigation of heat transfer and flow friction of a generalized power-law fluid in tape generated swirl flow inside a 25.0 mm i.d. circular tube, are presented. In order to reduce excessive pressure drops associated with full width twisted tapes, with less corresponding reduction in heat transfer coefficients, reduced width twisted tapes of widths ranging from 11.0 to 23.8 mm, which are lower than the tube inside diameter are used. Reduced width twisted tape inserts give 18%--56% lower isothermal friction factors than the full width tapes. Uniform wall temperature Nusselt numbers decrease only slightly by 5%--25%, for tape widths of 19.7 and 11.0 mm, respectively. Based on the constant pumping power criterion, the tapes of width 19.7 mm perform more or less like full width tapes. Correlations are presented for isothermal and heating friction factors and Nusselt numbers (under uniform wall temperature condition) for a fully developed laminar swirl flow, which are applicable to full width as well as reduced width twisted tapes, using a modified twist ratio as pitch to width ratio of the tape. The reduced width tapes offer 20%--50% savings in the tape material as compared to the full width tapes.
NASA Astrophysics Data System (ADS)
Khan, M.; Munir, A.; Shahzad, A.; Shah, A.
2015-03-01
A steady boundary layer flow and heat transfer over a radially stretching isothermal porous sheet is analyzed. Stretching is assumed to follow a radial power law, and the fluid is electrically conducting in the presence of a transverse magnetic field with a very small magnetic Reynolds number. The governing nonlinear partial differential equations are reduced to a system of nonlinear ordinary differential equations by using appropriate similarity transformations, which are solved analytically by the homotopy analysis method (HAM) and numerically by employing the shooting method with the adaptive Runge-Kutta method and Broyden's method in the domain [0,∞). Analytical expressions for the velocity and temperature fields are derived. The influence of pertinent parameters on the velocity and temperature profiles is discussed in detail. The skin friction coefficient and the local Nusselt number are calculated as functions of several influential parameters. The results predicted by both methods are demonstrated to be in excellent agreement. Moreover, HAM results for a particular problem are also compared with exact solutions.
NASA Astrophysics Data System (ADS)
Rabbi, Khan Md.; Shuvo, Moinuddin; Kabir, Rabiul Hasan; Mojumder, Satyajit; Saha, Sourav
2016-07-01
Mixed convection in a lid-driven square enclosure with a rotating cylinder inside has been analyzed using non-Newtonian ferrofluid (Fe3O4-water). Left vertical wall is heated while the right vertical wall is kept cold. Bottom wall and cylinder surface are assumed to be adiabatic. Top wall has a moving lid with a constant velocity U0. Galerkin method of finite element analysis has been used to solve the governing equations. Numerical accuracy of solution is ensured by the grid independency test. A variety of Richardson number (Ri = 0.1 - 10) at a governing Reynolds number (Re = 100), power law index (n = 0.5 - 1.5), rotational speed (Ω = 0 - 15) and solid volume fraction of ferrous particles (φ = 0 - 0.05) are employed for this present problem. To illustrate flow and thermal field, streamline and isotherms are included. Average Nusselt number plots are shown to show overall heat transfer rate. It is observed that better heat transfer is achieved at higher rotational speed (Ω), Richardson number (Ri) and power law index (n). This paper also concludes significant variation in streamline and isotherm patterns for higher solid volume fraction (φ) of non-Newtonian ferrofluid.
Newtonian and non-Newtonian blood flow in coiled cerebral aneurysms.
Morales, Hernán G; Larrabide, Ignacio; Geers, Arjan J; Aguilar, Martha L; Frangi, Alejandro F
2013-09-03
Endovascular coiling aims to isolate the aneurysm from blood circulation by altering hemodynamics inside the aneurysm and triggering blood coagulation. Computational fluid dynamics (CFD) techniques have the potential to predict the post-operative hemodynamics and to investigate the complex interaction between blood flow and coils. The purpose of this work is to study the influence of blood viscosity on hemodynamics in coiled aneurysms. Three image-based aneurysm models were used. Each case was virtually coiled with a packing density of around 30%. CFD simulations were performed in coiled and untreated aneurysm geometries using a Newtonian and a Non-Newtonian fluid models. Newtonian fluid slightly overestimates the intra-aneurysmal velocity inside the aneurysm before and after coiling. There were numerical differences between fluid models on velocity magnitudes in coiled simulations. Moreover, the non-Newtonian fluid model produces high viscosity (>0.007 [Pas]) at aneurysm fundus after coiling. Nonetheless, these local differences and high-viscous regions were not sufficient to alter the main flow patterns and velocity magnitudes before and after coiling. To evaluate the influence of coiling on intra-aneurysmal hemodynamics, the assumption of a Newtonian fluid can be used.
NASA Astrophysics Data System (ADS)
Botella, Olivier; Ait-Messaoud, Mazigh; Pertat, Adrien; Cheny, Yoann; Rigal, Claire
2015-04-01
This paper presents the extension of a well-established immersed boundary/cut-cell method, the LS-STAG method (Cheny and Botella in J Comput Phys 229:1043-1076, 2010), to non-Newtonian flow computations in 2D irregular geometries. One of the distinguished features of our IB method is to use level-set techniques in the cut-cells near the irregular boundary, where accurate discretization is of paramount importance for stability and accuracy of the computations. For this purpose, we present here an accurate discretization of the velocity gradients and shear rate in the cut-cells that fits elegantly in the framework of the velocity-pressure-stress staggered arrangement and the special quadratures developed previously for viscoelastic flows. After assessing the accuracy of the discretization on a benchmark solution for power-law fluids, the LS-STAG code is applied to the flow of various shear-thinning xanthan solutions in a wide-gap, non-coaxial, Taylor-Couette reactor for which rheological characterization, experimental flow measurements (PIV) and FLUENT simulations have recently been performed in our group. Our numerical investigation will give new insight on the flow patterns (onset, size and position of the recirculation zone) and will firmly correlate them to global flow properties such as shear-thinning index, generalized Reynolds number and torque ratio at the cylinders.
Non-newtonian Effects in Viscous Flows
NASA Technical Reports Server (NTRS)
Zak, Michail; Meyers, Ronald E.
1996-01-01
Revision of the mathematical formalism of fluid dynamics suggests that some physical inconsistencies (infinite time of approaching equilibrium and fully deterministic solutions to the Navier-Stokes equations) can be removed by relaxing the Lipschitz conditions, i.e., the boundedness of the derivatives, in the constitutive equations. Physically such a modification can be interpreted as an incorporation of an infinitesimal static friction in the constitutive law. A modified version of the Navier-Stokes equations is introduced, discussed, and illustrated by examples. It is demonstrated that all the new effects in the modified model emerge within vanishingly small neighborhoods of equilibrium states which are the only domains where the governing equations are different from classical.
Walker, Andrew M; Johnston, Clifton R; Rival, David E
2014-01-01
Particle image velocimetry (PIV) was used to investigate the influence of a non-Newtonian blood analog of aqueous xanthan gum on flow separation in laminar and transitional environments and in both steady and pulsatile flow. Initial steady pressure drop measurements in laminar and transitional flow for a Newtonian analog showed an extension of laminar behavior to Reynolds number (Re) ~ 2900 for the non-Newtonian case. On a macroscale level, this showed good agreement with porcine blood. Subsequently, PIV was used to measure flow patterns and turbulent statistics downstream of an axisymmetric stenosis in the aqueous xanthan gum solution and for a Newtonian analog at Re ~ 520 and Re ~ 1250. The recirculation length for the non-Newtonian case was reduced at Re ~ 520 resultant from increased viscosity at low shear strain rates. At Re ~ 1250, peak turbulent intensities and turbulent shear stresses were dampened by the non-Newtonian fluid in close proximity to the blockage outlet. Although the non-Newtonian case's recirculation length was increased at peak pulsatile flow, turbulent shear stress was found to be elevated for the Newtonian case downstream from the blockage, suggesting shear layer fragmentation and radial transport. Our findings conclude that the xanthan gum elastic polymer prolongs flow stabilization, which in turn emphasizes the importance of non-Newtonian blood characteristics on the resulting flow patterns in such cardiovascular environments.
Non-Newtonian Liquid Flow through Small Diameter Piping Components: CFD Analysis
NASA Astrophysics Data System (ADS)
Bandyopadhyay, Tarun Kanti; Das, Sudip Kumar
2016-10-01
Computational Fluid Dynamics (CFD) analysis have been carried out to evaluate the frictional pressure drop across the horizontal pipeline and different piping components, like elbows, orifices, gate and globe valves for non-Newtonian liquid through 0.0127 m pipe line. The mesh generation is done using GAMBIT 6.3 and FLUENT 6.3 is used for CFD analysis. The CFD results are verified with our earlier published experimental data. The CFD results show the very good agreement with the experimental values.
Theory of non-Newtonian viscosity of red blood cell suspension: effect of red cell deformation.
Murata, T
1983-01-01
The effects of the deformation of red blood cells on non-Newtonian viscosity of a concentrated red cell suspension are investigated theoretically. To simplify the problem an elastic spherical shell filled with an incompressible Newtonian fluid is considered as a model of a normal red cell. The equation of the surface of the shell suspended in a steady simple shear flow is calculated on the assumption that the deformation from a spherical shape is very small. The relative viscosity of a concentrated suspension of such particles is obtained based on the "free surface cell" method proposed by Happel. It is shown that the relative viscosity decreases as the shear rate increases.
NASA Astrophysics Data System (ADS)
Akbari, Omid Ali; Toghraie, Davood; Karimipour, Arash; Marzban, Ali; Ahmadi, Gholam Reza
2017-02-01
In this investigation, the behavior of non-Newtonian nanofluid hydrodynamic and heat transfer are simulated. In this study, we numerically simulated a laminar forced non-Newtonian nanofluid flow containing a 0.5 wt% carboxy methyl cellulose (CMC) solutionin water as the base fluid with alumina at volume fractions of 0.5 and 1.5 as the solid nanoparticle. Numerical solution was modelled in Cartesian coordinate system in a two-dimensional microchannel in Reynolds number range of 10≤Re≤1000. The analyzed geometrical space here was a rectangular part of whose upper and bottom walls was influenced by a constant temperature. The effect of volume fraction of the nanoparticles, Reynolds number and non-Newtonian nanofluids was studied. In this research, the changes pressure drop, the Nusselt number, dimensionless temperature and heat transfer coefficient, caused by the motion of non-Newtonian nanofluids are described. The results indicated that the increase of the volume fraction of the solid nanoparticles and a reduction in the diameter of the nanoparticles would improve heat transfer which is more significant in Reynolds number. The results of the introduced parameters in the form of graphs drawing and for different parameters are compared.
NASA Astrophysics Data System (ADS)
Marrero, Victor; Sahni, Onkar; Jansen, Kenneth; Tichy, John; Taylor, Charles
2008-11-01
In recent years the methods of computational fluid dynamics (CFD) have been applied to the human cardiovascular system to better understand the relationship between arterial blood flow and the disease process, for example in an abdominal aortic aneurysm (AAA). Obviously, the technical challenges associated with such modeling are formidable. Among the many problems to be addressed, in this paper we add yet another complication -- the known non-Newtonian nature of blood. In this preliminary study, we used a patient-based AAA model with rigid walls. The pulsatile nature of the flow and the RCR outflow boundary condition are considered. We use the Carreau-Yasuda model to describe the non-Newtonian viscosity variation. Preliminary results for 200K, 2M, and 8M elements mesh are presented for the Newtonian and non-Newtonian cases. The broad fundamental issue we wish to eventually resolve is whether or not non-Newtonian effects in blood flow are sufficiently strong in unhealthy vessels that they must be addressed in meaningful simulations. Interesting differences during the flow cycle shed light on the problem, but further research is needed.
Hippelheuser, James E; Lauric, Alexandra; Cohen, Alex D; Malek, Adel M
2014-11-28
Most computational fluid dynamic (CFD) simulations of aneurysm hemodynamics assume constant (Newtonian) viscosity, even though blood demonstrates shear-thinning (non-Newtonian) behavior. We sought to evaluate the effect of this simplifying assumption on hemodynamic forces within cerebral aneurysms, especially in regions of low wall shear stress, which are associated with rupture. CFD analysis was performed for both viscosity models using 3D rotational angiography volumes obtained for 26 sidewall aneurysms (12 with blebs, 12 ruptured), and parametric models incorporating blebs at different locations (inflow/outflow zone). Mean and lowest 5% values of time averaged wall shear stress (TAWSS) computed over the dome were compared using Wilcoxon rank-sum test. Newtonian modeling not only resulted in higher aneurysmal TAWSS, specifically in areas of low flow and blebs, but also showed no difference between aneurysms with or without blebs. In contrast, for non-Newtonian analysis, bleb-bearing aneurysms showed significantly lower 5% TAWSS compared to those without (p=0.005), despite no significant difference in mean dome TAWSS (p=0.32). Non-Newtonian modeling also accentuated the differences in dome TAWSS between ruptured and unruptured aneurysms (p<0.001). Parametric models further confirmed that realistic non-Newtonian viscosity resulted in lower bleb TAWSS and higher focal viscosity, especially when located in the outflow zone. The results show that adopting shear-thinning non-Newtonian blood viscosity in CFD simulations of intracranial aneurysms uncovered hemodynamic differences induced by bleb presence on aneurysmal surfaces, and significantly improved discriminant statistics used in risk stratification. These findings underline the possible implications of using a realistic model of blood viscosity in predictive computational hemodynamics.
Sharifi, Alireza; Niazmand, Hamid
2015-10-01
Carotid siphon is known as one of the risky sites among the human intracranial arteries, which is prone to formation of atherosclerotic lesions. Indeed, scientists believe that accumulation of low density lipoprotein (LDL) inside the lumen is the major cause of atherosclerosis. To this aim, three types of internal carotid artery (ICA) siphon have been constructed to examine variations of hemodynamic parameters in different regions of the arteries. Providing real physiological conditions, blood considered as non-Newtonian fluid and real velocity and pressure waveforms have been employed as flow boundary conditions. Moreover, to have a better estimation of risky sites, the accumulation of LDL particles has been considered, which has been usually ignored in previous relevant studies. Governing equations have been discretized and solved via open source OpenFOAM software. A new solver has been built to meet essential parameters related to the flow and mass transfer phenomena. In contrast to the common belief regarding negligible effect of blood non-Newtonian behavior inside large arteries, current study suggests that the non-Newtonian blood behavior is notable, especially on the velocity field of the U-type model. In addition, it is concluded that neglecting non-Newtonian effects underestimates the LDL accumulation up to 3% in the U-type model at the inner side of both its bends. However, in the V and C type models, non-Newtonian effects become relatively small. Results also emphasize that the outer part of the second bend at the downstream is also at risk similar to the inner part of the carotid bends. Furthermore, from findings it can be implied that the risky sites strongly depend on the ICA shape since the extension of the risky sites are relatively larger for the V-type model, while the LDL concentrations are higher for the C-type model.
Simulating non-Newtonian flows with the moving particle semi-implicit method with an SPH kernel
NASA Astrophysics Data System (ADS)
Xiang, Hao; Chen, Bin
2015-02-01
The moving particle semi-implicit (MPS) method and smoothed particle hydrodynamics (SPH) are commonly used mesh-free particle methods for free surface flows. The MPS method has superiority in incompressible flow simulation and simple programing. However, the crude kernel function is not accurate enough for the discretization of the divergence of the shear stress tensor by the particle inconsistency when the MPS method is extended to non-Newtonian flows. This paper presents an improved MPS method with an SPH kernel to simulate non-Newtonian flows. To improve the consistency of the partial derivative, the SPH cubic spline kernel and the Taylor series expansion are combined with the MPS method. This approach is suitable for all non-Newtonian fluids that can be described with τ = μ(|γ|) Δ (where τ is the shear stress tensor, μ is the viscosity, |γ| is the shear rate, and Δ is the strain tensor), e.g., the Casson and Cross fluids. Two examples are simulated including the Newtonian Poiseuille flow and container filling process of the Cross fluid. The results of Poiseuille flow are more accurate than the traditional MPS method, and different filling processes are obtained with good agreement with previous results, which verified the validation of the new algorithm. For the Cross fluid, the jet fracture length can be correlated with We0.28Fr0.78 (We is the Weber number, Fr is the Froude number).
Non-Newtonian Crystal- and Bubble-Rich Lava Rheology in Compression
NASA Astrophysics Data System (ADS)
Lavallee, Y.; Hess, K.; Cordonnier, B.; Dingwell, D. B.
2006-12-01
Volcanic eruption models are still hampered by the lack of multiphase magmatic rheology laws. Fortunately, the lack of sufficient rheological data for lavas bearing crystals and vesicles is now being systematically experimentally addressed. Most rheological models consider suspension rheology according to the Einstein- Roscoe equation or a modification of it. This approach does not contain a Non-Newtonian description (strain- rate dependence). Here, experiments using high-load, high-temperature uniaxial apparatus were carried out to simulate multiphase lava deformation under stresses ranging from 1 to 70 MPa. Samples from Unzen, Colima, Anak Krakatau and Bezymianny (containing 30, 50, 70 and 80 % phenocrysts, and 5, 8, 23 and 9 % vesicles, respectively) were chosen for this study. Obtained results reveal that multiphase lavas behave as pseudo-plastic fluids exhibiting an important component of shear thinning. The viscosity of all lavas decreases exponentially by ca. 1.5 log units between the strain rates of 10-6 and 10-3 s-1; point at which viscous heating and micro-cracking begin to be detected. The strong exponential dependence of the viscosity on strain rate holds the promise of yielding a Non-Newtonian rheology law and consequentially challenges the completeness of the Einstein-Roscoe equation to treat suspension rheology in volcanic eruption models.
Anisotropic power-law inflation
Kanno, Sugumi; Soda, Jiro; Watanabe, Masa-aki E-mail: jiro@tap.scphys.kyoto-u.ac.jp
2010-12-01
We study an inflationary scenario in supergravity model with a gauge kinetic function. We find exact anisotropic power-law inflationary solutions when both the potential function for an inflaton and the gauge kinetic function are exponential type. The dynamical system analysis tells us that the anisotropic power-law inflation is an attractor for a large parameter region.
Simulation of a pulsatile non-Newtonian flow past a stenosed 2D artery with atherosclerosis.
Tian, Fang-Bao; Zhu, Luoding; Fok, Pak-Wing; Lu, Xi-Yun
2013-09-01
Atherosclerotic plaque can cause severe stenosis in the artery lumen. Blood flow through a substantially narrowed artery may have different flow characteristics and produce different forces acting on the plaque surface and artery wall. The disturbed flow and force fields in the lumen may have serious implications on vascular endothelial cells, smooth muscle cells, and circulating blood cells. In this work a simplified model is used to simulate a pulsatile non-Newtonian blood flow past a stenosed artery caused by atherosclerotic plaques of different severity. The focus is on a systematic parameter study of the effects of plaque size/geometry, flow Reynolds number, shear-rate dependent viscosity and flow pulsatility on the fluid wall shear stress and its gradient, fluid wall normal stress, and flow shear rate. The computational results obtained from this idealized model may shed light on the flow and force characteristics of more realistic blood flow through an atherosclerotic vessel.
Gas-driven displacement of a non-Newtonian liquid in a radial Hele-Shaw cell
NASA Astrophysics Data System (ADS)
White, Andrew; Ward, Thomas
2012-11-01
The displacement of a non-Newtonian liquid by a less viscous fluid has applications in a number of industries such as lubricating oils, injection molding and cement placement in oil wells to name a few. A convenient geometry to study such a problem is that of the Hele-Shaw cell due to its ability to effectively reduce the flow to two dimensions when the gap spacing is much smaller than the other spatial dimensions. We will study the radial displacement of a finite drop of non-Newtonian shear-thinning and extensionally-thickening liquid by a gas at constant pressure in a Hele-Shaw cell with gap spacing O(10-100) microns. Different concentrations of a polymer in oil will be used to examine changes in the displacement rate, residual film thickness and resulting Saffman-Taylor instability as the viscoelastic time scale overtakes that of the bulk displacement.
NASA Astrophysics Data System (ADS)
Sui, Jize; Zhao, Peng; Cheng, Zhengdong; Zheng, Liancun; Zhang, Xinxin
2017-02-01
The rheological and heat-conduction constitutive models of micropolar fluids (MFs), which are important non-Newtonian fluids, have been, until now, characterized by simple linear expressions, and as a consequence, the non-Newtonian performance of such fluids could not be effectively captured. Here, we establish the novel nonlinear constitutive models of a micropolar fluid and apply them to boundary layer flow and heat transfer problems. The nonlinear power law function of angular velocity is represented in the new models by employing generalized "n-diffusion theory," which has successfully described the characteristics of non-Newtonian fluids, such as shear-thinning and shear-thickening fluids. These novel models may offer a new approach to the theoretical understanding of shear-thinning behavior and anomalous heat transfer caused by the collective micro-rotation effects in a MF with shear flow according to recent experiments. The nonlinear similarity equations with a power law form are derived and the approximate analytical solutions are obtained by the homotopy analysis method, which is in good agreement with the numerical solutions. The results indicate that non-Newtonian behaviors involving a MF depend substantially on the power exponent n and the modified material parameter K 0 introduced by us. Furthermore, the relations of the engineering interest parameters, including local boundary layer thickness, local skin friction, and Nusselt number are found to be fitted by a quadratic polynomial to n with high precision, which enables the extraction of the rapid predictions from a complex nonlinear boundary-layer transport system.
Non-Newtonian Characteristics of Gochujang and Chogochujang at Different Temperatures
Choi, Ji Eun; Lee, Jun Ho
2017-01-01
This study was conducted to determine the rheological properties of gochujang and chogochujang at different temperatures (25, 35, and 45°C). Rheological properties of the samples were determined using a rotational rheometer at a shear range of 1 to 40 s−1. Gochujang and chogochujang were found to be non-Newtonian fluids according to the Herschel-Bulkley model. Yield stress and consistency coefficient of gochujang at different temperatures were higher than those of chogochujang, whereas the opposite was observed for flow behavior index. Moreover, all rheological properties of gochujang and chogochujang decreased with increasing temperature. The consistency coefficient was related to temperature using an Arrhenius-type relationship. Gochujang (14.48 kJ/mol) had slightly higher activation energy than chogochujang (14.03 kJ/mol).
Rheological non-Newtonian behaviour of ethylene glycol-based Fe2O3 nanofluids
2011-01-01
The rheological behaviour of ethylene glycol-based nanofluids containing hexagonal scalenohedral-shaped α-Fe2O3 (hematite) nanoparticles at 303.15 K and particle weight concentrations up to 25% has been carried out using a cone-plate Physica MCR rheometer. The tests performed show that the studied nanofluids present non-Newtonian shear-thinning behaviour. In addition, the viscosity at a given shear rate is time dependent, i.e. the fluid is thixotropic. Finally, using strain sweep and frequency sweep tests, the storage modulus G', loss modulus G″ and damping factor were determined as a function of the frequency showing viscoelastic behaviour for all samples. PMID:22027018
Convection in ice I with non-Newtonian rheology: Application to the icy Galilean satellites
NASA Astrophysics Data System (ADS)
Barr, Amy Courtright
2004-12-01
Observations from the Galileo spacecraft suggest that the Jovian icy satellites Europa, Ganymede, and Callisto have liquid water oceans beneath their icy surfaces. The outer ice I shells of the satellites represent a barrier between their surfaces and their oceans and serve to decouple fluid motions in their deep interiors from their surfaces. Understanding heat and mass transport by convection within the outer ice I shells of the satellites is crucial to understanding their geophysical and astrobiological evolution. Recent laboratory experiments suggest that deformation in ice I is accommodated by several different creep mechanisms. Newtonian deformation creep accommodates strain in warm ice with small grain sizes. However, deformation in ice with larger grain sizes is controlled by grain-size-sensitive and dislocation creep, which are non-Newtonian. Previous studies of convection have not considered this complex rheological behavior. This thesis revisits basic geophysical questions regarding heat and mass transport in the ice I shells of the satellites using a composite Newtonian/ non-Newtonian rheology for ice I. The composite rheology is implemented in a numerical convection model developed for Earth's mantle to study the behavior of an ice I shell during the onset of convection and in the stagnant lid convection regime. The conditions required to trigger convection in a conductive ice I shell depend on the grain size of the ice, and the amplitude and wavelength of temperature perturbation issued to the ice shell. If convection occurs, the efficiency of heat and mass transport is dependent on the ice grain size as well. If convection occurs, fluid motions in the ice shells enhance the nutrient flux delivered to their oceans, and coupled with resurfacing events, may provide a sustainable biogeochemical cycle. The results of this thesis suggest that evolution of ice grain size in the satellites and the details of how tidal dissipation perturbs the ice shell to
Non-Newtonian perspectives on pulsatile blood-analog flows in a 180° curved artery model
NASA Astrophysics Data System (ADS)
van Wyk, Stevin; Prahl Wittberg, Lisa; Bulusu, Kartik V.; Fuchs, Laszlo; Plesniak, Michael W.
2015-07-01
Complex, unsteady fluid flow phenomena in the arteries arise due to the pulsations of the heart that intermittently pumps the blood to the extremities of the body. The many different flow waveform variations observed throughout the arterial network are a result of this process and a function of the vessel properties. Large scale secondary flow structures are generated throughout the aortic arch and larger branches of the arteries. An experimental 180° curved artery test section with physiological inflow conditions was used to validate the computational methods implemented in this study. Good agreement of the secondary flow structures is obtained between experimental and numerical studies of a Newtonian blood-analog fluid under steady-state and pulsatile, carotid artery flow rate waveforms. Multiple vortical structures, some of opposite rotational sense to Dean vortices, similar to Lyne-type vortices, were observed to form during the systolic portion of the pulse. Computational tools were used to assess the effect of blood-analog fluid rheology (i.e., Newtonian versus non-Newtonian). It is demonstrated that non-Newtonian, blood-analog fluid rheology results in shear layer instabilities that alter the formation of vortical structures during the systolic deceleration and onwards during diastole. Additional vortices not observed in the Newtonian cases appear at the inside and outside of the bend at various times during the pulsation. The influence of blood-analog shear-thinning viscosity decreases mean pressure losses in contrast to the Newtonian blood analog fluid.
Electro-hydrodynamic instability in a microchannel between a Newtonian and a non-Newtonian liquid
NASA Astrophysics Data System (ADS)
Ersoy, Gülsüm; Kerem Uguz, A.
2012-06-01
We perform linear stability analysis of the interface between a Newtonian fluid and a non-Newtonian fluid, assumed to obey the Upper Convective Maxwell model, flowing in a channel due to a pressure gradient subject to an electric field applied normal to the interface. The fluids are assumed to be immiscible, incompressible and leaky dielectric. A detailed parametric study of the effects of the system parameters, such as Weissenberg number, Reynolds number, applied potential and physical and electrical properties of the fluids, is conducted. It is found that increasing the applied voltage could be stabilizing or destabilizing depending on the electrical properties of the liquids, and increasing the Weissenberg number decreases the maximum growth rate without changing the corresponding wavenumber and increases the critical wavenumber. The effect of the height ratio of the liquids is analyzed through neutral curves for given electric numbers, i.e. applied potential. The critical wavenumber decreases with height ratio and converges to a value for all the electric numbers considered.
NASA Technical Reports Server (NTRS)
King, Scott D.; Hager, Bradford H.
1990-01-01
The relationship between oceanic trench viscosity and oceanic plate velocity is studied using a Newtonian rheology by varying the viscosity at the trench. The plate velocity is a function of the trench viscosity for fixed Rayleigh number and plate/slab viscosity. Slab velocities for non-Newtonian rheology calculations are significantly different from slab velocities from Newtonian rheology calculations at the same effective Rayleigh number. Both models give reasonable strain rates for the slab when compared with estimates of seismic strain rate. Non-Newtonian rheology eliminates the need for imposed weak zones and provides a self-consistent fluid dynamical mechanism for subduction in numerical convection models.
Power Law Distribution in Education
NASA Astrophysics Data System (ADS)
Gupta, Hari M.; Campanha, José R.; Prado, Fernando D.
We studied the statistical distribution of candidate's performance which is measured through their marks in university entrance examination (Vestibular) of UNESP (Universidade Estadual Paulista) for years 1998, 1999, and 2000. All students are divided in three groups: Physical, Biological and Humanities. We paid special attention to the examination of Portuguese language which is common for all and examinations for the particular area. We observed long ubiquitous power law tails in Physical and Biological sciences. This indicate the presence of strong positive feedback in sciences. We are able to explain completely these statistical distributions through Gradually Truncated Power law distributions which we developed recently to explain statistical behavior of financial market. The statistical distribution in case of Portuguese language and humanities is close to normal distribution. We discuss the possible reason for this peculiar behavior.
Bentzen, T R; Ratkovich, N; Madsen, S; Jensen, J C; Bak, S N; Rasmussen, M R
2012-01-01
Fouling is the main bottleneck of the widespread use of MBR systems. One way to decrease and/or control fouling is by process hydrodynamics. This can be achieved by the increase of liquid cross-flow velocity. In rotational cross-flow MBR systems, this is attained by the spinning of, for example, impellers. Validation of the CFD (computational fluid dynamics) model was made against laser Doppler anemometry (LDA) tangential velocity measurements (error less than 8%) using water as a fluid. The shear stress over the membrane surface was inferred from the CFD simulations for water. However, activated sludge (AS) is a non-Newtonian liquid, for which the CFD model was modified incorporating the non-Newtonian behaviour of AS. Shear stress and area-weighted average shear stress relationships were made giving error less that 8% compared with the CFD results. An empirical relationship for the area-weighted average shear stress was developed for water and AS as a function of the angular velocity and the total suspended solids concentration. These relationships can be linked to the energy consumption of this type of systems.
Effects of non-Newtonian gravity on the properties of strange stars
NASA Astrophysics Data System (ADS)
Lu, Zhen-Yan; Peng, Guang-Xiong; Zhou, Kai
2017-02-01
The properties of strange star matter are studied in the equivparticle model with inclusion of non-Newtonian gravity. It is found that the inclusion of non-Newtonian gravity makes the equation of state stiffer if Witten’s conjecture is true. Correspondingly, the maximum mass of strange stars becomes as large as two times the solar mass, and the maximum radius also becomes bigger. The coupling to boson mass ratio has been constrained within the stability range of strange quark matter.
Accurate prediction of wall shear stress in a stented artery: newtonian versus non-newtonian models.
Mejia, Juan; Mongrain, Rosaire; Bertrand, Olivier F
2011-07-01
A significant amount of evidence linking wall shear stress to neointimal hyperplasia has been reported in the literature. As a result, numerical and experimental models have been created to study the influence of stent design on wall shear stress. Traditionally, blood has been assumed to behave as a Newtonian fluid, but recently that assumption has been challenged. The use of a linear model; however, can reduce computational cost, and allow the use of Newtonian fluids (e.g., glycerine and water) instead of a blood analog fluid in an experimental setup. Therefore, it is of interest whether a linear model can be used to accurately predict the wall shear stress caused by a non-Newtonian fluid such as blood within a stented arterial segment. The present work compares the resulting wall shear stress obtained using two linear and one nonlinear model under the same flow waveform. All numerical models are fully three-dimensional, transient, and incorporate a realistic stent geometry. It is shown that traditional linear models (based on blood's lowest viscosity limit, 3.5 Pa s) underestimate the wall shear stress within a stented arterial segment, which can lead to an overestimation of the risk of restenosis. The second linear model, which uses a characteristic viscosity (based on an average strain rate, 4.7 Pa s), results in higher wall shear stress levels, but which are still substantially below those of the nonlinear model. It is therefore shown that nonlinear models result in more accurate predictions of wall shear stress within a stented arterial segment.
NASA Astrophysics Data System (ADS)
Kuchumov, Alex G.; Gilev, Valeriy; Popov, Vitaliy; Samartsev, Vladimir; Gavrilov, Vasiliy
2014-02-01
The paper presents an experimental study of pathological human bile taken from the gallbladder and bile ducts. The flow dependences were obtained for different types of bile from patients with the same pathology, but of different age and sex. The parameters of the Casson's and Carreau's equations were found for bile samples. Results on the hysteretic bile behavior at loading-unloading tests are also presented, which proved that the pathologic bile is a non-Newtonian thixotropic liquid. The viscosity of the gallbladder bile was shown to be higher compared to the duct bile. It was found that at higher shear stress the pathological bile behaves like Newtonian fluid, which is explained by reorientation of structural components. Moreover, some pathological bile flow in the biliary system CFD simulations were performed. The velocity and pressure distributions as well as flow rates in the biliary segments during the gallbladder refilling and emptying phases are obtained. The results of CFD simulations can be used for surgeons to assess the patient's condition and choose an adequate treatment.
Hatami, M; Hatami, J; Ganji, D D
2014-02-01
In this paper, heat transfer and flow analysis for a non-Newtonian third grade nanofluid flow in porous medium of a hollow vessel in presence of magnetic field are simulated analytically and numerically. Blood is considered as the base third grade non-Newtonian fluid and gold (Au) as nanoparticles are added to it. The viscosity of nanofluid is considered a function of temperature as Vogel's model. Least Square Method (LSM), Galerkin method (GM) and fourth-order Runge-Kutta numerical method (NUM) are used to solve the present problem. The influences of the some physical parameters such as Brownian motion and thermophoresis parameters on non-dimensional velocity and temperature profiles are considered. The results show that increasing the thermophoresis parameter (N(t)) caused an increase in temperature values in whole domain and an increase in nanoparticles concentration just near the inner wall of vessel. Furthermore by increasing the MHD parameter, velocity profiles decreased due to magnetic field effect.
NASA Astrophysics Data System (ADS)
Kim, Chang-Beom; Lim, Jaeho; Hong, Hyobong; Kresh, J. Yasha; Wootton, David M.
2015-07-01
Detailed knowledge of the blood velocity distribution over the cross-sectional area of a microvessel is important for several reasons: (1) Information about the flow field velocity gradients can suggest an adequate description of blood flow. (2) Transport of blood components is determined by the velocity profiles and the concentration of the cells over the cross-sectional area. (3) The velocity profile is required to investigate volume flow rate as well as wall shear rate and shear stress which are important parameters in describing the interaction between blood cells and the vessel wall. The present study shows the accurate measurement of non-Newtonian blood velocity profiles at different shear rates in a microchannel using a novel translating-stage optical method. Newtonian fluid velocity profile has been well known to be a parabola, but blood is a non-Newtonian fluid which has a plug flow region at the centerline due to yield shear stress and has different viscosities depending on shear rates. The experimental results were compared at the same flow conditions with the theoretical flow equations derived from Casson non-Newtonian viscosity model in a rectangular capillary tube. And accurate wall shear rate and shear stress were estimated for different flow rates based on these velocity profiles. Also the velocity profiles were modeled and compared with parabolic profiles, concluding that the wall shear rates were at least 1.46-3.94 times higher than parabolic distribution for the same volume flow rate.
Kabinejadian, Foad; Ghista, Dhanjoo N
2012-09-01
We have recently developed a novel design for coronary arterial bypass surgical grafting, consisting of coupled sequential side-to-side and end-to-side anastomoses. This design has been shown to have beneficial blood flow patterns and wall shear stress distributions which may improve the patency of the CABG, as compared to the conventional end-to-side anastomosis. In our preliminary computational simulation of blood flow of this coupled sequential anastomoses design, the graft and the artery were adopted to be rigid vessels and the blood was assumed to be a Newtonian fluid. Therefore, the present study has been carried out in order to (i) investigate the effects of wall compliance and non-Newtonian rheology on the local flow field and hemodynamic parameters distribution, and (ii) verify the advantages of the CABG coupled sequential anastomoses design over the conventional end-to-side configuration in a more realistic bio-mechanical condition. For this purpose, a two-way fluid-structure interaction analysis has been carried out. A finite volume method is applied to solve the three-dimensional, time-dependent, laminar flow of the incompressible, non-Newtonian fluid; the vessel wall is modeled as a linearly elastic, geometrically non-linear shell structure. In an iteratively coupled approach the transient shell equations and the governing fluid equations are solved numerically. The simulation results indicate a diameter variation ratio of up to 4% and 5% in the graft and the coronary artery, respectively. The velocity patterns and qualitative distribution of wall shear stress parameters in the distensible model do not change significantly compared to the rigid-wall model, despite quite large side-wall deformations in the anastomotic regions. However, less flow separation and reversed flow is observed in the distensible models. The wall compliance reduces the time-averaged wall shear stress up to 32% (on the heel of the conventional end-to-side model) and somewhat
Non-Newtonian rheology of bubble-bearing magmas: effects on conduit dynamics.
NASA Astrophysics Data System (ADS)
Colucci, Simone; Papale, Paolo; Montagna, Chiara
2015-04-01
Non-Newtonian rheology typically arises in magmas from the presence of a dispersed phase. In particular bubbles can reduce or increase the relative viscosity, depending on size and strain regime (i.e., capillary number), for example large bubbles, as well as low strain, reduce the apparent viscosity. In a Non-Newtonian regime it is not possible to define a strain-rate-independent viscosity and the velocity profile is complex. In this work we extended the 1D, steady, isothermal, multiphase non-homogeneous magma ascent model of Papale (2001) to 1.5D to include the Non-Newtonian effect of a bubble-bearing magma. The model has been tested with a basaltic test case. In this way we were able to calculate depth-dependent Non-newtonian velocity profiles across the conduit radius along with shear strain-rate and viscosity distributions. Moreover, the model could quantify the effects of the Non-Newtonian rheology on conduit flow dynamics, in terms of flow variables (e.g. velocity, pressure). P. Papale (2001). Dynamics of magma flow in volcanic conduits with variable fragmentation efficiency and nonequilibrium pumice degassing. JGR, 106, 11043-11065.
Pore scale simulations for the extension of the Darcy-Forchheimer law to shear thinning fluids
NASA Astrophysics Data System (ADS)
Tosco, Tiziana; Marchisio, Daniele; Lince, Federica; Boccardo, Gianluca; Sethi, Rajandrea
2014-05-01
Flow of non-Newtonian fluids through porous media at high Reynolds numbers is often encountered in chemical, pharmaceutical and food as well as petroleum and groundwater engineering and in many other industrial applications (1 - 2). In particular, the use of shear thinning polymeric solutions has been recently proposed to improve colloidal stability of micro- and nanoscale zerovalent iron particles (MZVI and NZVI) for groundwater remediation. In all abovementioned applications, it is of paramount importance to correctly predict the pressure drop resulting from non-Newtonian fluid flow through the porous medium. For small Reynolds numbers, usually up to 1, typical of laboratory column tests, the extended Darcy law is known to be applicable also to non Newtonian fluids, provided that all non-Newtonian effects are lumped together into a proper viscosity parameter (1,3). For higher Reynolds numbers (eg. close to the injection wells) non linearities between pressure drop and flow rate arise, and the Darcy-Forchheimer law holds for Newtonian fluids, while for non-Newtonian fluids, it has been demonstrated that, at least for simple rheological models (eg. power law fluids) a generalized Forchheimer law can be applied, even if the determination of the flow parameters (permeability K, inertial coefficient β, and equivalent viscosity) is not straightforward. This work (co-funded by European Union project AQUAREHAB FP7 - Grant Agreement Nr. 226565) aims at proposing an extended formulation of the Darcy-Forchheimer law also for shear-thinning fluids, and validating it against results of pore-scale simulations via computational fluid dynamics (4). Flow simulations were performed using Fluent 12.0 on four different 2D porous domains for Newtonian and non-Newtonian fluids (Cross, Ellis and Carreau models). The micro-scale flow simulation results are analyzed in terms of 'macroscale' pressure drop between inlet and outlet of the model domain as a function of flow rate. The
Determination of the Köthe-Toeplitz Duals over the Non-Newtonian Complex Field
Kadak, Uğur
2014-01-01
The important point to note is that the non-Newtonian calculus is a self-contained system independent of any other system of calculus. Therefore the reader may be surprised to learn that there is a uniform relationship between the corresponding operators of this calculus and the classical calculus. Several basic concepts based on non-Newtonian calculus are presented by Grossman (1983), Grossman and Katz (1978), and Grossman (1979). Following Grossman and Katz, in the present paper, we introduce the sets of bounded, convergent, null series and p-bounded variation of sequences over the complex field C* and prove that these are complete. We propose a quite concrete approach based on the notion of Köthe-Toeplitz duals with respect to the non-Newtonian calculus. Finally, we derive some inclusion relationships between Köthe space and solidness. PMID:25028678
Determination of the Köthe-Toeplitz duals over the non-Newtonian complex field.
Kadak, Uğur
2014-01-01
The important point to note is that the non-Newtonian calculus is a self-contained system independent of any other system of calculus. Therefore the reader may be surprised to learn that there is a uniform relationship between the corresponding operators of this calculus and the classical calculus. Several basic concepts based on non-Newtonian calculus are presented by Grossman (1983), Grossman and Katz (1978), and Grossman (1979). Following Grossman and Katz, in the present paper, we introduce the sets of bounded, convergent, null series and p-bounded variation of sequences over the complex field C* and prove that these are complete. We propose a quite concrete approach based on the notion of Köthe-Toeplitz duals with respect to the non-Newtonian calculus. Finally, we derive some inclusion relationships between Köthe space and solidness.
The Extensional Rheology of Non-Newtonian Materials
NASA Technical Reports Server (NTRS)
Spiegelberg, Stephen H.; McKinley, Gareth H.
1996-01-01
The evolution of the transient extensional stresses in dilute and semi-dilute viscoelastic polymer solutions are measured with a filament stretching rheometer of a design similar to that first introduced by Sridhar, et al. The solutions are polystyrene-based (PS) Boger fluids that are stretched at constant strain rates ranging from 0.6 less than or equal to epsilon(0) less than or equal to 4s(exp -1) and to Hencky strains of epsilon greater than 4. The test fluids all strain harden and Trouton ratios exceeding 1000 are obtained at high strains. The experimental data strain hardens at lower strain levels than predicted by bead-spring FENE models. In addition to measuring the transient tensile stress growth, we also monitor the decay of the tensile viscoelastic stress difference in the fluid column following cessation of uniaxial elongation as a function of the total imposed Hencky strain and the strain rate. The extensional stresses initially decay very rapidly upon cessation of uniaxial elongation followed by a slower viscoelastic relaxation, and deviate significantly from FENE relaxation predictions. The relaxation at long times t is greater than or equal to 5 s, is compromised by gravitational draining leading to non-uniform filament profiles. For the most elastic fluids, partial decohension of the fluid filament from the endplates of the rheometer is observed in tests conducted at high strain rates. This elastic instability is initiated near the rigid endplate fixtures of the device and it results in the progressive breakup of the fluid column into individual threads or 'fibrils' with a regular azimuthal spacing. These fibrils elongate and bifurcate as the fluid sample is elongated further. Flow visualization experiments using a modified stretching device show that the instability develops as a consequence of an axisymmetry-breaking meniscus instability in the nonhomogeneous region of highly deformed fluid near the rigid endplate.
Quantum signatures of non-Newtonian orbits in the asymmetric infinite square well.
Timberlake, Todd K; Nelson, Molly M
2009-03-01
An infinite square well with a rectangular step is one of the simplest systems to exhibit non-Newtonian ray-splitting periodic orbits in the classical limit. We examine eigenvalue spacings in the quantum version of this system. The sequence of spacings shows deviations from uniformity at energies just above the step height and distinct resonance features are visible at certain energies. Semiclassical analysis shows that these features are directly related to the presence of non-Newtonian orbits in the classical system. In addition, the resonance features are shown to produce revivals in suitably constructed wave packets peaked at the resonance energy.
Simultaneous pulsatile flow and oscillating wall of a non-Newtonian liquid
NASA Astrophysics Data System (ADS)
Herrera-Valencia, E. E.; Sánchez-Villavicencio, M. L.; Calderas, F.; Pérez-Camacho, M.; Medina-Torres, L.
2016-11-01
In this work, analytical predictions of the rectilinear flow of a non-Newtonian liquid are given. The fluid is subjected to a combined flow: A pulsatile time-dependent pressure gradient and a random longitudinal vibration at the wall acting simultaneously. The fluctuating component of the combined pressure gradient and oscillating flow is assumed to be of small amplitude and can be adequately represented by a weakly stochastic process, for which a quasi-static perturbation solution scheme is suggested, in terms of a small parameter. This flow is analyzed with the Tanner constitutive equation model with the viscosity function represented by the Ellis model. According to the coupled Tanner-Ellis model, the flow enhancement can be separated in two contributions (pulsatile and oscillating mechanisms) and the power requirement is always positive and can be interpreted as the sum of a pulsatile, oscillating, and the coupled systems respectively. Both expressions depend on the amplitude of the oscillations, the perturbation parameter, the exponent of the Ellis model (associated to the shear thinning or thickening mechanisms), and the Reynolds and Deborah numbers. At small wall stress values, the flow enhancement is dominated by the axial wall oscillations whereas at high wall stress values, the system is governed by the pulsating noise perturbation. The flow transition is obtained for a critical shear stress which is a function of the Reynolds number, dimensionless frequency and the ratio of the two amplitudes associated with the pulsating and oscillating perturbations. In addition, the flow enhancement is compared with analytical and numerical predictions of the Reiner-Phillipoff and Carreau models. Finally, the flow enhancement and power requirement are predicted using biological rheometric data of blood with low cholesterol content.
The numerical analysis of non-Newtonian blood flow in human patient-specific left ventricle.
Doost, Siamak N; Zhong, Liang; Su, Boyang; Morsi, Yosry S
2016-04-01
Recently, various non-invasive tools such as the magnetic resonance image (MRI), ultrasound imaging (USI), computed tomography (CT), and the computational fluid dynamics (CFD) have been widely utilized to enhance our current understanding of the physiological parameters that affect the initiation and the progression of the cardiovascular diseases (CVDs) associated with heart failure (HF). In particular, the hemodynamics of left ventricle (LV) has attracted the attention of the researchers due to its significant role in the heart functionality. In this study, CFD owing its capability of predicting detailed flow field was adopted to model the blood flow in images-based patient-specific LV over cardiac cycle. In most published studies, the blood is modeled as Newtonian that is not entirely accurate as the blood viscosity varies with the shear rate in non-linear manner. In this paper, we studied the effect of Newtonian assumption on the degree of accuracy of intraventricular hemodynamics. In doing so, various non-Newtonian models and Newtonian model are used in the analysis of the intraventricular flow and the viscosity of the blood. Initially, we used the cardiac MRI images to reconstruct the time-resolved geometry of the patient-specific LV. After the unstructured mesh generation, the simulations were conducted in the CFD commercial solver FLUENT to analyze the intraventricular hemodynamic parameters. The findings indicate that the Newtonian assumption cannot adequately simulate the flow dynamic within the LV over the cardiac cycle, which can be attributed to the pulsatile and recirculation nature of the flow and the low blood shear rate.
The stretching of an electrified non-Newtonian jet: A model for electrospinning
NASA Astrophysics Data System (ADS)
Feng, J. J.
2002-11-01
Electrospinning uses an external electrostatic field to accelerate and stretch a charged polymer jet, and may produce ultrafine "nanofibers." Many polymers have been successfully electrospun in the laboratory. Recently Hohman [et al.] [Phys. Fluids, 13, 2201 (2001)] proposed an electrohydrodynamic model for electrospinning Newtonian jets. A problem arises, however, with the boundary condition at the nozzle. Unless the initial surface charge density is zero or very small, the jet bulges out upon exiting the nozzle in a "ballooning instability," which never occurs in reality. In this paper, we will first describe a slightly different Newtonian model that avoids the instability. Well-behaved solutions are produced that are insensitive to the initial charge density, except inside a tiny "boundary layer" at the nozzle. Then a non-Newtonian viscosity function is introduced into the model and the effects of extension thinning and thickening are explored. Results show two distinct regimes of stretching. For a "mildly stretched" jet, the axial tensile force in the fiber resists stretching, so that extension thinning promotes stretching and thickening hinders stretching. For a "severely stretched" jet, on the other hand, the tensile force enhances stretching at the beginning of the jet and suppresses it farther downstream. The effects of extensional viscosity then depend on the competition between the upstream and downstream dynamics. Finally, we use an empirical correlation to simulate strain hardening typical of polymeric liquids. This generally steepens the axial gradient of the tensile stress. Stretching is more pronounced at the beginning but weakens later, and ultimately thicker fibers are produced because of strain hardening.
Non-Newtonian hydrodynamics for a dilute granular suspension under uniform shear flow.
Chamorro, Moisés G; Reyes, Francisco Vega; Garzó, Vicente
2015-11-01
We study in this work a steady shearing laminar flow with null heat flux (usually called "uniform shear flow") in a gas-solid suspension at low density. The solid particles are modeled as a gas of smooth hard spheres with inelastic collisions while the influence of the surrounding interstitial fluid on the dynamics of grains is modeled by means of a volume drag force, in the context of a rheological model for suspensions. The model is solved by means of three different but complementary routes, two of them being theoretical (Grad's moment method applied to the corresponding Boltzmann equation and an exact solution of a kinetic model adapted to granular suspensions) and the other being computational (Monte Carlo simulations of the Boltzmann equation). Unlike in previous studies on granular sheared suspensions, the collisional moment associated with the momentum transfer is determined in Grad's solution by including all the quadratic terms in the stress tensor. This theoretical enhancement allows for the detection and evaluation of the normal stress differences in the plane normal to the laminar flow. In addition, the exact solution of the kinetic model gives the explicit form of the velocity moments of the velocity distribution function. Comparison between our theoretical and numerical results shows in general a good agreement for the non-Newtonian rheological properties, the kurtosis (fourth velocity moment of the distribution function), and the velocity distribution of the kinetic model for quite strong inelasticity and not too large values of the (scaled) friction coefficient characterizing the viscous drag force. This shows the accuracy of our analytical results that allows us to describe in detail the flow dynamics of the granular sheared suspension.
Non-Newtonian Viscosity of Escherichia coli Suspensions
NASA Astrophysics Data System (ADS)
Gachelin, Jérémie; Miño, Gastón; Berthet, Hélène; Lindner, Anke; Rousselet, Annie; Clément, Éric
2013-06-01
The viscosity of an active suspension of E. coli bacteria is determined experimentally as a function of the shear rate using a Y-shaped microfluidic channel. From the relative suspension viscosity, we identify rheological thickening and thinning regimes as well as situations at low shear rate where the viscosity of the bacteria suspension can be lower than the viscosity of the suspending fluid. In addition, bacteria concentration and velocity profiles in the bulk are directly measured in the microchannel.
On line and double integrals in the non-Newtonian sense
NASA Astrophysics Data System (ADS)
ćakmak, Ahmet Faruk; Başar, Feyzi
2014-08-01
This paper is devoted to line and double integrals in the sense of non-Newtonian calculus (*-calculus). Moreover, in the sense of *-calculus, the fundamental theorem of calculus for line integrals and double integrals are stated and proved, and some applications are presented.
Numerical simulation of non-Newtonian free shear flows
NASA Technical Reports Server (NTRS)
Homsy, G. M.; Azaiez, J.
1993-01-01
Free shear flows, like those of mixing layers, are encountered in aerodynamics, in the atmosphere, and in the ocean as well as in many industrial applications such as flow reactors or combustion chambers. It is, therefore, crucial to understand the mechanisms governing the process of transition to turbulence in order to predict and control the evolution of the flow. Delaying transition to turbulence as far downstream as possible allows a gain in energy expenditure while accelerating the transition can be of interest in processes where high mixing is desired. Various methods, including the use of polymer additives, can be effective in controlling fluid flows. The drag reduction obtained by the addition of small amounts of high polymers has been an active area of research for the last three decades. It is now widely believed that polymer additives can affect the stability of a large variety of flows and that dilute solutions of these polymers have been shown to produce drag reductions of over 80 percent in internal flows and over 60 percent in external flows under a wide range of conditions. The major thrust of this work is to study the effects of polymer additives on the stability of the incompressible mixing layer through large scale numerical simulations. In particular, we focus on the two dimensional flow and examine how the presence of viscoelasticity may affect the typical structures of the flow, namely roll-up and pairing of vortices.
Newtonian to non-Newtonian flow transition in lung surfactants
NASA Astrophysics Data System (ADS)
Sadoughi, Amir; Hirsa, Amir; Lopez, Juan
2010-11-01
The lining of normal lungs is covered by surfactants, because otherwise the surface tension of the aqueous layer would be too large to allow breathing. A lack of functioning surfactants can lead to respiratory distress syndrome, a potentially fatal condition in both premature infants and adults, and a major cause of death in the US and world-wide. We use a home-built Brewster angle microscope on an optically accessible deep channel viscometer to simultaneously observe the mesoscale structures of DPPC, the primary constituent of lung surfactant, on water surface and measure the interfacial velocity field. The measured interfacial velocity is compared to Navier-Stokes computations with the Boussinesq-Scriven surface model. Results show that DPPC monolayer behaves i) purely elastically at low surface pressures on water, ii) viscoelastically at modest surface pressures, exhibiting non-zero surface shear viscosity that is independent of the shear rate and flow inertia, and iii) at surface pressures approaching film collapse, DPPC loses its fluid characteristics, and a Newtonian surface model no longer captures its hydrodynamics.
Power law inflation with electromagnetism
Luo, Xianghui; Isenberg, James
2013-07-15
We generalize Ringström’s global future causal stability results (Ringström 2009) [11] for certain expanding cosmological solutions of the Einstein-scalar field equations to solutions of the Einstein–Maxwell-scalar field system. In particular, after noting that the power law inflationary spacetimes (M{sup n+1},g{sup -hat}, ϕ{sup -hat}) considered by Ringström (2009) in [11] are solutions of the Einstein–Maxwell-scalar field system (with exponential potential) as well as of the Einstein-scalar field system (with the same exponential potential), we consider (nonlinear) perturbations of initial data sets of these spacetimes which include electromagnetic perturbations as well as gravitational and scalar perturbations. We show that if (as in Ringström (2009) [11]) we focus on pairs of relatively scaled open sets U{sub R{sub 0}}⊂U{sub 4R{sub 0}} on an initial slice of (M{sup n+1},g{sup -hat}), and if we choose a set of perturbed data which on U{sub 4R{sub 0}} is sufficiently close to that of (M{sup n+1},g{sup -hat},ϕ{sup -hat}, A{sup -hat} = 0), then in the maximal globally hyperbolic spacetime development (M{sup n+1},g,ϕ,A) of this data via the Einstein–Maxwell-scalar field equations, all causal geodesics emanating from U{sub R{sub 0}} are future complete (just as in (M{sup n+1},g{sup -hat})). We also verify that, in a certain sense, the future asymptotic behavior of the fields in the spacetime developments of the perturbed data sets does not differ significantly from the future asymptotic behavior of (M{sup n+1},g{sup -hat}, ϕ{sup -hat}, A{sup -hat} = 0). -- Highlights: •We prove stability of expanding solutions of the Einstein–Maxwell-scalar field equations. •All nearby solutions are geodesically complete. •The topology of the initial slice is irrelevant to our stability results.
Numerical Modeling of Mixing of Chemically Reacting, Non-Newtonian Slurry for Tank Waste Retrieval
Yuen, David A.; Onishi, Yasuo; Rustad, James R.; Michener, Thomas E.; Felmy, Andrew R.; Ten, Arkady A.; Hier, Catherine A.
2000-06-01
Many highly radioactive wastes will be retrieved by installing mixer pumps that inject high-speed jets to stir up the sludge, saltcake, and supernatant liquid in the tank, blending them into a slurry. This slurry will then be pumped out of the tank into a waste treatment facility. Our objectives are to investigate interactions-chemical reactions, waste rheology, and slurry mixing-occurring during the retrieval operation and to provide a scientific basis for the waste retrieval decision-making process. Specific objectives are to: (1) Evaluate numerical modeling of chemically active, non-Newtonian tank waste mixing, coupled with chemical reactions and realistic rheology; (2) Conduct numerical modeling analysis of local and global mixing of non-Newtonian and Newtonian slurries; and (3) Provide the bases to develop a scientifically justifiable, decision-making support tool for the tank waste retrieval operation.
Curious Fluid Flows: From Complex Fluid Breakup to Helium Wetting
NASA Astrophysics Data System (ADS)
Huisman, Fawn Mitsu
This work encompasses three projects; pinch-off dynamics in non-Newtonian fluids; helium wetting on alkali metals; and the investigation of quartz tuning forks as cryogenic pressure transducers. Chapter 1 discusses the breakup of a non-Newtonian yield stress fluid bridge. We measured the minimum neck radius, hmin, as a function of time and fit it to a power law with exponent n 1. We then compare n1 to exponent n2, obtained from a rotational rheometer using a Herschel-Bulkley model. We confirm n1=n2 for the widest variety of non-Newtonian fluids to date. When these fluids are diluted with a Newtonian fluid n1 does not equal n2. No current models predict that behavior, identifying a new class of fluid breakup. Chapter 2 presents the first chemical potential-temperature phase diagram of helium on lithium, sodium and gold, using a novel pressure measurement system. The growth and superfluid transition of a helium film on these substrates is measured via an oscillator for isotherms (fixed temperature, varying amount of helium gas), and quenches (fixed amount of helium gas, varying temperature). The chemical potential-temperature plot is similar for gold, lithium and sodium despite the large difference in the substrate binding energies. No signs of a 2-D liquid-vapor transition were seen. Chapter 3 discusses the creation of a 32.768 kHz quartz tuning fork in situ pressure transducer. Tuning forks are used to measure pressure at room temperature, but no work addresses their potential as cryogenic pressure transducers. We mapped out the behavior of a tuning fork as a function of pressure at 298, 7.0, 2.5, 1.6, 1.0 and 0.7 K by measuring the quality factor. The fork is sensitive to pressures above 0.1 mTorr, limiting its use as a pressure gauge at 0.6 K and below. The experimental curves were compared to a theoretical Q(P, T) function that was refined using the 298 K data. At cryogenic temperatures the formula breaks down in the viscous region and becomes inaccurate. The
Velocity and shear rate estimates of some non-Newtonian oscillatory flows in tubes
NASA Astrophysics Data System (ADS)
Kutev, N.; Tabakova, S.; Radev, S.
2016-10-01
The two-dimensional Newtonian and non-Newtonian (Carreau viscosity model used) oscillatory flows in straight tubes are studied theoretically and numerically. The corresponding analytical solution of the Newtonian flow and the numerical solution of the Carreau viscosity model flow show differences in velocity and shear rate. Some estimates for the velocity and shear rate differences are theoretically proved. As numerical examples the blood flow in different type of arteries and the polymer flow in pipes are considered.
Supersoft symmetry energy encountering non-Newtonian gravity in neutron stars.
Wen, De-Hua; Li, Bao-An; Chen, Lie-Wen
2009-11-20
Considering the non-Newtonian gravity proposed in grand unification theories, we show that the stability and observed global properties of neutron stars cannot rule out the supersoft nuclear symmetry energies at suprasaturation densities. The degree of possible violation of the inverse-square law of gravity in neutron stars is estimated using an equation of state of neutron-rich nuclear matter consistent with the available terrestrial laboratory data.
Supersoft Symmetry Energy Encountering Non-Newtonian Gravity in Neutron Stars
Wen Dehua; Li Baoan; Chen Liewen
2009-11-20
Considering the non-Newtonian gravity proposed in grand unification theories, we show that the stability and observed global properties of neutron stars cannot rule out the supersoft nuclear symmetry energies at suprasaturation densities. The degree of possible violation of the inverse-square law of gravity in neutron stars is estimated using an equation of state of neutron-rich nuclear matter consistent with the available terrestrial laboratory data.
Numerical Experiments in Complex Hæmodynamic Flows. Non-Newtonian Effects
NASA Astrophysics Data System (ADS)
Basombrío, Fernando G.; Dari, Enzo A.; Buscaglia, Gustavo C.; Feijóo, Raúl A.
Numerical experiments for non-trivial flows, close to realistic situations in hæmodynamics, are described and interpreted. Two geometries have been selected: an axisymmetric corrugated tube (with periodic boundary conditions) and a 3D bifurcation with an obstructed end (anastomosis). Results concern sensitivity of errors associated to the time-step size and mesh refinement, but essentially consist of the quantitative estimation of non-Newtonian effects based on Casson's rheological model, treated in retarded form. The time-step lag of such effects is the main reason for evaluating the sensitivity of errors. Due to the high computational cost characterizing the problems to be faced, we expect that the present results will be useful when real geometries should be modeled. The main conclusions are that non-Newtonian effects may be relevant (especially for secondary flows) and that, in most cases, for the same level of errors the use of Casson's law does not generate excessive additional computational costs. Thus, within this strategy, the user can accurately solve the problem using this rheological model without having to worry if the non-Newtonian effects are important or not.
Pulsatile non-Newtonian haemodynamics in a 3D bifurcating abdominal aortic aneurysm model.
Ma, J; Turan, A
2011-08-01
Numerical prediction of non-Newtonian blood flow in a 3D abdominal aortic aneurysm bifurcating model is carried out. The non-Newtonian Carreau model is used to characterise the shear thinning behaviour of the human blood. A physical inlet velocity waveform incorporating a radial velocity distribution reasonably representative of a practical case configuration is employed. Case studies subject to both equal and unequal outlet pressures at iliac bifurcations are presented to display convincingly the downstream pressure influences on the flow behaviour within the aneurysm. Simulations indicate that the non-Newtonian aspects of the blood cannot at all be neglected or given a cursory treatment. The wall shear stress (WSS) is found to change significantly at both the proximal and distal ends of the aneurysm. At the peak systole, the WSS is peak around the bifurcation point, whereas the WSS becomes zero in the bifurcation point. Differential downstream pressure fields display significant effects regarding the flow evolution in the iliac arteries, whereas little or no effects are observed directly on the flow details in the aneurysm.
Khan, M O; Steinman, D A; Valen-Sendstad, K
2016-10-01
Computational fluid dynamics (CFD) shows promise for informing treatment planning and rupture risk assessment for intracranial aneurysms. Much attention has been paid to the impact on predicted hemodynamics of various modelling assumptions and uncertainties, including the need for modelling the non-Newtonian, shear-thinning rheology of blood, with equivocal results. Our study clarifies this issue by contextualizing the impact of rheology model against the recently demonstrated impact of CFD solution strategy on the prediction of aneurysm flow instabilities. Three aneurysm cases were considered, spanning a range of stable to unstable flows. Simulations were performed using a high-resolution/accuracy solution strategy with Newtonian and modified-Cross rheology models and compared against results from a so-called normal-resolution strategy. Time-averaged and instantaneous wall shear stress (WSS) distributions, as well as frequency content of flow instabilities and dome-averaged WSS metrics, were minimally affected by the rheology model, whereas numerical solution strategy had a demonstrably more marked impact when the rheology model was fixed. We show that point-wise normalization of non-Newtonian by Newtonian WSS values tended to artificially amplify small differences in WSS of questionable physiological relevance in already-low WSS regions, which might help to explain the disparity of opinions in the aneurysm CFD literature regarding the impact of non-Newtonian rheology. Toward the goal of more patient-specific aneurysm CFD, we conclude that attention seems better spent on solution strategy and other likely "first-order" effects (eg, lumen segmentation and choice of flow rates), as opposed to "second-order" effects such as rheology.
Nesvizhevsky, V V; Protasov, K V
2005-01-01
An upper limit to non-Newtonian attractive forces is obtained from the measurement of quantum states of neutrons in the Earth's gravitational field. This limit improves the existing constraints in the nanometer range.
Power-law regularities in human language
NASA Astrophysics Data System (ADS)
Mehri, Ali; Lashkari, Sahar Mohammadpour
2016-11-01
Complex structure of human language enables us to exchange very complicated information. This communication system obeys some common nonlinear statistical regularities. We investigate four important long-range features of human language. We perform our calculations for adopted works of seven famous litterateurs. Zipf's law and Heaps' law, which imply well-known power-law behaviors, are established in human language, showing a qualitative inverse relation with each other. Furthermore, the informational content associated with the words ordering, is measured by using an entropic metric. We also calculate fractal dimension of words in the text by using box counting method. The fractal dimension of each word, that is a positive value less than or equal to one, exhibits its spatial distribution in the text. Generally, we can claim that the Human language follows the mentioned power-law regularities. Power-law relations imply the existence of long-range correlations between the word types, to convey an especial idea.
Hierarchical networks, power laws, and neuronal avalanches.
Friedman, Eric J; Landsberg, Adam S
2013-03-01
We show that in networks with a hierarchical architecture, critical dynamical behaviors can emerge even when the underlying dynamical processes are not critical. This finding provides explicit insight into current studies of the brain's neuronal network showing power-law avalanches in neural recordings, and provides a theoretical justification of recent numerical findings. Our analysis shows how the hierarchical organization of a network can itself lead to power-law distributions of avalanche sizes and durations, scaling laws between anomalous exponents, and universal functions-even in the absence of self-organized criticality or critical points. This hierarchy-induced phenomenon is independent of, though can potentially operate in conjunction with, standard dynamical mechanisms for generating power laws.
Deposition Velocities of Newtonian and Non-Newtonian Slurries in Pipelines
Poloski, Adam P.; Adkins, Harold E.; Abrefah, John; Casella, Andrew M.; Hohimer, Ryan E.; Nigl, Franz; Minette, Michael J.; Toth, James J.; Tingey, Joel M.; Yokuda, Satoru T.
2009-03-01
correlation used in the WTP design guide has been shown to be inaccurate for Hanford waste feed materials. The use of the Thomas (1979) correlation in the design guide is not conservative—In cases where 100% of the particles are smaller than 74 μm or particles are considered to be homogeneous due to yield stress forces suspending the particles the homogeneous fraction of the slurry can be set to 100%. In such cases, the predicted critical velocity based on the conservative Oroskar and Turian (1980) correlation is reduced to zero and the design guide returns a value from the Thomas (1979) correlation. The measured data in this report show that the Thomas (1979) correlation predictions often fall below that measured experimental values. A non-Newtonian deposition velocity design guide should be developed for the WTP— Since the WTP design guide is limited to Newtonian fluids and the WTP expects to process large quantities of such materials, the existing design guide should be modified address such systems. A central experimental finding of this testing is that the flow velocity required to reach turbulent flow increases with slurry rheological properties due to viscous forces dampening the formation of turbulent eddies. The flow becomes dominated by viscous forces rather than turbulent eddies. Since the turbulent eddies necessary for particle transport are not present, the particles will settle when crossing this boundary called the transitional deposition boundary. This deposition mechanism should be expected and designed for in the WTP.
Matrix transformations between certain sequence spaces over the non-Newtonian complex field.
Kadak, Uğur; Efe, Hakan
2014-01-01
In some cases, the most general linear operator between two sequence spaces is given by an infinite matrix. So the theory of matrix transformations has always been of great interest in the study of sequence spaces. In the present paper, we introduce the matrix transformations in sequence spaces over the field ℂ(*) and characterize some classes of infinite matrices with respect to the non-Newtonian calculus. Also we give the necessary and sufficient conditions on an infinite matrix transforming one of the classical sets over ℂ(*) to another one. Furthermore, the concept for sequence-to-sequence and series-to-series methods of summability is given with some illustrated examples.
Postglacial rebound with a non-Newtonian upper mantle and a Newtonian lower mantle rheology
NASA Technical Reports Server (NTRS)
Gasperini, Paolo; Yuen, David A.; Sabadini, Roberto
1992-01-01
A composite rheology is employed consisting of both linear and nonlinear creep mechanisms which are connected by a 'transition' stress. Background stress due to geodynamical processes is included. For models with a non-Newtonian upper-mantle overlying a Newtonian lower-mantle, the temporal responses of the displacements can reproduce those of Newtonian models. The average effective viscosity profile under the ice-load at the end of deglaciation turns out to be the crucial factor governing mantle relaxation. This can explain why simple Newtonian rheology has been successful in fitting the uplift data over formerly glaciated regions.
NASA Technical Reports Server (NTRS)
Pappalardo, R. T.; Barr, A. C.
2004-01-01
Numerical modeling of non-Newtonian convection in ice shows that convection controlled by grain boundary sliding rheology may occur in Europa. This modeling confirms that thermal convection alone cannot produce significant dome elevations. Domes may instead be produced by diapirs initiated by thermal convection that in turn induces compositional segregation. Exclusion of impurities from warm upwellings would allow sufficient buoyancy for icy plumes to account for the observed approximately 100 m topography of domes, provided the ice shell has a small effective elastic thickness (approximately 0.2 to 0.5 km) and contains low eutectic-point impurities at the few percent level.
Heat transfer analysis in an annular cone subjected to power law variations
NASA Astrophysics Data System (ADS)
Salman Ahmed, N. J.; Al-Rashed, Abdullah A. A. A.; Yunus Khan, T. M.; Kamangar, Sarfaraz; Athani, Abdulgaphur; Anjum Badruddin, Irfan
2016-09-01
Present study deals with the analysis of heat transfer and fluid flow behavior in an annular cone fixed with saturated porous medium. The inner surface of the cone is assumed to have power law variable wall temperature. The governing partial differential equations are solved using well known Finite Element Method (FEM). The coupled nonlinear differential equations are converted into the algebraic equations by using Galerkin method. A 3 noded triangular element is used to divide the porous domain into smaller segments. The effects of various geometrical parameters on the cone angle are presented. It is found that the effect of cone angle on the heat transfer characteristics and fluid flow behavior is considerably significant. The fluid moment is found to shift towards the upper side of cone with increase in the power law coefficient. The fluid velocity decreases with increase in the power law coefficient.
Walker, Andrew M; Xiao, Yao; Johnston, Clifton R; Rival, David E
2013-01-01
Although information pertaining to the viscous characterization of HES 130/0.4 Voluven® and HES 260/0.45 Pentaspan® is available, quantification is limited to 100% concentrations. We focus here on the quantification of their viscous behavior along with HES 130/0.4 Volulyte® in a shear thinning non-Newtonian blood analog of aqueous xanthan gum and glycerol. Dynamic viscosities of multiple batches of HES fluids were measured through capillary viscometry. The viscous behavior of 100%, 25% and 12.5% concentrations were then measured through a closed flow loop across physiologically relevant flow rates. Measured viscosities were 2.57 millipascal second (mPa·s) 6.52 mPa·s and 2.48 mPa·s for HES 130/0.4 Voluven®, HES 260/0.45 and HES 130/0.4 Volulyte®, respectively. Pipe flow analysis found that all HES fluids displayed Newtonian behavior at 100% concentrations. 25% concentrations of both HES 130/0.4 fluids decreased analog viscosity 23%-29% at a flow rate of 1.0 ml/s and 16%-21% at a flow rate of 22.5 ml/s. At a flow rate of 22.5 ml/s, 25% and 12.5% concentrations of HES 260/0.45 resulted in analog viscosity changes of 3.9%-4.5%. Capillary viscosity reductions of approximately 7% and 14.5% in HES 130/0.4 Voluven® and HES 260/0.45 suggest changes in molecular composition to batches previously measured. Maintenance of analog viscosity suggests that HES 260/0.45 would be suitable as a high viscosity plasma expander in extreme hemodilution through preservation of microcirculatory function and wall shear stress (WSS).
Power law analysis of the human microbiome.
Ma, Zhanshan Sam
2015-11-01
Taylor's (1961, Nature, 189:732) power law, a power function (V = am(b) ) describing the scaling relationship between the mean and variance of population abundances of organisms, has been found to govern the population abundance distributions of single species in both space and time in macroecology. It is regarded as one of few generalities in ecology, and its parameter b has been widely applied to characterize spatial aggregation (i.e. heterogeneity) and temporal stability of single-species populations. Here, we test its applicability to bacterial populations in the human microbiome using extensive data sets generated by the US-NIH Human Microbiome Project (HMP). We further propose extending Taylor's power law from the population to the community level, and accordingly introduce four types of power-law extensions (PLEs): type I PLE for community spatial aggregation (heterogeneity), type II PLE for community temporal aggregation (stability), type III PLE for mixed-species population spatial aggregation (heterogeneity) and type IV PLE for mixed-species population temporal aggregation (stability). Our results show that fittings to the four PLEs with HMP data were statistically extremely significant and their parameters are ecologically sound, hence confirming the validity of the power law at both the population and community levels. These findings not only provide a powerful tool to characterize the aggregations of population and community in both time and space, offering important insights into community heterogeneity in space and/or stability in time, but also underscore the three general properties of power laws (scale invariance, no average and universality) and their specific manifestations in our four PLEs.
NASA Astrophysics Data System (ADS)
Weidman, Patrick
2017-02-01
Boundary-layer solutions to Banks' problem for the flow induced by power-law stretching of a plate are obtained for two generalizations that include arbitrary transverse plate shearing motion. In one extension an arbitrary transverse shearing motion is the product of the power-law stretching. In the other extension the streamwise stretching coordinate is added to an arbitrary transverse shearing and together raised to the power of stretching. In addition we find that Banks' power law stretching may be accompanied by orthogonal power-law shear. In all cases, the original boundary-value problem of Banks [1] is recovered. Results are illustrated with velocity profiles both at the plate and at fixed height in the fluid above the plate.
Non-Newtonian flow of an ultralow-melting chalcogenide liquid in strongly confined geometry
Wang, Siyuan; Jain, Chhavi; Wondraczek, Katrin; Kobelke, Jens; Wondraczek, Lothar; Troles, Johann; Caillaud, Celine; Schmidt, Markus A.
2015-05-18
The flow of high-viscosity liquids inside micrometer-size holes can be substantially different from the flow in the bulk, non-confined state of the same liquid. Such non-Newtonian behavior can be employed to generate structural anisotropy in the frozen-in liquid, i.e., in the glassy state. Here, we report on the observation of non-Newtonian flow of an ultralow melting chalcogenide glass inside a silica microcapillary, leading to a strong deviation of the shear viscosity from its value in the bulk material. In particular, we experimentally show that the viscosity is radius-dependent, which is a clear indication that the microscopic rearrangement of the glass network needs to be considered if the lateral confinement falls below a certain limit. The experiments have been conducted using pressure-assisted melt filling, which provides access to the rheological properties of high-viscosity melt flow under previously inaccessible experimental conditions. The resulting flow-induced structural anisotropy can pave the way towards integration of anisotropic glasses inside hybrid photonic waveguides.
Numerical Analysis of Shear Thickening Fluids for Blast Mitigation Applications
2011-12-01
Newtonian model to describe NNF is the Power-Law Model. It is also called the Ostwald-de Waele relationship. The mathematical relationship is given by τ...using the Ostwald de Waele model, a power law index of 1.5 was assigned. Flow acceleration of 0.3 m/s2 and 0.4 m/s2 were applied to the non- Newtonian
A source-sink model of the generation of plate tectonics from non-Newtonian mantle flow
Bercovici, D.
1995-02-01
A model of mantle convection which generates plate tectonics requires strain rate- or stress-dependent rheology in order to produce strong platelike flows with weak margins as well as strike-slip deformation and plate spin (i.e., toroidal motion). Here, we employ a simple model of source-sink driven surface flow to determine the form of such a rheology that is appropriate for Earth`s present-day plate motions. In this model, lithospheric motion is treated as shallow layer flow driven by sources and sinks which correspond to spreading centers and subduction zones, respectively. Two plate motion models are used to derive the source sink field. As originally implied in the simpler Cartesian version of this model, the classical power law rheologies do not generate platelike flows as well as the hypothetical Whitehead-Gans stick-slip rheology (which incorporates a simple self-lubrication mechanism). None of the fluid rheologies examined, however, produce more than approximately 60% of the original maximum shear. For either plate model, the viscosity fields produced by the power law rheologies are diffuse, and the viscosity lows over strike-slip shear zones or pseudo-margins are not as small as over the prescribed convergent-divergent margins. In contrast, the stick-slip rheology generates very platelike viscosity fields, with sharp gradients at the plate boundaries, and margins with almost uniformly low viscosity. Power law rheologies with high viscosity contrasts, however, lead to almost equally favorable comparisons, though these also yield the least platelike viscosity fields. This implies that the magnitude of toroidal flow and platelike strength distributions are not necessarily related and thus may present independent constraints on the determination of a self-consistent plate-mantle rheology.
A source-sink model of the generation of plate tectonics from non-Newtonian mantle flow
NASA Technical Reports Server (NTRS)
Bercovici, David
1995-01-01
A model of mantle convection which generates plate tectonics requires strain rate- or stress-dependent rheology in order to produce strong platelike flows with weak margins as well as strike-slip deformation and plate spin (i.e., toroidal motion). Here, we employ a simple model of source-sink driven surface flow to determine the form of such a rheology that is appropriate for Earth's present-day plate motions. In this model, lithospheric motion is treated as shallow layer flow driven by sources and sinks which correspond to spreading centers and subduction zones, respectively. Two plate motion models are used to derive the source sink field. As originally implied in the simpler Cartesian version of this model, the classical power law rheologies do not generate platelike flows as well as the hypothetical Whitehead-Gans stick-slip rheology (which incorporates a simple self-lubrication mechanism). None of the fluid rheologies examined, however, produce more than approximately 60% of the original maximum shear. For either plate model, the viscosity fields produced by the power law rheologies are diffuse, and the viscosity lows over strike-slip shear zones or pseudo-margins are not as small as over the prescribed convergent-divergent margins. In contrast, the stick-slip rheology generates very platelike viscosity fields, with sharp gradients at the plate boundaries, and margins with almost uniformly low viscosity. Power law rheologies with high viscosity contrasts, however, lead to almost equally favorable comparisons, though these also yield the least platelike viscosity fields. This implies that the magnitude of toroidal flow and platelike strength distributions are not necessarily related and thus may present independent constraints on the determination of a self-consistent plate-mantle rheology.
Fractal power law in literary English
NASA Astrophysics Data System (ADS)
Gonçalves, L. L.; Gonçalves, L. B.
2006-02-01
We present in this paper a numerical investigation of literary texts by various well-known English writers, covering the first half of the twentieth century, based upon the results obtained through corpus analysis of the texts. A fractal power law is obtained for the lexical wealth defined as the ratio between the number of different words and the total number of words of a given text. By considering as a signature of each author the exponent and the amplitude of the power law, and the standard deviation of the lexical wealth, it is possible to discriminate works of different genres and writers and show that each writer has a very distinct signature, either considered among other literary writers or compared with writers of non-literary texts. It is also shown that, for a given author, the signature is able to discriminate between short stories and novels.
Zipf's law, power laws and maximum entropy
NASA Astrophysics Data System (ADS)
Visser, Matt
2013-04-01
Zipf's law, and power laws in general, have attracted and continue to attract considerable attention in a wide variety of disciplines—from astronomy to demographics to software structure to economics to linguistics to zoology, and even warfare. A recent model of random group formation (RGF) attempts a general explanation of such phenomena based on Jaynes' notion of maximum entropy applied to a particular choice of cost function. In the present paper I argue that the specific cost function used in the RGF model is in fact unnecessarily complicated, and that power laws can be obtained in a much simpler way by applying maximum entropy ideas directly to the Shannon entropy subject only to a single constraint: that the average of the logarithm of the observable quantity is specified.
Relativity, nonextensivity, and extended power law distributions.
Silva, R; Lima, J A S
2005-11-01
A proof of the relativistic theorem by including nonextensive effects is given. As it happens in the nonrelativistic limit, the molecular chaos hypothesis advanced by Boltzmann does not remain valid, and the second law of thermodynamics combined with a duality transformation implies that the parameter lies on the interval [0,2]. It is also proven that the collisional equilibrium states (null entropy source term) are described by the relativistic power law extension of the exponential Juttner distribution which reduces, in the nonrelativistic domain, to the Tsallis power law function. As a simple illustration of the basic approach, we derive the relativistic nonextensive equilibrium distribution for a dilute charged gas under the action of an electromagnetic field . Such results reduce to the standard ones in the extensive limit, thereby showing that the nonextensive entropic framework can be harmonized with the space-time ideas contained in the special relativity theory.
Power laws governing epidemics in isolated populations
NASA Astrophysics Data System (ADS)
Rhodes, C. J.; Anderson, R. M.
1996-06-01
TEMPORAL changes in the incidence of measles virus infection within large urban communities in the developed world have been the focus of much discussion in the context of the identification and analysis of nonlinear and chaotic patterns in biological time series1-11. In contrast, the measles records for small isolated island populations are highly irregular, because of frequent fade-outs of infection12-14, and traditional analysis15 does not yield useful insight. Here we use measurements of the distribution of epidemic sizes and duration to show that regularities in the dynamics of such systems do become apparent. Specifically, these biological systems are characterized by well-defined power laws in a manner reminiscent of other nonlinear, spatially extended dynamical systems in the physical sciences16-19. We further show that the observed power-law exponents are well described by a simple lattice-based model which reflects the social interaction between individual hosts.
Elastically driven surface plumes in rimming flow of a non-Newtonian fluid.
Seiden, Gabriel; Steinberg, Victor
2012-11-01
A polymer solution partially filling a rotating horizontal drum undergoes an elastically driven instability at low Reynolds numbers. This instability manifests itself through localized plumelike bursts, perturbing the free liquid surface. Here we present an expanded experimental account regarding the dynamics of individual plumes and the statistics pertaining to the complex collective interaction between plumes, which leads to plume coagulation. We also present a detailed description of an optical technique that enables the visualization and measurement of surface perturbations in coating flows within a rotating horizontal drum.
NASA Technical Reports Server (NTRS)
Jaishankar, Aditya; Haward, Simon; Hall, Nancy Rabel; Magee, Kevin; McKinley, Gareth
2012-01-01
The primary objective of SHERE II is to study the effect of torsional preshear on the subsequent extensional behavior of filled viscoelastic suspensions. Microgravity environment eliminates gravitational sagging that makes Earth-based experiments of extensional rheology challenging. Experiments may serve as an idealized model system to study the properties of lunar regolith-polymeric binder based construction materials. Filled polymeric suspensions are ubiquitous in foods, cosmetics, detergents, biomedical materials, etc.
2007-11-02
34Therrmanechanical Equations Governing a Material with Prescribed Temperature-Dependent Density, with Applications to Nonisothernal Plane Poiseuille Flow ", D...1-0431 Materials/Modeling, Simulation , & Design of Experiments 6. AUTHORS M. Gregory Forest & Stephen E. Bechtel 7. PERFORMING ORGANIZATION NAME(S...made significant progress in each of these general areas. We produced high resolution models and codes that simulate molten fiber manufacturing
Effects of Flow and Non-Newtonian Fluids on Nonspherical Cavitation Bubbles,
1983-04-10
which incLudes stress accumulation with fading memory was employed by Fogler and Goddard (1970. 1971), who specified a relaxation modulus (memory... Fogler and Goddard present large elastic effects, i.e. changes in the R(t) profiles, but for parameter values which minimize surface 1’ .1 23 tension...also on its appropriate time derivative in a differential model or on the pertinent past values for an Integral equation. Follow- ing Fogler and
MHD boundary-layer flow of a non-Newtonian nanofluid past a stretching sheet with a heat source/sink
NASA Astrophysics Data System (ADS)
Madhu, M.; Kishan, N.
2016-09-01
The goal of the present paper is to examine the magnetohydrodynamic effects on the boundary layer flow of the Jeffrey fluid model for a non-Newtonian nanofluid past a stretching sheet with considering the effects of a heat source/sink. The governing partial differential equations are reduced to a set of coupled nonlinear ordinary differential equations by using suitable similarity transformations. These equations are then solved by the variational finite element method. The profiles of the velocity, temperature, and nanoparticle volume fraction are presented graphically, and the values of the Nusselt and Sherwood numbers are tabulated. The present results are compared with previously published works and are found to be in good agreement with them.
Test of non-Newtonian gravitational forces at micrometer range with two-dimensional force mapping
NASA Astrophysics Data System (ADS)
Wang, Jianbo; Guan, Shengguo; Chen, Kai; Wu, Wenjie; Tian, Zhaoyang; Luo, Pengshun; Jin, Aizi; Yang, Shanqing; Shao, Chenggang; Luo, Jun
2016-12-01
We report an isoelectronic test of non-Newtonian forces at micrometer range by sensing the lateral force between a gold sphere and a density modulation source mass using a soft cantilever. Two-dimensional (2D) force mapping, in combination with in situ topographic imaging, is applied to verify the isoelectronic property of the surface. The force signal is found to be electrostatic force dominated, which is correlated with the density modulation structure for thinner gold coating and reduced by thicker gold coating and thermal annealing. Maximum likelihood estimation is used to extract the constraint on the hypothetical force based on the 2D data, and the experiment sets a constraint on the Yukawa type forces without subtraction of the model dependent force background. This result would be a meaningful complementary to previous tests with different methods.
Matrix Transformations between Certain Sequence Spaces over the Non-Newtonian Complex Field
Efe, Hakan
2014-01-01
In some cases, the most general linear operator between two sequence spaces is given by an infinite matrix. So the theory of matrix transformations has always been of great interest in the study of sequence spaces. In the present paper, we introduce the matrix transformations in sequence spaces over the field ℂ* and characterize some classes of infinite matrices with respect to the non-Newtonian calculus. Also we give the necessary and sufficient conditions on an infinite matrix transforming one of the classical sets over ℂ* to another one. Furthermore, the concept for sequence-to-sequence and series-to-series methods of summability is given with some illustrated examples. PMID:25110740
Exact Solutions for Stokes' Flow of a Non-Newtonian Nanofluid Model: A Lie Similarity Approach
NASA Astrophysics Data System (ADS)
Aziz, Taha; Aziz, A.; Khalique, C. M.
2016-07-01
The fully developed time-dependent flow of an incompressible, thermodynamically compatible non-Newtonian third-grade nanofluid is investigated. The classical Stokes model is considered in which the flow is generated due to the motion of the plate in its own plane with an impulsive velocity. The Lie symmetry approach is utilised to convert the governing nonlinear partial differential equation into different linear and nonlinear ordinary differential equations. The reduced ordinary differential equations are then solved by using the compatibility and generalised group method. Exact solutions for the model equation are deduced in the form of closed-form exponential functions which are not available in the literature before. In addition, we also derived the conservation laws associated with the governing model. Finally, the physical features of the pertinent parameters are discussed in detail through several graphs.
Flow of a Non-Newtonian Liquid with a Free Surface
NASA Astrophysics Data System (ADS)
Borzenko, E. I.; Shrager, G. R.
2016-07-01
A fountain flow of a non-Newtonian liquid filling a vertical plane channel was investigated. The problem of this flow was solved by the finite-difference method on the basis of a system of complete equations of motion with natural boundary conditions on the free surface of the liquid. The stability of calculations was provided by regularization of the rheological Ostwald-de Waele law. It is shown that the indicated flow is divided into a zone of two-dimensional flow in the neighborhood of the free surface and a zone of one-dimensional flow at a distance from this surface. A parametric investigation of the dependence of the kinetic characteristics of the fountain flow and the behavior of its free surface on the determining criteria of this flow and its rheological parameters has been performed.
Frogs use a viscoelastic tongue and non-Newtonian saliva to catch prey.
Noel, Alexis C; Guo, Hao-Yuan; Mandica, Mark; Hu, David L
2017-02-01
Frogs can capture insects, mice and even birds using only their tongue, with a speed and versatility unmatched in the world of synthetic materials. How can the frog tongue be so sticky? In this combined experimental and theoretical study, we perform a series of high-speed films, material tests on the tongue, and rheological tests of the frog saliva. We show that the tongue's unique stickiness results from a combination of a soft, viscoelastic tongue coupled with non-Newtonian saliva. The tongue acts like a car's shock absorber during insect capture, absorbing energy and so preventing separation from the insect. The shear-thinning saliva spreads over the insect during impact, grips it firmly during tongue retraction, and slides off during swallowing. This combination of properties gives the tongue 50 times greater work of adhesion than known synthetic polymer materials such as the sticky-hand toy. These principles may inspire the design of reversible adhesives for high-speed application.
The Non-Newtonian Rheology of Real Magmas: insights into 3D microstructures
NASA Astrophysics Data System (ADS)
Pistone, M.; Caricchi, L.; Ulmer, P.; Reusser, E.; Marone, F.; Burlini, L.
2010-12-01
We present high-resolution 3D microstructures of three-phase magmas composed of melt, bubbles and crystals in different proportions deformed at magmatic pressure and temperature conditions. This study aims to constrain the dependence of rheological and physical properties of magmas on the viscosity of the silicate melt, the applied deformation rate, the relative contents of crystals and bubbles and on the interactions between these phases. The starting material is composed of a hydrous haplogranitic melt containing H2O (2.26 wt%) and CO2 (624 ppm) and different proportions of quartz crystals (between 24 and 65 vol%; 63-125 μm in diameter) and bubbles (between 9 and 12 vol%; 5-150 μm in diameter). Experiments were performed in simple shear using a HT-HP internally-heated Paterson-type rock deformation apparatus (Paterson and Olgaard, 2000) at strain rates ranging between 5×10-5 s-1 and 4×10-3 s-1, at a constant pressure of 200 MPa and temperatures ranging between 723 and 1023 K. Synchrotron based X-ray tomographic microscopy performed at the TOMCAT beamline (Stampanoni et al., 2006) at the Swiss Light Source enabled quantitative evaluation of the 3D microstructure. At high temperature and low strain rate conditions the silicate melt behaves as a Newtonian liquid (Webb and Dingwell, 1990). Higher deformation rates and the contemporary presence of gas bubbles and solid crystals make magma rheology more complex and non-Newtonian behaviour occurs. In all experimental runs two different non-Newtonian effects were observed: shear thinning (decrease of viscosity with increasing strain rate) in high crystal-content magmas (55-65 vol% crystals; 9-10 vol% bubbles) and shear thickening (increase of viscosity with increasing strain rate) in magmas at lower degree of crystallinity (24 vol% crystals; 12 vol% bubbles). Both behaviours were observed at intermediate crystal-content (44 vol% crystals; 12 vol% bubbles), with an initial thickening that subsequently gives way to
Thermocapillary flow of a non-Newtonian nanoliquid film over an unsteady stretching sheet
NASA Astrophysics Data System (ADS)
Narayana, Mahesha; Metri, Prashant G.; Silvestrov, Sergei
2017-01-01
The influence of surface tension on the laminar flow of a thin film of a non-Newtonian nanoliquid over an unsteady stretching sheet is considered. Surface tension is assumed vary linearly with temperature. An effective medium theory (EMT) based model is used for the thermal conductivity of the nanoliquid. Metal and metal oxide nanoparticles are considered in carboxymethyl cellulose (CMC) - water base liquid. The unsteady boundary layer equations are transformed to a system of non-linear ordinary differential equations with the application of similarity transformations. Resultant two-point boundary value problem is solved numerically using a shooting method together with Runge-Kutta-Fehlberg and Newton-Raphson schemes. The effect of surface tension on the dynamics of the considered problem is presented graphically and analyzed in detail. The clear liquid results form special case of the present study.
Magnetohydrodynamic third-grade non-Newtonian nanofluid flow through a porous coaxial cylinder
NASA Astrophysics Data System (ADS)
Sadikin, Zubaidah; Kechil, Seripah Awang
2015-10-01
The convective flow of third grade non-Newtonian nanofluid through porous coaxial cylinders with inclined magnetic field is investigated. The governing partial differential equations are transformed to a system of nonlinear ordinary differential equations using the non-dimensional quantities. The transformed system of nonlinear ordinary differential equations is solved numerically using the fourth-order Runge-Kutta method. The viscosity of the nanofluid is considered as a function of temperature in form of Vogel's model. Numerical solutions are obtained for the velocity, temperature and nanoparticles concentration. The effects of the some physical parameters particularly the angle of inclination, the magnetic, Brownian motion and thermophoresis parameters on non-dimensional velocity, temperature and nanoparticles concentration are analyzed. It is found that as the angle of inclination of magnetic field increases, the velocity decreases. The results also show that increasing the thermophoresis parameter and Brownian motion, the temperature increases. By increasing the Brownian motion or decreasing the thermophoresis parameter, nanoparticles concentration increases.
Wen, Jun; Liu, Kai; Khoshmanesh, Khashayar; Jiang, Wentao; Zheng, Tinghui
2015-01-01
The classic single-phase Newtonian blood flow model ignores the motion of red blood cells (RBCs) and their interaction with plasma. To address these issues, we adopted a multiphase non-Newtonian model to carry out a comparative study between a helical artery bypass graft (ABG) and a conventional ABG in which the blood flow is composed of plasma and RBCs. The investigation focused on the mechanism of RBC buildup in an ABG but the haemodynamic parameters obtained by single-phase and multiphase models were also compared. The aggregation of RBCs along the inside wall of a conventional ABG and at the heel of its distal anastomosis was predicted while a poor aggregation was observed along the helical ABG. In addition, RBCs were observed to gradually sediment along the gravity direction. However, the computed haemodynamic parameters by multiphase model qualitatively agreed well with those by single-phase model. It was concluded that (1) the single-phase computational fluid dynamics (CFD) is reasonable to do the computation of haemodynamic parameters in ABGs; (2) secondary flow does not definitely produce buildup of RBCs in the inside curvature, its configuration played an important role in the movement of RBCs and the dominating one-way rotating flow in a helical ABG guaranteed no buildup of RBCs on its inside wall and (3) gravity direction is important for the movement of RBCs which may help to explain why doing exercise is good for human health. This study helps to shed light on the migration of RBCs in ABGs, which cannot be explored by single-phase CFD models, and provides more understanding of the underlying flow mechanism for ABG failure.
NASA Astrophysics Data System (ADS)
Dhanai, Ruchika; Rana, Puneet; Kumar, Lokendra
2016-05-01
The motivation behind the present analysis is to focus on magneto-hydrodynamic flow and heat transfer characteristics of non-Newtonian fluid (Sisko fluid) past a permeable nonlinear shrinking sheet utilizing nanoparticles involving convective boundary condition. The non-homogenous nanofluid transport model considering the effect of Brownian motion, thermophoresis, suction/injection and no nanoparticle flux at the sheet with convective boundary condition has been solved numerically by the RKF45 method with shooting technique. Critical points for various pertinent parameters are evaluated in this study. The dual solutions (both first and second solutions) are captured in certain range of material constant (nc< n < ∞) , mass transfer parameter (sc < s < ∞) and shrinking parameter (χc < χ < 0) . For both the branches (upper and lower branch), the rate of heat transfer is an increasing function of the power-law index, Prandtl number and Biot number, whereas it is a decreasing function of the material constant and thermophoresis parameter.
Deshpande, S.D.
1985-01-01
Non-Newtonian liquid-gas stratified flow data in 0.026- and 0.052-m-diameter pipes were obtained. Interfacial level gradients between the two phases were observed. The Heywood-Charles model is found to be valid for pseudoplastic liquid-gas uniform stratified flow. Two-phase drag reduction in non-Newtonian systems was not achieved as the transition to semi-slug flow occurred before the model criteria were reached. Interfacial liquid and gas shear stresses were compared. A new parameter ..sigma../sup 2/ is introduced which is a numerical indication of the interfacial level gradient. Two-phase drag reduction was experimentally observed in polymer solution-air plug-slug flow in 0.026- and 0.052-m-diameter pipes. The Hubbard-Dukler pressure drop model was extended to non-Newtonian systems. Reasonable agreement between the experiment and the model predictions is obtained. However, more work needs to be done in order to better understand the two-phase drag reduction phenomena. Liquid holdup correlations were developed for both Newtonian and non-Newtonian systems which successfully correlate the holdup over a wide range of parameters. The Petukhov correlation is found to be better than the Dittus-Boelter correlation in predicting the single-phase water heat-transfer coefficients.
Power-law cosmic expansion in f(R) gravity models
Goheer, Naureen; Larena, Julien; Dunsby, Peter K. S.
2009-09-15
We show that within the class of f(R) gravity theories, Friedmann-Lemaitre-Robertson-Walker power-law perfect fluid solutions only exist for R{sup n} gravity. This significantly restricts the set of exact cosmological solutions which have similar properties to what is found in standard general relativity.
Spectra that behave like power-laws are not necessarily power-laws
NASA Astrophysics Data System (ADS)
Podesta, John J.
2016-02-01
It is shown that measured power spectral densities (spectra) that closely resemble power-law spectra may, in fact, have mathematical forms that are not power laws in the mathematical sense. If power spectral estimates show a good fit to a straight line on a log-log plot over a finite frequency range, that is not sufficient evidence to conclude that the mathematical form of the spectrum is, in fact, a power-law over that range. It is also pointed out that to accurately fit a power-law function to experimental data using linear least squares techniques in log-log space, as is often done in practice, it is essential that the data is uniformly distributed along the abscissa in log-space (in the stochastic sense) or, otherwise, the data must be linearly interpolated onto a uniform grid to ensure that the data employed in the fitting procedure is equally weighted along the abscissa. These two important points are not widely appreciated by researchers in the field and the pitfalls associated with commonly used fitting techniques are often overlooked in the analysis of solar wind data.
Power laws and fragility in flow networks☆
Shore, Jesse; Chu, Catherine J.; Bianchi, Matt T.
2015-01-01
What makes economic and ecological networks so unlike other highly skewed networks in their tendency toward turbulence and collapse? Here, we explore the consequences of a defining feature of these networks: their nodes are tied together by flow. We show that flow networks tend to the power law degree distribution (PLDD) due to a self-reinforcing process involving position within the global network structure, and thus present the first random graph model for PLDDs that does not depend on a rich-get-richer function of nodal degree. We also show that in contrast to non-flow networks, PLDD flow networks are dramatically more vulnerable to catastrophic failure than non-PLDD flow networks, a finding with potential explanatory power in our age of resource- and financial-interdependence and turbulence. PMID:26082568
Experimental investigation of non-Newtonian/Newtonian liquid-liquid flow in microchannel
NASA Astrophysics Data System (ADS)
Roumpea, Eynagelia-Panagiota; Weheliye, Weheliye; Chinaud, Maxime; Angeli, Panagiota; Lyes Kahouadji Collaboration; Omar. K. Matar Collaboration
2015-11-01
Plug flow of an organic phase and an aqueous non-Newtonian solution was investigated experimentally in a quartz microchannel with I.D. 200 μm. The aqueous phase was a glycerol solution where 1000 and 2000 ppm of xanthan gum was added while the organic phase was silicon oil with 155 and 5 cSt viscosity. The two phases were brought together in a T-junction and their flowrates varied from 0.3 to 6 ml/hr. High speed imaging was used to study the characteristics of the plugs and the effect of the liquid properties on the flow patterns while a two-colour micro-PIV technique was used to investigate velocity profiles and circulation patterns within the plugs. The experimental results revealed that plug length was affected by both flowrate and viscosity. In all cases investigated, a film of the continuous phase always surrounded the plugs and its thickness was compared with existing literature models. Circulation patterns inside plugs were obtained by subtracting the plug velocity and found to be depended on the plug length and the amount of xanthan gum in the aqueous phase. Finally, the dimensionless circulation time was calculated and plotted as a function of the plug length. Department of Chemical Engineering South Kensington Campus Imperial College London SW7 2AZ.
NASA Astrophysics Data System (ADS)
Bose, Sayan; Banerjee, Moloy
2015-01-01
Magnetic nanoparticles drug carriers continue to attract considerable interest for drug targeting in the treatment of cancer and other pathological conditions. Magnetic carrier particles with surface-bound drug molecules are injected into the vascular system upstream from the desired target site, and are captured at the target site via a local applied magnetic field. Herein, a numerical investigation of steady magnetic drug targeting (MDT) using functionalized magnetic micro-spheres in partly occluded blood vessel having a 90° bent is presented considering the effects of non-Newtonian characteristics of blood. An Eulerian-Lagrangian technique is adopted to resolve the hemodynamic flow and the motion of the magnetic particles in the flow using ANSYS FLUENT. An implantable infinitely long cylindrical current carrying conductor is used to create the requisite magnetic field. Targeted transport of the magnetic particles in a partly occluded vessel differs distinctly from the same in a regular unblocked vessel. Parametric investigation is conducted and the influence of the insert configuration and its position from the central plane of the artery (zoffset), particle size (dp) and its magnetic property (χ) and the magnitude of current (I) on the "capture efficiency" (CE) is reported. Analysis shows that there exists an optimum regime of operating parameters for which deposition of the drug carrying magnetic particles in a target zone on the partly occluded vessel wall can be maximized. The results provide useful design bases for in vitro set up for the investigation of MDT in stenosed blood vessels.
Raffai, Peter; Szeifert, Gabor; Matone, Luca; Bartos, Imre; Marka, Zsuzsa; Aso, Yoichi; Ricci, Fulvio; Marka, Szabolcs
2011-10-15
We present an experimental opportunity for the future to measure possible violations to Newton's 1/r{sup 2} law in the 0.1-10 m range using dynamic gravity field generators (DFG) and taking advantage of the exceptional sensitivity of modern interferometric techniques. The placement of a DFG in proximity to one of the interferometer's suspended test masses generates a change in the local gravitational field that can be measured at a high signal to noise ratio. The use of multiple DFGs in a null-experiment configuration allows us to test composition-independent non-Newtonian gravity significantly beyond the present limits. Advanced and third-generation gravitational-wave detectors are representing the state-of-the-art in interferometric distance measurement today, therefore, we illustrate the method through their sensitivity to emphasize the possible scientific reach. Nevertheless, it is expected that due to the technical details of gravitational-wave detectors, DFGs shall likely require dedicated custom-configured interferometry. However, the sensitivity measure we derive is a solid baseline indicating that it is feasible to consider probing orders of magnitude into the pristine parameter well beyond the present experimental limits significantly cutting into the theoretical parameter space.
Numerical Simulations of Non-Newtonian Convection in Ice: Application to Europa
NASA Technical Reports Server (NTRS)
Barr, A. C.; Pappalardo, R. T.
2003-01-01
Numerical simulations of solid state convection in Europa's ice shell have so far been limited to consideration of Newtonian flow laws, where the viscosity of ice is strongly dependent upon temperature, predicting that a stagnant lid should form at the top (10-40%) of a convecting ice shell. Such large thicknesses seem to contradict estimates of the effective elastic thickness of Europa s ice shell during its geologically active period. Recent laboratory experiments characterize the rheology of ice as the sum of contributions from several temperature and strain rate-dependent creep mechanisms. We present the results of numerical simulations of convection within Europa s ice shell using the finite-element model Citcom, applying the non-Newtonian rheology of grain boundry sliding. Our calculations suggest a shallower brittle/ductile transition and larger interior convective velocities compared to Newtonian rheology. The flow field is time-dependent, with small, localized upwellings and downwellings at the thermal boundary layers that have minimal topographic expression at the surface.
Non-Newtonian stress tensor and thermal conductivity tensor in granular plane shear flow
NASA Astrophysics Data System (ADS)
Alam, Meheboob; Saha, Saikat
2014-11-01
The non-Newtonian stress tensor and the heat flux in the plane shear flow of smooth inelastic disks are analysed from the Grad-level moment equations using the anisotropic Gaussian as a reference. Closed-form expressions for shear viscosity, pressure, first normal stress difference (N1) and the dissipation rate are given as functions of (i) the density or the area fraction (ν), (ii) the restitution coefficient (e), (iii) the dimensionless shear rate (R), (iv) the temperature anisotropy [ η, the difference between the principal eigenvalues of the second moment tensor] and (v) the angle (ϕ) between the principal directions of the shear tensor and the second moment tensor. Particle simulation data for a sheared hard-disk system is compared with theoretical results, with good agreement for p, μ and N1 over a large range of density. In contrast, the predictions from a Navier-Stokes order constitutive model are found to deviate significantly from both the simulation and the moment theory even at moderate values of e. We show that the gradient of the deviatoric part of the kinetic stress drives a heat current and the thermal conductivity is characterized by an anisotropic 2nd rank tensor for which explicit expressions are derived.
Fluid flow phenomena in the generation of boron carbide suspensions in magnesium melts
NASA Technical Reports Server (NTRS)
Ilegbusi, O. J.; Szekely, J.
1988-01-01
A mathematical representation is developed for the behavior of moderately concentrated magnesium-boron carbide suspensions when subjected to electromagnetic stirring or mechanical agitation. A power-law relationship is employed for the apparent non-Newtonian viscosity of the suspension.
Power-law spatial dispersion from fractional Liouville equation
Tarasov, Vasily E.
2013-10-15
A microscopic model in the framework of fractional kinetics to describe spatial dispersion of power-law type is suggested. The Liouville equation with the Caputo fractional derivatives is used to obtain the power-law dependence of the absolute permittivity on the wave vector. The fractional differential equations for electrostatic potential in the media with power-law spatial dispersion are derived. The particular solutions of these equations for the electric potential of point charge in this media are considered.
On the flow of a non-Newtonian liquid induced by intestine-like contractions.
Phan-Thien, N; Low, H T
1989-02-01
This paper considers the flow of an inelastic liquid which is generated by contractions like those of the intestine. Unlike regular peristaltic motion, these contractions occur locally over a finite length and have a finite amplitude. We adopt a contraction model due to Macagno and Christensen and repeat their analysis for an inelastic liquid. Our analysis, which is based on a Boundary Element Method, indicates that the net flow rate depends very weakly on the power-law index. The pumping action is therefore similar to that of a positive displacement pump.
Stochastic dynamics and a power law for measles variability.
Keeling, M; Grenfell, B
1999-01-01
Since the discovery of a power law scaling between the mean and variance of natural populations, this phenomenon has been observed for a variety of species. Here, we show that the same form of power law scaling also occurs in measles case reports in England and Wales. Remarkably this power law holds over four orders of magnitude. We consider how the natural experiment of vaccination affects the slope of the power law. By examining simple generic models, we are able to predict the effects of stochasticity and coupling and we propose a new phenomenon associated with the critical community size. PMID:10365402
NASA Astrophysics Data System (ADS)
Ciriello, Valentina; Longo, Sandro; Chiapponi, Luca; Di Federico, Vittorio
2016-06-01
We develop a model to grasp the combined effect of rheology and spatial stratifications on two-dimensional non-Newtonian gravity-driven flow in porous media. We consider a power-law constitutive equation for the fluid, and a monomial variation of permeability and porosity along the vertical direction (transverse to the flow) or horizontal direction (parallel to the flow). Under these assumptions, similarity solutions are derived in semi-analytical form for thin gravity currents injected into a two-dimensional porous medium and having constant or time-varying volume. The extent and shape of the porous domain affected by the injection is significantly influenced by the interplay of model parameters. These describe the fluid (flow behaviour index n), the spatial heterogeneity (coefficients β, γ, δ, ω for variations of permeability and porosity in the horizontal or vertical direction), and the type of release (volume exponent α). Theoretical results are validated against two sets of experiments with α = 1 (constant inflow) conducted with a stratified porous medium (simulated by superimposing layers of glass beads of different diameter) and a Hele-Shaw analogue for power-law fluid flow, respectively. In the latter case, a recently established Hele-Shaw analogy is extended to the variation of properties parallel to the flow direction. Comparison with experimental results shows that the proposed model is able to capture the propagation of the current front and the current profile.
Physics of Life: A Model for Non-Newtonian Properties of Living Systems
NASA Technical Reports Server (NTRS)
Zak, Michail
2010-01-01
This innovation proposes the reconciliation of the evolution of life with the second law of thermodynamics via the introduction of the First Principle for modeling behavior of living systems. The structure of the model is quantum-inspired: it acquires the topology of the Madelung equation in which the quantum potential is replaced with the information potential. As a result, the model captures the most fundamental property of life: the progressive evolution; i.e. the ability to evolve from disorder to order without any external interference. The mathematical structure of the model can be obtained from the Newtonian equations of motion (representing the motor dynamics) coupled with the corresponding Liouville equation (representing the mental dynamics) via information forces. All these specific non-Newtonian properties equip the model with the levels of complexity that matches the complexity of life, and that makes the model applicable for description of behaviors of ecological, social, and economical systems. Rather than addressing the six aspects of life (organization, metabolism, growth, adaptation, response to stimuli, and reproduction), this work focuses only on biosignature ; i.e. the mechanical invariants of life, and in particular, the geometry and kinematics of behavior of living things. Living things obey the First Principles of Newtonian mechanics. One main objective of this model is to extend the First Principles of classical physics to include phenomenological behavior on living systems; to develop a new mathematical formalism within the framework of classical dynamics that would allow one to capture the specific properties of natural or artificial living systems such as formation of the collective mind based upon abstract images of the selves and non-selves; exploitation of this collective mind for communications and predictions of future expected characteristics of evolution; and for making decisions and implementing the corresponding corrections if
NASA Astrophysics Data System (ADS)
Le, N. T. P.; Xiao, H.; Myong, R. S.
2014-09-01
The discontinuous Galerkin (DG) method has been popular as a numerical technique for solving the conservation laws of gas dynamics. In the present study, we develop an explicit modal DG scheme for multi-dimensional conservation laws on unstructured triangular meshes in conjunction with non-Newtonian implicit nonlinear coupled constitutive relations (NCCR). Special attention is given to how to treat the complex non-Newtonian type constitutive relations arising from the high degree of thermal nonequilibrium in multi-dimensional gas flows within the Galerkin framework. The Langmuir velocity slip and temperature jump conditions are also implemented into the two-dimensional DG scheme for high Knudsen number flows. As a canonical scalar case, Newtonian and non-Newtonian convection-diffusion Burgers equations are studied to develop the basic building blocks for the scheme. In order to verify and validate the scheme, we applied the scheme to a stiff problem of the shock wave structure for all Mach numbers and to the two-dimensional hypersonic rarefied and low-speed microscale gas flows past a circular cylinder. The computational results show that the NCCR model yields the solutions in better agreement with the direct simulation Monte Carlo (DSMC) data than the Newtonian linear Navier-Stokes-Fourier (NSF) results in all cases of the problem studied.
Yokuda, Satoru T.; Poloski, Adam P.; Adkins, Harold E.; Casella, Andrew M.; Hohimer, Ryan E.; Karri, Naveen K.; Luna, Maria; Minette, Michael J.; Tingey, Joel M.
2009-05-11
The External Flowsheet Review Team (EFRT) has identified the issues relating to the Waste Treatment and Immobilization Plant (WTP) pipe plugging. Per the review’s executive summary, “Piping that transports slurries will plug unless it is properly designed to minimize this risk. This design approach has not been followed consistently, which will lead to frequent shutdowns due to line plugging.” To evaluate the potential for plugging, testing was performed to determine critical velocities for the complex WTP piping layout. Critical velocity is defined as the point at which a moving bed of particles begins to form on the pipe bottom during slurry-transport operations. Pressure drops across the fittings of the test pipeline were measured with differential pressure transducers, from which the critical velocities were determined. A WTP prototype flush system was installed and tested upon the completion of the pressure-drop measurements. We also provide the data for the overflow relief system represented by a WTP complex piping geometry with a non-Newtonian slurry. A waste simulant composed of alumina (nominally 50 μm in diameter) suspended in a kaolin clay slurry was used for this testing. The target composition of the simulant was 10 vol% alumina in a suspending medium with a yield stress of 3 Pa. No publications or reports are available to confirm the critical velocities for the complex geometry evaluated in this testing; therefore, for this assessment, the results were compared to those reported by Poloski et al. (2008) for which testing was performed for a straight horizontal pipe. The results of the flush test are compared to the WTP design guide 24590-WTP-GPG-M-0058, Rev. 0 (Hall 2006) in an effort to confirm flushing-velocity requirements.
The invariances of power law size distributions.
Frank, Steven A
2016-01-01
Size varies. Small things are typically more frequent than large things. The logarithm of frequency often declines linearly with the logarithm of size. That power law relation forms one of the common patterns of nature. Why does the complexity of nature reduce to such a simple pattern? Why do things as different as tree size and enzyme rate follow similarly simple patterns? Here I analyze such patterns by their invariant properties. For example, a common pattern should not change when adding a constant value to all observations. That shift is essentially the renumbering of the points on a ruler without changing the metric information provided by the ruler. A ruler is shift invariant only when its scale is properly calibrated to the pattern being measured. Stretch invariance corresponds to the conservation of the total amount of something, such as the total biomass and consequently the average size. Rotational invariance corresponds to pattern that does not depend on the order in which underlying processes occur, for example, a scale that additively combines the component processes leading to observed values. I use tree size as an example to illustrate how the key invariances shape pattern. A simple interpretation of common pattern follows. That simple interpretation connects the normal distribution to a wide variety of other common patterns through the transformations of scale set by the fundamental invariances.
Piecewise power laws in individual learning curves.
Donner, Yoni; Hardy, Joseph L
2015-10-01
The notion that human learning follows a smooth power law (PL) of diminishing gains is well-established in psychology. This characteristic is observed when multiple curves are averaged, potentially masking more complex dynamics underpinning the curves of individual learners. Here, we analyzed 25,280 individual learning curves, each comprising 500 measurements of cognitive performance taken from four cognitive tasks. A piecewise PL (PPL) model explained the individual learning curves significantly better than a single PL, controlling for model complexity. The PPL model allows for multiple PLs connected at different points in the learning process. We also explored the transition dynamics between PL curve component pieces. Performance in later pieces typically surpassed that in earlier pieces, after a brief drop in performance at the transition point. The transition rate was negatively associated with age, even after controlling for overall performance. Our results suggest at least two processes at work in individual learning curves: locally, a gradual, smooth improvement, with diminishing gains within a specific strategy, which is modeled well as a PL; and globally, a discrete sequence of strategy shifts, in which each strategy is better in the long term than the ones preceding it. The piecewise extension of the classic PL of practice has implications for both individual skill acquisition and theories of learning.
Power law exponents characterizing human DNA
NASA Astrophysics Data System (ADS)
Provata, A.; Oikonomou, Th.
2007-05-01
The size distributions of all known coding and noncoding DNA sequences are studied in all human chromosomes. In a unified approach, both introns and intergenic regions are treated as noncoding regions. The distributions of noncoding segments Pnc(S) of size S present long tails Pnc(S)˜S-1-μnc , with exponents μnc ranging between 0.71 (for chromosome 13) and 1.2 (for chromosome 19). On the contrary, the exponential, short-range decay terms dominate in the distributions of coding (exon) segments Pc(S) in all chromosomes. Aiming to address the emergence of these statistical features, minimal, stochastic, mean-field models are proposed, based on randomly aggregating DNA strings with duplication, influx and outflux of genomic segments. These minimal models produce both the short-range statistics in the coding and the observed power law and fractal statistics in the noncoding DNA. The minimal models also demonstrate that although the two systems (coding and noncoding) coexist, alternating on the same linear chain, they act independently: the coding as a closed, equilibrium system and the noncoding as an open, out-of-equilibrium one.
The invariances of power law size distributions
Frank, Steven A.
2016-01-01
Size varies. Small things are typically more frequent than large things. The logarithm of frequency often declines linearly with the logarithm of size. That power law relation forms one of the common patterns of nature. Why does the complexity of nature reduce to such a simple pattern? Why do things as different as tree size and enzyme rate follow similarly simple patterns? Here I analyze such patterns by their invariant properties. For example, a common pattern should not change when adding a constant value to all observations. That shift is essentially the renumbering of the points on a ruler without changing the metric information provided by the ruler. A ruler is shift invariant only when its scale is properly calibrated to the pattern being measured. Stretch invariance corresponds to the conservation of the total amount of something, such as the total biomass and consequently the average size. Rotational invariance corresponds to pattern that does not depend on the order in which underlying processes occur, for example, a scale that additively combines the component processes leading to observed values. I use tree size as an example to illustrate how the key invariances shape pattern. A simple interpretation of common pattern follows. That simple interpretation connects the normal distribution to a wide variety of other common patterns through the transformations of scale set by the fundamental invariances. PMID:27928497
Power law models of stock indices
NASA Astrophysics Data System (ADS)
Tse, Man Kit
Viewing the stock market as a self-organized system, Sornette and Johansen introduced physics-based models to study the dynamics of stock market crashes from the perspective of complex systems. This involved modeling stock market Indices using a mathematical power law exhibiting log-periodicity as the system approaches a market crash, which acts like a critical point in a thermodynamic system. In this dissertation, I aim to investigate stock indices to determine whether or not they exhibit log-periodic oscillations, according to the models proposed by Sornette, as they approach a crash. In addition to analyzing stock market crashes in the frequency domain using the discrete Fourier transform and the Lomb-Scargle periodogram, I perform a detailed analysis of the stock market crash models through parameter estimation and model testing. I find that the probability landscapes have a complex topography and that there is very little evidence that these phase transition-based models accurately describe stock market crashes.
Rate-Controlling Mechanisms in Five-Power-Law Creep
Michael E. Kassner
2004-04-20
OAK-B135 Rate-Controlling Mechanisms in Five-Power-Law Creep. The initial grant emphasized the rate-controlling processes for five power-law creep. The effort has six aspects: (1) Theory of Taylor hardening from the Frank dislocation network in five power law substructures. (2) The dual dynamical and hardening nature of dislocations in five power law substructures. (3) Determination of the existence of long-range internal stress in five-power law creep dislocation substructures. (4) Dynamic recovery mechanisms associated with dislocation heterogeneities during five power law creep. (5) Versatility of five power law creep concept to other (hcp) crystal structures. (6) Writing of a book on ''Fundamental of Creep in Metals and Alloys'' by M.E. Kassner and Maria-Teresa Perez-Frado (postdoctoral scholar, funded by this project) Elsevier Press, 2004, in press. These areas are consistent with the original goals of this project as delineated in the original proposal to Basic Energy Sciences. The progress in each of these areas will be discussed separately and there will be an attempt to tie each aspect together so as to allow a summary regarding the conclusions with respect to the rate-controlling mechanisms of five power-law creep.
Discovery of power-laws in chemical space.
Benz, Ryan W; Swamidass, S Joshua; Baldi, Pierre
2008-06-01
Power-law distributions have been observed in a wide variety of areas. To our knowledge however, there has been no systematic observation of power-law distributions in chemoinformatics. Here, we present several examples of power-law distributions arising from the features of small, organic molecules. The distributions of rigid segments and ring systems, the distributions of molecular paths and circular substructures, and the sizes of molecular similarity clusters all show linear trends on log-log rank/ frequency plots, suggesting underlying power-law distributions. The number of unique features also follow Heaps'-like laws. The characteristic exponents of the power-laws lie in the 1.5-3 range, consistently with the exponents observed in other power-law phenomena. The power-law nature of these distributions leads to several applications including the prediction of the growth of available data through Heaps' law and the optimal allocation of experimental or computational resources via the 80/20 rule. More importantly, we also show how the power-laws can be leveraged to efficiently compress chemical fingerprints in a lossless manner, useful for the improved storage and retrieval of molecules in large chemical databases.
ERIC Educational Resources Information Center
Collyer, A. A.
1973-01-01
Discusses theories underlying Newtonian and non-Newtonian fluids by explaining flow curves exhibited by plastic, shear-thining, and shear-thickening fluids and Bingham plastic materials. Indicates that the exact mechanism governing shear-thickening behaviors is a problem of further study. (CC)
Fractional power-law spatial dispersion in electrodynamics
Tarasov, Vasily E.; Trujillo, Juan J.
2013-07-15
Electric fields in non-local media with power-law spatial dispersion are discussed. Equations involving a fractional Laplacian in the Riesz form that describe the electric fields in such non-local media are studied. The generalizations of Coulomb’s law and Debye’s screening for power-law non-local media are characterized. We consider simple models with anomalous behavior of plasma-like media with power-law spatial dispersions. The suggested fractional differential models for these plasma-like media are discussed to describe non-local properties of power-law type. -- Highlights: •Plasma-like non-local media with power-law spatial dispersion. •Fractional differential equations for electric fields in the media. •The generalizations of Coulomb’s law and Debye’s screening for the media.
Resurrecting power law inflation in the light of Planck results
Unnikrishnan, Sanil; Sahni, Varun E-mail: varun@iucaa.ernet.in
2013-10-01
It is well known that a canonical scalar field with an exponential potential can drive power law inflation (PLI). However, the tensor-to-scalar ratio in such models turns out to be larger than the stringent limit set by recent Planck results. We propose a new model of power law inflation for which the scalar spectra index, the tensor-to-scalar ratio and the non-gaussianity parameter f{sub N{sub L}{sup equil}} are in excellent agreement with Planck results. Inflation, in this model, is driven by a non-canonical scalar field with an inverse power law potential. The Lagrangian for our model is structurally similar to that of a canonical scalar field and has a power law form for the kinetic term. A simple extension of our model resolves the graceful exit problem which usually afflicts models of power law inflation.
Unsteady solute dispersion in Herschel-Bulkley fluid in a tube with wall absorption
NASA Astrophysics Data System (ADS)
Rana, Jyotirmoy; Murthy, P. V. S. N.
2016-11-01
The axial dispersion of solute in a pulsatile flow of Herschel-Bulkley fluid through a straight circular tube is investigated considering absorption/reaction at the tube wall. The solute dispersion process is described by adopting the generalized dispersion model suggested by Sankarasubramanian and Gill ["Unsteady convective diffusion with interphase mass transfer," Proc. R. Soc. A 333, 115-132 (1973)]. Firstly the exchange, convection, and dispersion coefficients are determined for small and large time, and then the axial mean concentration of a solute in the tube is determined. The effect of power-law index l, yield stress of fluid τy, wall absorption parameter β, amplitude of fluctuating pressure component e, and Womersley frequency parameter α on the convection, dispersion, and mean concentration of solute is discussed for a Herschel-Bulkley fluid in the tube. The single frequency period in the oscillation of dispersion coefficient K2 is observed for small values of α while the double frequency period is noticed for large values of α at small time. Only positive dispersion occurs for small values of α. Both positive and negative dispersion is seen for large values of α. Also, the occurrence of negative dispersion is influenced by the parameters l, τy, β, and e for large values of α. A comparative study of the convection, dispersion, and mean concentration of solute among the Newtonian and non-Newtonian Herschel-Bulkley, power-law, Bingham, and Casson [J. Rana and P. V. S. N. Murthy, "Solute dispersion in pulsatile casson fluid flow in a tube with wall absorption," J. Fluid Mech. 793, 877-914 (2016)] fluid models is presented at small and large time. Also, large time behaviour of non-Newtonian Carreau and Carreau-Yasuda fluid models [J. Rana and P. V. S. N. Murthy, "Unsteady solute dispersion in non-Newtonian fluid flow in a tube with wall absorption," Proc. R. Soc. A 472, 20160294 (2016)] is considered for comparison with other discussed fluid models
Power laws in citation distributions: evidence from Scopus.
Brzezinski, Michal
Modeling distributions of citations to scientific papers is crucial for understanding how science develops. However, there is a considerable empirical controversy on which statistical model fits the citation distributions best. This paper is concerned with rigorous empirical detection of power-law behaviour in the distribution of citations received by the most highly cited scientific papers. We have used a large, novel data set on citations to scientific papers published between 1998 and 2002 drawn from Scopus. The power-law model is compared with a number of alternative models using a likelihood ratio test. We have found that the power-law hypothesis is rejected for around half of the Scopus fields of science. For these fields of science, the Yule, power-law with exponential cut-off and log-normal distributions seem to fit the data better than the pure power-law model. On the other hand, when the power-law hypothesis is not rejected, it is usually empirically indistinguishable from most of the alternative models. The pure power-law model seems to be the best model only for the most highly cited papers in "Physics and Astronomy". Overall, our results seem to support theories implying that the most highly cited scientific papers follow the Yule, power-law with exponential cut-off or log-normal distribution. Our findings suggest also that power laws in citation distributions, when present, account only for a very small fraction of the published papers (less than 1 % for most of science fields) and that the power-law scaling parameter (exponent) is substantially higher (from around 3.2 to around 4.7) than found in the older literature.
Kelly; Humphrey
1998-03-01
Considerable debate has occurred over the use of hydrofoil impellers in large-scale fermentors to improve mixing and mass transfer in highly viscous non-Newtonian systems. Using a computational fluid dynamics software package (Fluent, version 4.30) extensive calculations were performed to study the effect of impeller speed (70-130 rpm), broth rheology (value of power law flow behavior index from 0.2 to 0.6), and distance between the cooling coil bank and the fermentor wall (6-18 in.) on flow near the perimeter of a large (75-m3) fermentor equipped with A315 impellers. A quadratic model utilizing the data was developed in an attempt to correlate the effect of A315 impeller speed, power law flow behavior index, and distance between the cooling coil bank and the fermentor wall on the average axial velocity in the coil bank-wall region. The results suggest that there is a potential for slow or stagnant flow in the coil bank-wall region which could result in poor oxygen and heat transfer for highly viscous fermentations. The results also indicate that there is the potential for slow or stagnant flow in the region between the top impeller and the gas headspace when flow through the coil bank-wall region is slow. Finally, a simple guideline was developed to allow fermentor design engineers to predict the degree of flow behind a bank of helical cooling coils in a large fermentor with hydrofoil flow impellers.
Hariharan, Prasanna; D'Souza, Gavin; Horner, Marc; Malinauskas, Richard A; Myers, Matthew R
2015-09-01
As part of an ongoing effort to develop verification and validation (V&V) standards for using computational fluid dynamics (CFD) in the evaluation of medical devices, we have developed idealized flow-based verification benchmarks to assess the implementation of commonly cited power-law based hemolysis models in CFD. Verification process ensures that all governing equations are solved correctly and the model is free of user and numerical errors. To perform verification for power-law based hemolysis modeling, analytical solutions for the Eulerian power-law blood damage model (which estimates hemolysis index (HI) as a function of shear stress and exposure time) were obtained for Couette and inclined Couette flow models, and for Newtonian and non-Newtonian pipe flow models. Subsequently, CFD simulations of fluid flow and HI were performed using Eulerian and three different Lagrangian-based hemolysis models and compared with the analytical solutions. For all the geometries, the blood damage results from the Eulerian-based CFD simulations matched the Eulerian analytical solutions within ∼1%, which indicates successful implementation of the Eulerian hemolysis model. Agreement between the Lagrangian and Eulerian models depended upon the choice of the hemolysis power-law constants. For the commonly used values of power-law constants (α = 1.9-2.42 and β = 0.65-0.80), in the absence of flow acceleration, most of the Lagrangian models matched the Eulerian results within 5%. In the presence of flow acceleration (inclined Couette flow), moderate differences (∼10%) were observed between the Lagrangian and Eulerian models. This difference increased to greater than 100% as the beta exponent decreased. These simplified flow problems can be used as standard benchmarks for verifying the implementation of blood damage predictive models in commercial and open-source CFD codes. The current study only used power-law model as an illustrative example to emphasize the need
NASA Technical Reports Server (NTRS)
Borgia, Andrea; Spera, Frank J.
1990-01-01
This work discusses the propagation of errors for the recovery of the shear rate from wide-gap concentric cylinder viscometric measurements of non-Newtonian fluids. A least-square regression of stress on angular velocity data to a system of arbitrary functions is used to propagate the errors for the series solution to the viscometric flow developed by Krieger and Elrod (1953) and Pawlowski (1953) ('power-law' approximation) and for the first term of the series developed by Krieger (1968). A numerical experiment shows that, for measurements affected by significant errors, the first term of the Krieger-Elrod-Pawlowski series ('infinite radius' approximation) and the power-law approximation may recover the shear rate with equal accuracy as the full Krieger-Elrod-Pawlowski solution. An experiment on a clay slurry indicates that the clay has a larger yield stress at rest than during shearing, and that, for the range of shear rates investigated, a four-parameter constitutive equation approximates reasonably well its rheology. The error analysis presented is useful for studying the rheology of fluids such as particle suspensions, slurries, foams, and magma.
The Viscosity of Polymeric Fluids.
ERIC Educational Resources Information Center
Perrin, J. E.; Martin, G. C.
1983-01-01
To illustrate the behavior of polymeric fluids and in what respects they differ from Newtonian liquids, an experiment was developed to account for the shear-rate dependence of non-Newtonian fluids. Background information, procedures, and results are provided for the experiment. Useful in transport processes, fluid mechanics, or physical chemistry…
NASA Astrophysics Data System (ADS)
Langlois, Dominic; Cousineau, Denis; Thivierge, J. P.
2014-01-01
The coordination of activity amongst populations of neurons in the brain is critical to cognition and behavior. One form of coordinated activity that has been widely studied in recent years is the so-called neuronal avalanche, whereby ongoing bursts of activity follow a power-law distribution. Avalanches that follow a power law are not unique to neuroscience, but arise in a broad range of natural systems, including earthquakes, magnetic fields, biological extinctions, fluid dynamics, and superconductors. Here, we show that common techniques that estimate this distribution fail to take into account important characteristics of the data and may lead to a sizable misestimation of the slope of power laws. We develop an alternative series of maximum likelihood estimators for discrete, continuous, bounded, and censored data. Using numerical simulations, we show that these estimators lead to accurate evaluations of power-law distributions, improving on common approaches. Next, we apply these estimators to recordings of in vitro rat neocortical activity. We show that different estimators lead to marked discrepancies in the evaluation of power-law distributions. These results call into question a broad range of findings that may misestimate the slope of power laws by failing to take into account key aspects of the observed data.
Langlois, Dominic; Cousineau, Denis; Thivierge, J P
2014-01-01
The coordination of activity amongst populations of neurons in the brain is critical to cognition and behavior. One form of coordinated activity that has been widely studied in recent years is the so-called neuronal avalanche, whereby ongoing bursts of activity follow a power-law distribution. Avalanches that follow a power law are not unique to neuroscience, but arise in a broad range of natural systems, including earthquakes, magnetic fields, biological extinctions, fluid dynamics, and superconductors. Here, we show that common techniques that estimate this distribution fail to take into account important characteristics of the data and may lead to a sizable misestimation of the slope of power laws. We develop an alternative series of maximum likelihood estimators for discrete, continuous, bounded, and censored data. Using numerical simulations, we show that these estimators lead to accurate evaluations of power-law distributions, improving on common approaches. Next, we apply these estimators to recordings of in vitro rat neocortical activity. We show that different estimators lead to marked discrepancies in the evaluation of power-law distributions. These results call into question a broad range of findings that may misestimate the slope of power laws by failing to take into account key aspects of the observed data.
Thresholded Power law Size Distributions of Instabilities in Astrophysics
NASA Astrophysics Data System (ADS)
Aschwanden, Markus J.
2015-11-01
Power-law-like size distributions are ubiquitous in astrophysical instabilities. There are at least four natural effects that cause deviations from ideal power law size distributions, which we model here in a generalized way: (1) a physical threshold of an instability; (2) incomplete sampling of the smallest events below a threshold x0; (3) contamination by an event-unrelated background xb; and (4) truncation effects at the largest events due to a finite system size. These effects can be modeled in the simplest terms with a “thresholded power law” distribution function (also called generalized Pareto [type II] or Lomax distribution), N(x){dx}\\propto {(x+{x}0)}-a{dx}, where x0 > 0 is positive for a threshold effect, while x0 < 0 is negative for background contamination. We analytically derive the functional shape of this thresholded power law distribution function from an exponential growth evolution model, which produces avalanches only when a disturbance exceeds a critical threshold x0. We apply the thresholded power law distribution function to terrestrial, solar (HXRBS, BATSE, RHESSI), and stellar flare (Kepler) data sets. We find that the thresholded power law model provides an adequate fit to most of the observed data. Major advantages of this model are the automated choice of the power law fitting range, diagnostics of background contamination, physical instability thresholds, instrumental detection thresholds, and finite system size limits. When testing self-organized criticality models that predict ideal power laws, we suggest including these natural truncation effects.
Statistical analyses support power law distributions found in neuronal avalanches.
Klaus, Andreas; Yu, Shan; Plenz, Dietmar
2011-01-01
The size distribution of neuronal avalanches in cortical networks has been reported to follow a power law distribution with exponent close to -1.5, which is a reflection of long-range spatial correlations in spontaneous neuronal activity. However, identifying power law scaling in empirical data can be difficult and sometimes controversial. In the present study, we tested the power law hypothesis for neuronal avalanches by using more stringent statistical analyses. In particular, we performed the following steps: (i) analysis of finite-size scaling to identify scale-free dynamics in neuronal avalanches, (ii) model parameter estimation to determine the specific exponent of the power law, and (iii) comparison of the power law to alternative model distributions. Consistent with critical state dynamics, avalanche size distributions exhibited robust scaling behavior in which the maximum avalanche size was limited only by the spatial extent of sampling ("finite size" effect). This scale-free dynamics suggests the power law as a model for the distribution of avalanche sizes. Using both the Kolmogorov-Smirnov statistic and a maximum likelihood approach, we found the slope to be close to -1.5, which is in line with previous reports. Finally, the power law model for neuronal avalanches was compared to the exponential and to various heavy-tail distributions based on the Kolmogorov-Smirnov distance and by using a log-likelihood ratio test. Both the power law distribution without and with exponential cut-off provided significantly better fits to the cluster size distributions in neuronal avalanches than the exponential, the lognormal and the gamma distribution. In summary, our findings strongly support the power law scaling in neuronal avalanches, providing further evidence for critical state dynamics in superficial layers of cortex.
Helmholtz solitons in power-law optical materials
Christian, J. M.; McDonald, G. S.; Potton, R. J.; Chamorro-Posada, P.
2007-09-15
A nonlinear Helmholtz equation for optical materials with regimes of power-law type of nonlinearity is proposed. This model captures the evolution of broad beams at any angle with respect to the reference direction in a wide range of media, including some semiconductors, doped glasses, and liquid crystals. Exact analytical soliton solutions are presented for a generic nonlinearity, within which known Kerr solitons comprise a subset. Three general conservation laws are also reported. Analysis and numerical simulations examine the stability of the Helmholtz power-law solitons. A propagation feature, associated with spatial solitons in power-law media, constituting a class of oscillatory solution, is identified.
NASA Astrophysics Data System (ADS)
Shintaku, Hirofumi; Yonemura, Tsubasa; Tsuru, Kazuaki; Isoyama, Takashi; Yambe, Tomoyuki; Kawano, Satoyuki
In this study, we construct an experimental apparatus for a prototype artificial heart and lung (AHL) by installing hollow fibers into the cylindrical tube of the vibrating flow pump (VFP). The oxygenation characteristics are investigated both by experiments using bovine blood and by numerical analyses based on the computational fluid dynamics. The analyses are carried out at the Reynolds numbers Re ranged from O(1) to O(103), which are determined based on the experimental conditions. The blood flow and the diffusion of oxygen gas are analyzed based on the Newtonian/non-Newtonian, unsteady, incompressible and axisymmetric Navier-Stokes equations, and the advection-diffusion equation. The results show that the oxygenation rate increases in proportion to Re1/3, where the phenomenon corresponds to the decreasing thickness of the concentration boundary layer with Re. Although the effects of the vibrating flow and the rheology of the blood are clearly appeared on the velocity field, their effects on the gas exchange are relatively small at the ranges of prescribed Reynolds numbers. Furthermore, the numerical results in terms of the oxygenation rate are compared with the experimental ones. The basic design data of VFP were accumulated for the development of AHL in the clinical applications.
Simple power law for transport ratio with bimodal distributions of coarse sediments under waves
NASA Astrophysics Data System (ADS)
Calantoni, Joseph; Thaxton, Christopher S.
2008-03-01
Morphodynamic models of coastal evolution require relatively simple parameterizations of sediment transport for application over larger scales. Here we present a transport parameterization for bimodal distributions of coarse quartz grains using simulations from a discrete particle model for sheet flow and near sheet flow conditions. The discrete particle model simulates the simplest one-dimensional fluid using a turbulent eddy viscosity determined from a mixing length coupled to particle motions. The motions of individual sand grains are simulated using spherical elements. Newton's second law in translational and rotational forms is solved for every particle in the domain as determined by both grain-grain and grain-fluid interactions. The forcing from idealized monochromatic waves is accomplished by specifying a spatially constant, time varying horizontal pressure gradient acting on the simulation domain. Consequently, the time series of the free-stream fluid acceleration and velocity are also fixed. Simulations cover a range of wave forcing, diameter ratios for the large and small grains in the bimodal size distribution, and mass ratios of large to small grains in the simulation domain, for a total of 243 unique simulation conditions. The simulation results are successfully parameterized with a simple power law that allows for the prediction of the transport rates of each size fraction in the bimodal distribution. The simple power law determined from simulations provides favorable predictions of transport rates for each size fraction when applied to available laboratory data for sheet flow with bimodal size distributions. It is important to note that rapid vertical kinematic sorting of grains by size is explicitly simulated with the model and thus implicitly captured by the power law. Discussion focuses on practical application of the power law.
Fractal ladder models and power law wave equations
Kelly, James F.; McGough, Robert J.
2009-01-01
The ultrasonic attenuation coefficient in mammalian tissue is approximated by a frequency-dependent power law for frequencies less than 100 MHz. To describe this power law behavior in soft tissue, a hierarchical fractal network model is proposed. The viscoelastic and self-similar properties of tissue are captured by a constitutive equation based on a lumped parameter infinite-ladder topology involving alternating springs and dashpots. In the low-frequency limit, this ladder network yields a stress-strain constitutive equation with a time-fractional derivative. By combining this constitutive equation with linearized conservation principles and an adiabatic equation of state, a fractional partial differential equation that describes power law attenuation is derived. The resulting attenuation coefficient is a power law with exponent ranging between 1 and 2, while the phase velocity is in agreement with the Kramers–Kronig relations. The fractal ladder model is compared to published attenuation coefficient data, thus providing equivalent lumped parameters. PMID:19813816
Fractal ladder models and power law wave equations.
Kelly, James F; McGough, Robert J
2009-10-01
The ultrasonic attenuation coefficient in mammalian tissue is approximated by a frequency-dependent power law for frequencies less than 100 MHz. To describe this power law behavior in soft tissue, a hierarchical fractal network model is proposed. The viscoelastic and self-similar properties of tissue are captured by a constitutive equation based on a lumped parameter infinite-ladder topology involving alternating springs and dashpots. In the low-frequency limit, this ladder network yields a stress-strain constitutive equation with a time-fractional derivative. By combining this constitutive equation with linearized conservation principles and an adiabatic equation of state, a fractional partial differential equation that describes power law attenuation is derived. The resulting attenuation coefficient is a power law with exponent ranging between 1 and 2, while the phase velocity is in agreement with the Kramers-Kronig relations. The fractal ladder model is compared to published attenuation coefficient data, thus providing equivalent lumped parameters.
Singularity problems of the power law for modeling creep compliance
NASA Technical Reports Server (NTRS)
Dillard, D. A.; Hiel, C.
1985-01-01
An explanation is offered for the extreme sensitivity that has been observed in the power law parameters of the T300/934 graphite epoxy material systems during experiments to evaluate the system's viscoelastic response. It is shown that the singularity associated with the power law can explain the sensitivity as well as the observed variability in the calculated parameters. Techniques for minimizing errors are suggested.
Hidden power law patterns in the top European football leagues
NASA Astrophysics Data System (ADS)
Da Silva, Sergio; Matsushita, Raul; Silveira, Eliza
2013-11-01
Because sports are stylized combat, sports may follow power laws similar to those found for wars, individual clashes, and acts of terrorism. We show this fact for football (soccer) by adjusting power laws that show a close relationship between rank and points won by the clubs participating in the latest seasons of the top fifteen European football leagues. In addition, we use Shannon entropy for gauging league competitive balance. As a result, we are able to rank the leagues according to competitiveness.
Interdisciplinary Research Programs in Geophysical Fluid Dynamics
2007-09-30
scientific disciplines that deal with the dynamics of stratified fluids, rotating fluids, fluid with phase changes and non-Newtonian fluids. To formulate...clearing-house for the mathematical, experimental and computational techniques which serve astrophysics, climate science, geodynamics, meteorology and... Zika , Physical Oceanography, University of New South Wales, “The stability of cascading flows”. RESULTS The Principal Lectures and Fellows
Systematic harmonic power laws inter-relating multiple fundamental constants
NASA Astrophysics Data System (ADS)
Chakeres, Donald; Buckhanan, Wayne; Andrianarijaona, Vola
2017-01-01
Power laws and harmonic systems are ubiquitous in physics. We hypothesize that 2, π, the electron, Bohr radius, Rydberg constant, neutron, fine structure constant, Higgs boson, top quark, kaons, pions, muon, Tau, W, and Z when scaled in a common single unit are all inter-related by systematic harmonic powers laws. This implies that if the power law is known it is possible to derive a fundamental constant's scale in the absence of any direct experimental data of that constant. This is true for the case of the hydrogen constants. We created a power law search engine computer program that randomly generated possible positive or negative powers searching when the product of logical groups of constants equals 1, confirming they are physically valid. For 2, π, and the hydrogen constants the search engine found Planck's constant, Coulomb's energy law, and the kinetic energy law. The product of ratios defined by two constants each was the standard general format. The search engine found systematic resonant power laws based on partial harmonic fraction powers of the neutron for all of the constants with products near 1, within their known experimental precision, when utilized with appropriate hydrogen constants. We conclude that multiple fundamental constants are inter-related within a harmonic power law system.
Liu, Biyue; Tang, Dalin
2011-01-01
The objective of this work is to investigate the effect of non-Newtonian properties of blood on the wall shear stress (WSS) in atherosclerotic coronary arteries using both Newtonian and non-Newtonian models. Numerical simulations were performed to examine how the spatial and temporal WSS distributions are influenced by the stenosis size, blood viscosity, and flow rate. The computational results demonstrated that blood viscosity properties had considerable effect on the magnitude of the WSS, especially where disturbed flow was observed. The WSS distribution is highly non-uniform both temporally and spatially, especially in the stenotic region. The maximum WSS occurred at the proximal side of the stenosis, near the outer wall in the curved artery with no stenosis. The lumen area near the inner wall distal to the stenosis region experienced a lower WSS during the entire cardiac cycle. Among the factors of stenosis size, blood viscosity, and flow rate, the size of the stenosis has the most significant effect on the spatial and temporal WSS distributions qualitatively and quantitatively. PMID:21379375
Unsteady Boundary-Layer Flow over Jerked Plate Moving in a Free Stream of Viscoelastic Fluid
Mehmood, Ahmer; Ali, Asif; Saleem, Najma
2014-01-01
This study aims to investigate the unsteady boundary-layer flow of a viscoelastic non-Newtonian fluid over a flat surface. The plate is suddenly jerked to move with uniform velocity in a uniform stream of non-Newtonian fluid. Purely analytic solution to governing nonlinear equation is obtained. The solution is highly accurate and valid for all values of the dimensionless time 0 ≤ τ < ∞. Flow properties of the viscoelastic fluid are discussed through graphs. PMID:24892060
Phase diagram of softly repulsive systems: the Gaussian and inverse-power-law potentials.
Prestipino, Santi; Saija, Franz; Giaquinta, Paolo V
2005-10-08
We redraw, using state-of-the-art methods for free-energy calculations, the phase diagrams of two reference models for the liquid state: the Gaussian and inverse-power-law repulsive potentials. Notwithstanding the different behaviors of the two potentials for vanishing interparticle distances, their thermodynamic properties are similar in a range of densities and temperatures, being ruled by the competition between the body-centered-cubic (bcc) and face-centered-cubic (fcc) crystalline structures and the fluid phase. We confirm the existence of a reentrant bcc phase in the phase diagram of the Gaussian-core model, just above the triple point. We also trace the bcc-fcc coexistence line of the inverse-power-law model as a function of the power exponent n and relate the common features in the phase diagrams of such systems to the softness degree of the interaction.
Breaking of non-Newtonian character in flows through a porous medium.
Chevalier, T; Rodts, S; Chateau, X; Chevalier, C; Coussot, P
2014-02-01
From NMR measurements we show that the velocity field of a yield stress fluid flowing through a disordered well-connected porous medium is very close to that for a Newtonian fluid. In particular, it is shown that no arrested regions exist even at very low velocities, for which the solid regime is expected to be dominant. This suggests that these results obtained for strongly nonlinear fluid can be extrapolated to any nonlinear fluid. We deduce a generalized form of Darcy's law for such materials and provide insight into the physical origin of the coefficients involved in this expression, which are shown to be moments of the second invariant of the strain rate tensor.
A generalization of the power law distribution with nonlinear exponent
NASA Astrophysics Data System (ADS)
Prieto, Faustino; Sarabia, José María
2017-01-01
The power law distribution is usually used to fit data in the upper tail of the distribution. However, commonly it is not valid to model data in all the range. In this paper, we present a new family of distributions, the so-called Generalized Power Law (GPL), which can be useful for modeling data in all the range and possess power law tails. To do that, we model the exponent of the power law using a non-linear function which depends on data and two parameters. Then, we provide some basic properties and some specific models of that new family of distributions. After that, we study a relevant model of the family, with special emphasis on the quantile and hazard functions, and the corresponding estimation and testing methods. Finally, as an empirical evidence, we study how the debt is distributed across municipalities in Spain. We check that power law model is only valid in the upper tail; we show analytically and graphically the competence of the new model with municipal debt data in the whole range; and we compare the new distribution with other well-known distributions including the Lognormal, the Generalized Pareto, the Fisk, the Burr type XII and the Dagum models.
Distortion of power law blinking with binning and thresholding
Amecke, Nicole; Heber, André; Cichos, Frank
2014-03-21
Fluorescence intermittency is a random switching between emitting (on) and non-emitting (off) periods found for many single chromophores such as semiconductor quantum dots and organic molecules. The statistics of the duration of on- and off-periods are commonly determined by thresholding the emission time trace of a single chromophore and appear to be power law distributed. Here we test with the help of simulations if the experimentally determined power law distributions can actually reflect the underlying statistics. We find that with the experimentally limited time resolution real power law statistics with exponents α{sub on/off} ≳ 1.6, especially if α{sub on} ≠ α{sub off} would not be observed as such in the experimental data after binning and thresholding. Instead, a power law appearance could simply be obtained from the continuous distribution of intermediate intensity levels. This challenges much of the obtained data and the models describing the so-called power law blinking.
NASA Astrophysics Data System (ADS)
Brook, Martin; Hebblewhite, Bruce; Mitra, Rudrajit
2016-04-01
The size-scaling of rock fractures is a well-studied problem in geology, especially for permeability quantification. The intensity of fractures may control the economic exploitation of fractured reservoirs because fracture intensity describes the abundance of fractures potentially available for fluid flow. Moreover, in geotechnical engineering, fractures are important for parameterisation of stress models and excavation design. As fracture data is often collected from widely-spaced boreholes where core recovery is often incomplete, accurate interpretation and representation of fracture aperture-frequency relationships from sparse datasets is important. Fracture intensity is the number of fractures encountered per unit length along a sample scanline oriented perpendicular to the fractures in a set. Cumulative frequency of fractures (F) is commonly related to fracture aperture (A) in the form of a power-law (F = aA-b), with variations in the size of the a coefficient between sites interpreted to equate to fracture frequency for a given aperture (A). However, a common flaw in this approach is that even a small change in b can have a large effect on the response of the fracture frequency (F) parameter. We compare fracture data from the Late Permian Rangal Coal Measures from Australia's Bowen Basin, with fracture data from Jurassic carbonates from the Sierra Madre Oriental, northeastern Mexico. Both power-law coefficient a and exponent b control the fracture aperture-frequency relationship in conjunction with each other; that is, power-laws with relatively low a coefficients have relatively high b exponents and vice versa. Hence, any comparison of different power-laws must take both a and b into consideration. The corollary is that different sedimentary beds in the Sierra Madre carbonates do not show ˜8× the fracture frequency for a given fracture aperture, as based solely on the comparison of coefficient a. Rather, power-law "sensitivity factors" developed from both
NASA Astrophysics Data System (ADS)
Jain, Rajat; Mahto, Triveni K.; Mahto, Vikas
2016-02-01
In the present study, polyacrylamide grafted xanthan gum/multiwalled carbon nanotubes (PA-g-XG/MWCNT) nanocomposite was synthesized by free radical polymerization technique using potassium persulfate as an initiator. The polyacrylamide was grafted on xanthan gum backbone in the presence of MWCNT. The synthesized nanocomposite was characterized by X-ray diffraction technique (XRD), and Fourier transform infrared spectroscopy analysis (FT-IR). The morphological characteristics of the nanocomposite were analyzed by field emission scanning electron microscopy (FESEM) and atomic force microscopy (AFM) analyses. Also, its temperature resistance property was observed with Thermogravimetric analysis (TGA). The effect of nanocomposite on the rheological properties of the developed drilling fluid system was analyzed with a strain controlled rheometer and Fann viscometer. Flow curves were drawn for the developed water based drilling fluid system at elevated temperatures. The experimental data were fitted to Bingham, power-law, and Herschel Bulkley flow models. It was observed that the Herschel Bulkley flow model predict the flow behavior of the developed system more accurately. Further, nanocomposite exhibited non-Newtonian shear thinning flow behavior in the developed drilling fluid system. Nanocomposite showed high temperature stability and had a significant effect on the rheological properties of the developed drilling fluid system as compared to conventionally used partially hydrolyzed polyacrylamide (PHPA) polymer.
Simulation of Droplet Generation in a Non-Newtonian Dense Granular Suspension
NASA Astrophysics Data System (ADS)
Mårtensson, Gustaf; Svensson, Martin; Mark, Andreas; Edelvik, Fredrik
2015-11-01
As with the jet printing of dyes and other low-viscosity fluids, the jetting of dense fluid suspensions is dependent on the repeatable break-off of the fluid filament into well-formed droplets. It is well known that the break-off of dense suspensions is dependent on the volume fraction of the solid phase, particle size and morphology, fluid phase viscosity et cetera, see for example van Deen et al. (2013). The purpose of this study is to propose a novel simulation framework and to show that it captures the main effects such as droplet shape, volume and speed in a cylindrical duct test configuration. The granular suspension is modelled as a mixed single phase suspension, where the local thermodynamic properties are determined by the mixture level. The simulations are performed with IBOFlow, a multiphase flow solver, coupled with LaStFEM, a large strain FEM solver. To study how the droplet generation is affected by the acceleration of the fluid, simulations are performed for a series of actuation profiles. The simulation results were compared to experimental data obtained from an industrial jetting head. The simulations exhibit qualitative agreement with the experimental data. A sensitivity to the inlet boundary condition with respect to the resulting droplet speed was observed. Thanks to Swedish Research Council (Grant 2010-4334).
A power law approach to orifice flow rate calibration.
Rhinehart, R Russell; Gebreyohannes, Solomon; Sridhar, Upasana Manimegalai; Patrachari, Anirudh; Rahaman, M S
2011-04-01
Although standards for orifice flow meter design, installation, and calibration are supported herein, noncompliant devices exist in many pilot-, lab-scale, and on-board applications. For these, a common calibration practice is to preserve the ideal square root relation and determine a device specific discharge coefficient value. This work provides theoretical and empirical analyses to support relaxing the square root relation between orifice pressure drop and flow rate for noncompliant devices. The resulting power law relation is shown to improve accuracy, precision, and rangeability. Whether a device specific square root or power law model is used, it requires off-line or in-line calibration data. As such, a power law calibration model may only be useful for on-board and small-scale applications.
Between disorder and order: A case study of power law
NASA Astrophysics Data System (ADS)
Cao, Yong; Zhao, Youjie; Yue, Xiaoguang; Xiong, Fei; Sun, Yongke; He, Xin; Wang, Lichao
2016-08-01
Power law is an important feature of phenomena in long memory behaviors. Zipf ever found power law in the distribution of the word frequencies. In physics, the terms order and disorder are Thermodynamic or statistical physics concepts originally and a lot of research work has focused on self-organization of the disorder ingredients of simple physical systems. It is interesting what make disorder-order transition. We devise an experiment-based method about random symbolic sequences to research regular pattern between disorder and order. The experiment results reveal power law is indeed an important regularity in transition from disorder to order. About these results the preliminary study and analysis has been done to explain the reasons.
Power-law relations in random networks with communities.
Stegehuis, Clara; van der Hofstad, Remco; van Leeuwaarden, Johan S H
2016-07-01
Most random graph models are locally tree-like-do not contain short cycles-rendering them unfit for modeling networks with a community structure. We introduce the hierarchical configuration model (HCM), a generalization of the configuration model that includes community structures, while properties such as the size of the giant component, and the size of the giant percolating cluster under bond percolation can still be derived analytically. Viewing real-world networks as realizations of HCM, we observe two previously undiscovered power-law relations: between the number of edges inside a community and the community sizes, and between the number of edges going out of a community and the community sizes. We also relate the power-law exponent τ of the degree distribution with the power-law exponent of the community-size distribution γ. In the case of extremely dense communities (e.g., complete graphs), this relation takes the simple form τ=γ-1.
Power-law hereditariness of hierarchical fractal bones.
Deseri, Luca; Di Paola, Mario; Zingales, Massimiliano; Pollaci, Pietro
2013-12-01
In this paper, the authors introduce a hierarchic fractal model to describe bone hereditariness. Indeed, experimental data of stress relaxation or creep functions obtained by compressive/tensile tests have been proved to be fit by power law with real exponent 0 ⩽ β ⩽1. The rheological behavior of the material has therefore been obtained, using the Boltzmann-Volterra superposition principle, in terms of real order integrals and derivatives (fractional-order calculus). It is shown that the power laws describing creep/relaxation of bone tissue may be obtained by introducing a fractal description of bone cross-section, and the Hausdorff dimension of the fractal geometry is then related to the exponent of the power law.
Edge effect on the power law distribution of granular avalanches.
Lorincz, Kinga A; Wijngaarden, Rinke J
2007-10-01
Many punctuated phenomena in nature are claimed [e.g., by the theory of self-organized criticality (SOC)] to be power-law distributed. In our experiments on a three-dimensional pile of long-grained rice, we find that by only changing the boundary condition of the system, we switch from such power-law-distributed avalanche sizes to quasiperiodic system-spanning avalanches. Conversely, by removing ledges the incidence of system-spanning avalanches is significantly reduced. This may offer a perspective on new avalanche prevention schemes. In addition, our findings may help to explain why the archetype of SOC, the sandpile, was found to have power-law-distributed avalanches in some experiments, while in other experiments quasiperiodic system-spanning avalanches were found.
General 2.5 power law of metallic glasses
Zeng, Qiaoshi; Lin, Yu; Liu, Yijin; Zeng, Zhidan; Shi, Crystal Y.; Zhang, Bo; Lou, Hongbo; Sinogeikin, Stanislav V.; Kono, Yoshio; Kenney-Benson, Curtis; Park, Changyong; Yang, Wenge; Wang, Weihua; Sheng, Hongwei; Mao, Ho-kwang; Mao, Wendy L.
2016-01-01
Metallic glass (MG) is an important new category of materials, but very few rigorous laws are currently known for defining its “disordered” structure. Recently we found that under compression, the volume (V) of an MG changes precisely to the 2.5 power of its principal diffraction peak position (1/q1). In the present study, we find that this 2.5 power law holds even through the first-order polyamorphic transition of a Ce68Al10Cu20Co2 MG. This transition is, in effect, the equivalent of a continuous “composition” change of 4f-localized “big Ce” to 4f-itinerant “small Ce,” indicating the 2.5 power law is general for tuning with composition. The exactness and universality imply that the 2.5 power law may be a general rule defining the structure of MGs. PMID:26831105
Robust Statistical Detection of Power-Law Cross-Correlation
NASA Astrophysics Data System (ADS)
Blythe, Duncan A. J.; Nikulin, Vadim V.; Müller, Klaus-Robert
2016-06-01
We show that widely used approaches in statistical physics incorrectly indicate the existence of power-law cross-correlations between financial stock market fluctuations measured over several years and the neuronal activity of the human brain lasting for only a few minutes. While such cross-correlations are nonsensical, no current methodology allows them to be reliably discarded, leaving researchers at greater risk when the spurious nature of cross-correlations is not clear from the unrelated origin of the time series and rather requires careful statistical estimation. Here we propose a theory and method (PLCC-test) which allows us to rigorously and robustly test for power-law cross-correlations, correctly detecting genuine and discarding spurious cross-correlations, thus establishing meaningful relationships between processes in complex physical systems. Our method reveals for the first time the presence of power-law cross-correlations between amplitudes of the alpha and beta frequency ranges of the human electroencephalogram.
NASA Astrophysics Data System (ADS)
Nabwey, Hossam A.; Boumazgour, Mohamed; Rashad, A. M.
2017-03-01
The group method analysis is applied to study the steady mixed convection stagnation-point flow of a non-Newtonian nanofluid towards a vertical stretching surface. The model utilized for the nanofluid incorporates the Brownian motion and thermophoresis effects. Applying the one-parameter transformation group which reduces the number of independent variables by one and thus, the system of governing partial differential equations has been converted to a set of nonlinear ordinary differential equations, and these equations are then computed numerically using the implicit finite-difference scheme. Comparison with previously published studies is executed and the results are found to be in excellent agreement. Results for the velocity, temperature, and the nanoparticle volume fraction profiles as well as the local skin-friction coefficient and local Nusselt number are presented in graphical and tabular forms, and discussed for different values of the governing parameters to show interesting features of the solutions.
Time-Resolved imaging Studies of Laser-Induced Jet Formation in Non-Newtonian Liquid Films
NASA Astrophysics Data System (ADS)
Turkoz, Emre; Arnold, Craig
2016-11-01
Blister-actuated laser-induced forward transfer (BA-LIFT) is a nozzle-less printing technique that offers an alternative to inkjet printing. The lack of a nozzle allows for a wider range of inks since clogging is not a concern. In this work, a focused laser pulse is absorbed within a polymer layer coated with a thin liquid film. The pulse causes a rapidly expanding blister to be formed that induces a liquid jet. Various well-studied non-Newtonian solutions are tested to examine how the shear-thinning and shear-thickening characteristics affect jet formation. The time delay between pulses is varied along with the energy, and different regimes of transfer are identified. We explore how Ohnesorge number, Weber number and spot size affect the jet formation and evaluate parameters that lead to breakup of jets into droplets.
NASA Technical Reports Server (NTRS)
Barr, Amy C.; Pappalardo, Robert T.
2005-01-01
Ice I exhibits a complex rheology at temperature and pressure conditions appropriate for the interiors of the outer ice I shells of Europa, Ganymede, and Callisto. We use numerical methods to determine the conditions required to trigger convection in an ice I shell with a stress-, temperature-, and grain-size-dependent rheology measured in laboratory experiments by Goldsby and Kohlstedt [2001] (henceforth GK2001). Triggering convection from an initially conductive ice shell with a non-Newtonian rheology for ice I requires that a finite-amplitude temperature perturbation be issued to the ice shell [2]. Here, we characterize the amplitude and wavelength of temperature perturbation required to initiate convection in the outer ice I shells of Europa, Ganymede, and Callisto using the GK2001 rheology for a range of ice grain sizes.
Universal power law behaviors in genomic sequences and evolutionary models
NASA Astrophysics Data System (ADS)
Martignetti, Loredana; Caselle, Michele
2007-08-01
We study the length distribution of a particular class of DNA sequences known as the 5' untranslated regions exons. These exons belong to the messenger RNA of protein coding genes, but they are not coding (they are located upstream of the coding portion of the mRNA) and are thus less constrained from an evolutionary point of view. We show that in both mice and humans these exons show a very clean power law decay in their length distribution and suggest a simple evolutionary model, which may explain this finding. We conjecture that this power law behavior could indeed be a general feature of higher eukaryotes.
Soliton solutions with power-law nonlinearity in inhomogeneous media
NASA Astrophysics Data System (ADS)
Dai, Chao-Qing; Yu, Fang-Bo
2013-04-01
We construct the relation between the variable coefficient nonlinear Schrödinger equations with power-law nonlinearity and the constant coefficient one via a transformation. Based on this transformation, we analytically obtain the closed-form bright and dark soliton solutions for variable coefficient nonlinear Schrödinger equations with power-law nonlinearity, third-order dispersion and self-steepening effect. The dynamic behaviors of bright and dark solitons in dispersion-decreasing fibers with hyperbolic, exponential, linear, logarithmic and Gaussian profiles are analyzed.
Power Laws, Flicker Noise, and the Barkhausen Effect
1993-10-01
AD-A274 702 AD TECHNICAL REPORT ARCCB-TR-93038 POWER LAWS, FLICKER NOISE, AND THE BARKHAUSEN EFFECT DTIC ELECTE JA~N 211994 3 L.V. MEISEL S D P.J...CATES C&MORD October 1993 Fuel 4. TITLE AND SUBTITU S. FUNDING NUMBERS POWER LAWS. FUCKER NOISE. AND THE BARKHAUSEN EFFECT AMCMS: 611L02.H61L1 6. AUTHOR... Barkhausen effect was studied in three ferromagnetic metals: an amorphous alloy, iron. and alumel. The data exhibit all the characteristics of self
Power-law statistics for avalanches in a martensitic transformation.
Ahluwalia, R; Ananthakrishna, G
2001-04-30
We devise a two-dimensional model that mimics the recently observed power-law distributions for the amplitudes and durations of the acoustic emission signals observed during martensitic transformation [Vives et al., Phys. Rev. Lett. 72, 1694 (1994)]. We include a threshold mechanism, long-range interaction between the transformed domains, inertial effects, and dissipation arising due to the motion of the interface. The model exhibits thermal hysteresis and, more importantly, it shows that the energy is released in the form of avalanches with power-law distributions for their amplitudes and durations. Computer simulations also reveal morphological features similar to those observed in real systems.
An active particle in a complex fluid
NASA Astrophysics Data System (ADS)
Datt, Charu; Natale, Giovanniantonio; Hatzikiriakos, Savvas G.; Elfring, Gwynn J.
2016-11-01
Active particles are self-driven units capable of converting stored or ambient free-energy into systematic movement. We discuss here the case when such particles move through non-Newtonian fluids. Neglecting inertial forces, we employ the reciprocal theorem to calculate the propulsion velocity of a single swimmer in a weakly non-Newtonian fluid with background flow. We also derive a general expression for the velocity of an active particle modelled as a squirmer in a second-order fluid. We then discuss how active colloids are affected by the medium rheology, namely viscoelasticity and shear-thinning.
Medical practices display power law behaviors similar to spoken languages
2013-01-01
Background Medical care commonly involves the apprehension of complex patterns of patient derangements to which the practitioner responds with patterns of interventions, as opposed to single therapeutic maneuvers. This complexity renders the objective assessment of practice patterns using conventional statistical approaches difficult. Methods Combinatorial approaches drawn from symbolic dynamics are used to encode the observed patterns of patient derangement and associated practitioner response patterns as sequences of symbols. Concatenating each patient derangement symbol with the contemporaneous practitioner response symbol creates “words” encoding the simultaneous patient derangement and provider response patterns and yields an observed vocabulary with quantifiable statistical characteristics. Results A fundamental observation in many natural languages is the existence of a power law relationship between the rank order of word usage and the absolute frequency with which particular words are uttered. We show that population level patterns of patient derangement: practitioner intervention word usage in two entirely unrelated domains of medical care display power law relationships similar to those of natural languages, and that–in one of these domains–power law behavior at the population level reflects power law behavior at the level of individual practitioners. Conclusions Our results suggest that patterns of medical care can be approached using quantitative linguistic techniques, a finding that has implications for the assessment of expertise, machine learning identification of optimal practices, and construction of bedside decision support tools. PMID:24007376
The power laws of nanoscale forces under ambient conditions.
Lai, Chia-Yun; Olukan, Tuza; Santos, Sergio; Al Ghaferi, Amal; Chiesa, Matteo
2015-12-25
We report a power law derived from experimental atomic force microscopy (AFM) data suggesting a nano to mesoscale transition in force-distance dependencies. Our results are in relative agreement with the Hamaker and Lifshitz theories for van der Waals forces for the larger tip radii only.
Constraints on cosmological parameters in power-law cosmology
NASA Astrophysics Data System (ADS)
Rani, Sarita; Altaibayeva, A.; Shahalam, M.; Singh, J. K.; Myrzakulov, R.
2015-03-01
In this paper, we examine observational constraints on the power law cosmology; essentially dependent on two parameters H0 (Hubble constant) and q (deceleration parameter). We investigate the constraints on these parameters using the latest 28 points of H(z) data and 580 points of Union2.1 compilation data and, compare the results with the results of ΛCDM . We also forecast constraints using a simulated data set for the future JDEM, supernovae survey. Our studies give better insight into power law cosmology than the earlier done analysis by Kumar [arXiv:1109.6924] indicating it tuning well with Union2.1 compilation data but not with H(z) data. However, the constraints obtained on i.e. H0 average and q average using the simulated data set for the future JDEM, supernovae survey are found to be inconsistent with the values obtained from the H(z) and Union2.1 compilation data. We also perform the statefinder analysis and find that the power-law cosmological models approach the standard ΛCDM model as q → -1. Finally, we observe that although the power law cosmology explains several prominent features of evolution of the Universe, it fails in details.
Constraints on cosmological parameters in power-law cosmology
Rani, Sarita; Singh, J.K.; Altaibayeva, A.; Myrzakulov, R.; Shahalam, M. E-mail: aziza.bibol@mail.ru E-mail: jainendrrakumar@rediffmail.com
2015-03-01
In this paper, we examine observational constraints on the power law cosmology; essentially dependent on two parameters H{sub 0} (Hubble constant) and q (deceleration parameter). We investigate the constraints on these parameters using the latest 28 points of H(z) data and 580 points of Union2.1 compilation data and, compare the results with the results of ΛCDM . We also forecast constraints using a simulated data set for the future JDEM, supernovae survey. Our studies give better insight into power law cosmology than the earlier done analysis by Kumar [arXiv:1109.6924] indicating it tuning well with Union2.1 compilation data but not with H(z) data. However, the constraints obtained on i.e. H{sub 0} average and q average using the simulated data set for the future JDEM, supernovae survey are found to be inconsistent with the values obtained from the H(z) and Union2.1 compilation data. We also perform the statefinder analysis and find that the power-law cosmological models approach the standard ΛCDM model as q → −1. Finally, we observe that although the power law cosmology explains several prominent features of evolution of the Universe, it fails in details.
Ali, N; Javid, K; Sajid, M; Anwar Bég, O
2016-01-01
Peristaltic motion of a non-Newtonian Carreau fluid is analyzed in a curved channel under the long wavelength and low Reynolds number assumptions, as a simulation of digestive transport. The flow regime is shown to be governed by a dimensionless fourth-order, nonlinear, ordinary differential equation subject to no-slip wall boundary conditions. A well-tested finite difference method based on an iterative scheme is employed for the solution of the boundary value problem. The important phenomena of pumping and trapping associated with the peristaltic motion are investigated for various values of rheological parameters of Carreau fluid and curvature of the channel. An increase in Weissenberg number is found to generate a small eddy in the vicinity of the lower wall of the channel, which is enhanced with further increase in Weissenberg number. For shear-thinning bio-fluids (power-law rheological index, n < 1) greater Weissenberg number displaces the maximum velocity toward the upper wall. For shear-thickening bio-fluids, the velocity amplitude is enhanced markedly with increasing Weissenberg number.
Free Convective Nonaligned Non-Newtonian Flow with Non-linear Thermal Radiation
NASA Astrophysics Data System (ADS)
Rana, S.; Mehmood, R.; Narayana, PV S.; Akbar, N. S.
2016-12-01
The present study explores the free convective oblique Casson fluid over a stretching surface with non-linear thermal radiation effects. The governing physical problem is modelled and transformed into a set of coupled non-linear ordinary differential equations by suitable similarity transformation, which are solved numerically with the help of shooting method keeping the convergence control of 10-5 in computations. Influence of pertinent physical parameters on normal, tangential velocity profiles and temperature are expressed through graphs. Physical quantities of interest such as skin friction coefficients and local heat flux are investigated numerically.
NASA Astrophysics Data System (ADS)
Chun, Myung-Suk; Chun, Byoungjin; Lee, Ji-Young; Complex Fluids Team
2016-11-01
We investigate the externally time-dependent pulsatile electrokinetic viscous flows by extending the previous simulations concerning the electrokinetic microfluidics for different geometries. The external body force originated from between the nonlinear Poisson-Boltzmann field and the flow-induced electric field is employed in the Cauchy momentum equation, and then the Nernst-Planck equation in connection with the net current conservation is coupled. Our explicit model allows one to quantify the effects of the oscillating frequency and conductance of the Stern layer, considering the shear thinning effect and the strong electric double layer interaction. This presentation reports the new results regarding the implication of optimum frequency pressure pulsations toward realizing mechanical to electrical energy transfer with high conversion efficiencies. These combined factors for different channel dimension are examined in depth to obtain possible enhancements of streaming current, with taking advantage of pulsating pressure field. From experimental verifications by using electrokinetic power chip, it is concluded that our theoretical framework can serve as a useful basis for micro/nanofluidics design and potential applications to the enhanced energy conversion. NRF of Korea (No.2015R1A2A1A15052979) and KIST (No.2E26490).
Broniarz-Press, L; Sosnowski, T R; Matuszak, M; Ochowiak, M; Jabłczyńska, K
2015-05-15
The paper contains results of the experimental study on atomization process of aqueous solutions of glycerol and aqueous solutions of glycerol-polyacrylamide (Rokrysol WF1) in an ultrasonic inhaler. In experiments the different concentration aqueous solutions of glycerol and glycerol-polyacrylamide have been tested. The results have been obtained by the use of laser diffraction technique. The differences between characteristics of ultrasonic atomization for test liquids have been observed. The analysis of drop size histograms shows that the different sizes of drops have been formed during atomization process. The present study confirmed the previous reports which suggested that the drops size changes with the increase in viscosity of solution changes in spray characteristics were also observed. It has been shown that the shear and extensional viscosities affect the process of atomization.
Deviation from Power Law Behavior in Landslide Phenomenon
NASA Astrophysics Data System (ADS)
Li, L.; Lan, H.; Wu, Y.
2013-12-01
Power law distribution of magnitude is widely observed in many natural hazards (e.g., earthquake, floods, tornadoes, and forest fires). Landslide is unique as the size distribution of landslide is characterized by a power law decrease with a rollover in the small size end. Yet, the emergence of the rollover, i.e., the deviation from power law behavior for small size landslides, remains a mystery. In this contribution, we grouped the forces applied on landslide bodies into two categories: 1) the forces proportional to the volume of failure mass (gravity and friction), and 2) the forces proportional to the area of failure surface (cohesion). Failure occurs when the forces proportional to volume exceed the forces proportional to surface area. As such, given a certain mechanical configuration, the failure volume to failure surface area ratio must exceed a corresponding threshold to guarantee a failure. Assuming all landslides share a uniform shape, which means the volume to surface area ratio of landslide regularly increase with the landslide volume, a cutoff of landslide volume distribution in the small size end can be defined. However, in realistic landslide phenomena, where heterogeneities of landslide shape and mechanical configuration are existent, a simple cutoff of landslide volume distribution does not exist. The stochasticity of landslide shape introduce a probability distribution of the volume to surface area ratio with regard to landslide volume, with which the probability that the volume to surface ratio exceed the threshold can be estimated regarding values of landslide volume. An experiment based on empirical data showed that this probability can induce the power law distribution of landslide volume roll down in the small size end. We therefore proposed that the constraints on the failure volume to failure surface area ratio together with the heterogeneity of landslide geometry and mechanical configuration attribute for the deviation from power law
The origin of power-law rheology in foams
NASA Astrophysics Data System (ADS)
Hwang, Hyun Joo; Riggleman, Robert; Crocker, John
Soft glassy matter (SGM) such as foams, emulsions, and colloids, exhibit interesting rheological properties that have long defied explanation. In particular, the shear modulus of these materials displays weak power law frequency dependence. To understand the origin of this property in more depth, we have built a three-dimensional, modified Bubble Dynamics model. The bubbles interact with a purely repulsive harmonic potential and ripen according to diffusion-based governing equations. Notably, the bubble motion has a Levy flight character, in addition to being spatially correlated in the form of avalanches. Microrheology studies reveal that the power-law shear modulus is the result of constraint release driven by the bubbles' super-diffusive motion combined with simple yield of the resulting stress. The super-diffusive motion of the bubbles, in turn, is the result of the system taking a fractal path in configuration space. We shall discuss the origins of this fractal scaling.
Power-law distribution in Japanese racetrack betting
NASA Astrophysics Data System (ADS)
Ichinomiya, Takashi
2006-08-01
Gambling is one of the basic economic activities that humans indulge in. An investigation of gambling activities provides deep insights into the economic actions of people and sheds lights on the study of econophysics. In this paper we present an analysis of the distribution of the final odds of the races organized by the Japan Racing Association. The distribution of the final odds Po(x) indicates a clear power-law Po(x)∝1/x, where x represents the final odds. This power-law can be explained on the basis of the assumption that every bettor bets his money on the horse that appears to be the strongest in a race.
Power law behavior of the zigzag transition in Yukawa clusters
Sheridan, T. E.; Magyar, Andrew L.
2010-11-15
We provide direct experimental evidence that the width of a Yukawa cluster exhibits power law behavior during the one-dimensional (1D) to two-dimensional (2D) zigzag transition. Configurations of small dusty (complex) plasma clusters confined in a biharmonic potential well are characterized as the well anisotropy is varied. When the anisotropy is large the particles are in a 1D straight-line configuration. As the anisotropy is decreased the cluster undergoes a zigzag transition to a 2D configuration. The measured dependence of cluster width on anisotropy follows a power law. A second transition from the zigzag to an elliptical configuration is also observed. The results are in very good agreement with a model of identical particles interacting through a Yukawa potential.
Power Laws and Market Crashes ---Empirical Laws on Bursting Bubbles---
NASA Astrophysics Data System (ADS)
Kaizoji, T.
In this paper, we quantitatively investigate the statistical properties of a statistical ensemble of stock prices. We selected 1200 stocks traded on the Tokyo Stock Exchange, and formed a statistical ensemble of daily stock prices for each trading day in the 3-year period from January 4, 1999 to December 28, 2001, corresponding to the period of the forming of the internet bubble in Japn, and its bursting in the Japanese stock market. We found that the tail of the complementary cumulative distribution function of the ensemble of stock prices in the high value of the price is well described by a power-law distribution, P (S > x) ˜ x^{-α}, with an exponent that moves in the range of 1.09 < α < 1.27. Furthermore, we found that as the power-law exponents α approached unity, the bubbles collapsed. This suggests that Zipf's law for stock prices is a sign that bubbles are going to burst.
Probability distributions and confidence intervals for simulated power law noise.
Ashby, Neil
2015-01-01
A method for simulating power law noise in clocks and oscillators is presented based on modification of the spectrum of white phase noise, then Fourier transforming to the time domain. Symmetric real matrices are introduced whose traces-the sums of their eigenvalues-are equal to the Allan variances, in overlapping or non-overlapping forms, as well as for the corresponding forms of the modified Allan variance. We show that the standard expressions for spectral densities, and their relations to Allan variance, are obtained with this method. The matrix eigenvalues determine probability distributions for observing a variance at an arbitrary value of the sampling interval τ, and hence for estimating confidence in the measurements. Examples are presented for the common power-law noises. Extension to other variances such as the Hadamard variance, and variances with dead time, are discussed.
COSMOLOGY OF CHAMELEONS WITH POWER-LAW COUPLINGS
Mota, David F.; Winther, Hans A.
2011-05-20
In chameleon field theories, a scalar field can couple to matter with gravitational strength and still evade local gravity constraints due to a combination of self-interactions and the couplings to matter. Originally, these theories were proposed with a constant coupling to matter; however, the chameleon mechanism also extends to the case where the coupling becomes field dependent. We study the cosmology of chameleon models with power-law couplings and power-law potentials. It is found that these generalized chameleons, when viable, have a background expansion very close to {Lambda}CDM, but can in some special cases enhance the growth of the linear perturbations at low redshifts. For the models we consider, it is found that this region of the parameter space is ruled out by local gravity constraints. Imposing a coupling to dark matter only, the local constraints are avoided, and it is possible to have observable signatures on the linear matter perturbations.
Lévy flights with power-law absorption.
Cattivelli, Luca; Agliari, Elena; Sartori, Fabio; Cassi, Davide
2015-10-01
We consider a particle performing a stochastic motion on a one-dimensional lattice with jump lengths distributed according to a power law with exponent μ+1. Assuming that the walker moves in the presence of a distribution a(x) of targets (traps) depending on the spatial coordinate x, we study the probability that the walker will eventually find any target (will eventually be trapped). We focus on the case of power-law distributions a(x)∼x(-α) and we find that, as long as μ<α, there is a finite probability that the walker will never be trapped, no matter how long the process is. This result is shown via analytical arguments and numerical simulations which also evidence the emergence of slow searching (trapping) times in finite-size system. The extension of this finding to higher-dimensional structures is also discussed.
NMR imaging and hydrodynamic analysis of neutrally buoyant non-Newtonian slurry flows
Bouillard, J.X.; Sinton, S.W.
1995-02-01
The flow of solids loaded suspension in cylindrical pipes has been the object of intense experimental and theoretical investigations in recent years. These types of flows are of great interest in chemical engineering because of their important use in many industrial manufacturing processes. Such flows are for example encountered in the manufacture of solid-rocket propellants, advanced ceramics, reinforced polymer composites, in heterogenous catalytic reactors, and in the pipeline transport of liquid-solids suspensions. In most cases, the suspension microstructure and the degree of solids dispersion greatly affect the final performance of the manufactured product. For example, solid propellant pellets need to be extremely-well dispersed in gel matrices for use as rocket engine solid fuels. The homogeneity of pellet dispersion is critical to allow good uniformity of the burn rate, which in turn affects the final mechanical performance of the engine. Today`s manufacturing of such fuels uses continuous flow processes rather than batch processes. Unfortunately, the hydrodynamics of such flow processes is poorly understood and is difficult to assess because it requires the simultaneous measurements of liquid/solids phase velocities and volume fractions. Due to the recent development in pulsed Fourier Transform NMR imaging, NMR imaging is now becoming a powerful technique for the non intrusive investigation of multi-phase flows. This paper reports and exposes a state-of-the-art experimental and theoretical methodology that can be used to study such flows. The hydrodynamic model developed for this study is a two-phase flow shear thinning model with standard constitutive fluid/solids interphase drag and solids compaction stresses. this model shows good agreement with experimental data and the limitations of this model are discussed.
Gwynllyw, D.Rh.; Phillips, T.N.
1994-12-31
The journal bearing is an essential part of all internal combustion engines as a means of transferring the energy from the piston rods to the rotating crankshaft. It consists essentially of an inner cylinder (the journal), which is part of the crankshaft, and an outer cylinder (the bearing), which is at the end of the piston rod. In general, the two cylinders are eccentric and there is a lubricating film of oil separating the two surfaces. The addition of polymers to mineral (Newtonian) oils to minimize the variation of viscosity with temperature has the added effect of introducing strain-dependent viscosity and elasticity. The physical problem has many complicating features which need to be modelled. It is a fully three-dimensional problem which means that significant computational effort is required to solve the problem numerically. The system is subject to dynamic loading in which the journal is allowed to move under the forces the fluid imparts on it and also any other loads such as that imparted by the engine force. The centre of the journal traces out a nontrivial locus in space. In addition, there is significant deformation of the bearing and journal and extensive cavitation of the oil lubricant. In the present study the authors restrict themselves to the two-dimensional statically loaded problem. In previous work a single domain spectral method was used which employed a bipolar coordinate transformation to map the region between the journal and the bearing onto a rectangle. The flow variables were then approximated on this rectangle using Fourier-Chebyshev expansions. However, to allow for future possible deformation of the journal and bearing surfaces due to increased load in the dynamically loaded case they have decided to use a more versatile spectral element formulation.
Castellanos, Maria Monica; Pathak, Jai A.; Leach, William; Bishop, Steven M.; Colby, Ralph H.
2014-01-01
A monoclonal antibody solution displays an increase in low shear rate viscosity upon aggregation after prolonged incubation at 40°C. The morphology and interactions leading to the formation of the aggregates responsible for this non-Newtonian character are resolved using small-angle neutron scattering. Our data show a weak repulsive barrier before proteins aggregate reversibly, unless a favorable contact with high binding energy occurs. Two types of aggregates were identified after incubation at 40°C: oligomers with radius of gyration ∼10 nm and fractal submicrometer particles formed by a slow reaction-limited aggregation process, consistent with monomers colliding many times before finding a favorable strong interaction site. Before incubation, these antibody solutions are Newtonian liquids with no increase in low shear rate viscosity and no upturn in scattering at low wavevector, whereas aggregated solutions under the same conditions have both of these features. These results demonstrate that fractal submicrometer particles are responsible for the increase in low shear rate viscosity and low wavevector upturn in scattered intensity of aggregated antibody solutions; both are removed from aggregated samples by filtering. PMID:25028888
Power law distribution of dividends in horse races
NASA Astrophysics Data System (ADS)
Park, K.; Domany, E.
2001-02-01
We discovered that the distribution of dividends in Korean horse races follows a power law. A simple model of betting is proposed, which reproduces the observed distribution. The model provides a mechanism to arrive at the true underlying winning probabilities, which are initially unknown, in a self-organized collective fashion, through the dynamic process of betting. Numerical simulations yield excellent agreement with the empirical data.
Power law relationships for rain attenuation and reflectivity
NASA Technical Reports Server (NTRS)
Devasirvatham, D. M. J.; Hodge, D. B.
1978-01-01
The equivalent reflectivity, specific attenuation and volumetric backscatter cross section of rain are calculated and tabulated at a number of frequencies from 1 to 500 GHz using classical Mie theory. The first two parameters are shown to be closely approximated as functions of rain rate by the power law aR to the b power. The a's and b's are also tabulated and plotted for convenient reference.
Power-law cosmology, SN Ia, and BAO
Dolgov, Aleksander; Halenka, Vitali; Tkachev, Igor E-mail: vithal@umich.edu
2014-10-01
We revise observational constraints on the class of models of modified gravity which at low redshifts lead to a power-law cosmology. To this end we use available public data on Supernova Ia and on baryon acoustic oscillations. We show that the expansion regime a(t) ∼ t{sup β} with β close to 3/2 in a spatially flat universe is a good fit to these data.
Power law cosmology model comparison with CMB scale information
NASA Astrophysics Data System (ADS)
Tutusaus, Isaac; Lamine, Brahim; Blanchard, Alain; Dupays, Arnaud; Zolnierowski, Yves; Cohen-Tanugi, Johann; Ealet, Anne; Escoffier, Stéphanie; Le Fèvre, Olivier; Ilić, Stéphane; Pisani, Alice; Plaszczynski, Stéphane; Sakr, Ziad; Salvatelli, Valentina; Schücker, Thomas; Tilquin, André; Virey, Jean-Marc
2016-11-01
Despite the ability of the cosmological concordance model (Λ CDM ) to describe the cosmological observations exceedingly well, power law expansion of the Universe scale radius, R (t )∝tn, has been proposed as an alternative framework. We examine here these models, analyzing their ability to fit cosmological data using robust model comparison criteria. Type Ia supernovae (SNIa), baryonic acoustic oscillations (BAO) and acoustic scale information from the cosmic microwave background (CMB) have been used. We find that SNIa data either alone or combined with BAO can be well reproduced by both Λ CDM and power law expansion models with n ˜1.5 , while the constant expansion rate model (n =1 ) is clearly disfavored. Allowing for some redshift evolution in the SNIa luminosity essentially removes any clear preference for a specific model. The CMB data are well known to provide the most stringent constraints on standard cosmological models, in particular, through the position of the first peak of the temperature angular power spectrum, corresponding to the sound horizon at recombination, a scale physically related to the BAO scale. Models with n ≥1 lead to a divergence of the sound horizon and do not naturally provide the relevant scales for the BAO and the CMB. We retain an empirical footing to overcome this issue: we let the data choose the preferred values for these scales, while we recompute the ionization history in power law models, to obtain the distance to the CMB. In doing so, we find that the scale coming from the BAO data is not consistent with the observed position of the first peak of the CMB temperature angular power spectrum for any power law cosmology. Therefore, we conclude that when the three standard probes (SNIa, BAO, and CMB) are combined, the Λ CDM model is very strongly favored over any of these alternative models, which are then essentially ruled out.
Robust Statistical Detection of Power-Law Cross-Correlation
Blythe, Duncan A. J.; Nikulin, Vadim V.; Müller, Klaus-Robert
2016-01-01
We show that widely used approaches in statistical physics incorrectly indicate the existence of power-law cross-correlations between financial stock market fluctuations measured over several years and the neuronal activity of the human brain lasting for only a few minutes. While such cross-correlations are nonsensical, no current methodology allows them to be reliably discarded, leaving researchers at greater risk when the spurious nature of cross-correlations is not clear from the unrelated origin of the time series and rather requires careful statistical estimation. Here we propose a theory and method (PLCC-test) which allows us to rigorously and robustly test for power-law cross-correlations, correctly detecting genuine and discarding spurious cross-correlations, thus establishing meaningful relationships between processes in complex physical systems. Our method reveals for the first time the presence of power-law cross-correlations between amplitudes of the alpha and beta frequency ranges of the human electroencephalogram. PMID:27250630
Spectrum of power laws for curved hand movements.
Huh, Dongsung; Sejnowski, Terrence J
2015-07-21
In a planar free-hand drawing of an ellipse, the speed of movement is proportional to the -1/3 power of the local curvature, which is widely thought to hold for general curved shapes. We investigated this phenomenon for general curved hand movements by analyzing an optimal control model that maximizes a smoothness cost and exhibits the -1/3 power for ellipses. For the analysis, we introduced a new representation for curved movements based on a moving reference frame and a dimensionless angle coordinate that revealed scale-invariant features of curved movements. The analysis confirmed the power law for drawing ellipses but also predicted a spectrum of power laws with exponents ranging between 0 and -2/3 for simple movements that can be characterized by a single angular frequency. Moreover, it predicted mixtures of power laws for more complex, multifrequency movements that were confirmed with human drawing experiments. The speed profiles of arbitrary doodling movements that exhibit broadband curvature profiles were accurately predicted as well. These findings have implications for motor planning and predict that movements only depend on one radian of angle coordinate in the past and only need to be planned one radian ahead.
Scaling range of power laws that originate from fluctuation analysis
NASA Astrophysics Data System (ADS)
Grech, Dariusz; Mazur, Zygmunt
2013-05-01
We extend our previous study of scaling range properties performed for detrended fluctuation analysis (DFA) [Physica A0378-437110.1016/j.physa.2013.01.049 392, 2384 (2013)] to other techniques of fluctuation analysis (FA). The new technique, called modified detrended moving average analysis (MDMA), is introduced, and its scaling range properties are examined and compared with those of detrended moving average analysis (DMA) and DFA. It is shown that contrary to DFA, DMA and MDMA techniques exhibit power law dependence of the scaling range with respect to the length of the searched signal and with respect to the accuracy R2 of the fit to the considered scaling law imposed by DMA or MDMA methods. This power law dependence is satisfied for both uncorrelated and autocorrelated data. We find also a simple generalization of this power law relation for series with a different level of autocorrelations measured in terms of the Hurst exponent. Basic relations between scaling ranges for different techniques are also discussed. Our findings should be particularly useful for local FA in, e.g., econophysics, finances, or physiology, where the huge number of short time series has to be examined at once and wherever the preliminary check of the scaling range regime for each of the series separately is neither effective nor possible.
Scaling range of power laws that originate from fluctuation analysis.
Grech, Dariusz; Mazur, Zygmunt
2013-05-01
We extend our previous study of scaling range properties performed for detrended fluctuation analysis (DFA) [Physica A 392, 2384 (2013)] to other techniques of fluctuation analysis (FA). The new technique, called modified detrended moving average analysis (MDMA), is introduced, and its scaling range properties are examined and compared with those of detrended moving average analysis (DMA) and DFA. It is shown that contrary to DFA, DMA and MDMA techniques exhibit power law dependence of the scaling range with respect to the length of the searched signal and with respect to the accuracy R^{2} of the fit to the considered scaling law imposed by DMA or MDMA methods. This power law dependence is satisfied for both uncorrelated and autocorrelated data. We find also a simple generalization of this power law relation for series with a different level of autocorrelations measured in terms of the Hurst exponent. Basic relations between scaling ranges for different techniques are also discussed. Our findings should be particularly useful for local FA in, e.g., econophysics, finances, or physiology, where the huge number of short time series has to be examined at once and wherever the preliminary check of the scaling range regime for each of the series separately is neither effective nor possible.
Deposition Velocities of Non-Newtonian Slurries in Pipelines: Complex Simulant Testing
Poloski, Adam P.; Bonebrake, Michael L.; Casella, Andrew M.; Johnson, Michael D.; Toth, James J.; Adkins, Harold E.; Chun, Jaehun; Denslow, Kayte M.; Luna, Maria; Tingey, Joel M.
2009-07-01
One of the concerns expressed by the External Flowsheet Review Team (EFRT) is about the potential for pipe plugging at the Waste Treatment and Immobilization Plant (WTP). Per the review’s executive summary, “Piping that transports slurries will plug unless it is properly designed to minimize this risk. This design approach has not been followed consistently, which will lead to frequent shutdowns due to line plugging.” To evaluate the potential for plugging, deposition-velocity tests were performed on several physical simulants to determine whether the design approach is conservative. Deposition velocity is defined as the velocity below which particles begin to deposit to form a moving bed of particles on the bottom of a straight horizontal pipe during slurry-transport operations. The deposition velocity depends on the system geometry and the physical properties of the particles and fluid. An experimental program was implemented to test the stability-map concepts presented in WTP-RPT-175 Rev. 01. Two types of simulant were tested. The first type of simulant was similar to the glass-bead simulants discussed in WTP-RPT-175 Rev. 0 ; it consists of glass beads with a nominal particle size of 150 µm in a kaolin/water slurry. The initial simulant was prepared at a target yield stress of approximately 30 Pa. The yield stress was then reduced, stepwise, via dilution or rheological modifiers, ultimately to a level of <1 Pa. At each yield-stress step, deposition-velocity testing was performed. Testing over this range of yield-stress bounds the expected rheological operating window of the WTP and allows the results to be compared to stability-map predictions for this system. The second simulant was a precipitated hydroxide that simulates HLW pretreated sludge from Hanford waste tank AZ-101. Testing was performed in a manner similar to that for the first simulant over a wide range of yield stresses; however, an additional test of net-positive suction-head required (NPSHR
An efficient implicit unstructured finite volume solver for generalised Newtonian fluids
NASA Astrophysics Data System (ADS)
Jalali, Alireza; Sharbatdar, Mahkame; Ollivier-Gooch, Carl
2016-03-01
An implicit finite volume solver is developed for the steady-state solution of generalised Newtonian fluids on unstructured meshes in 2D. The pseudo-compressibility technique is employed to couple the continuity and momentum equations by transforming the governing equations into a hyperbolic system. A second-order accurate spatial discretisation is provided by performing a least-squares gradient reconstruction within each control volume of unstructured meshes. A central flux function is used for the convective terms and a solution jump term is added to the averaged component for the viscous terms. Global implicit time-stepping using successive evolution-relaxation is utilised to accelerate the convergence to steady-state solutions. The performance of our flow solver is examined for power-law and Carreau-Yasuda non-Newtonian fluids in different geometries. The effects of model parameters and Reynolds number are studied on the convergence rate and flow features. Our results verify second-order accuracy of the discretisation and also fast and efficient convergence to the steady-state solution for a wide range of flow variables.
Mass transport in a thin layer of power-law mud under surface waves
NASA Astrophysics Data System (ADS)
Liu, Jie; Bai, Yuchuan; Xu, Dong
2017-02-01
The mass transport velocity in a two-layer system is studied theoretically. The wave motion is driven by a periodic pressure load on the free water surface, and mud in the lower layer is described by a power-law rheological model. Perturbation analysis is performed to the second order to find the mean Eulerian velocity. A numerical iteration method is employed to solve the non-linear governing equation at the leading order. The influence of rheological properties on fluid motion characteristics including the flow field, the surface displacement, the mass transport velocity, and the net discharge rates are investigated based on theoretical results. Theoretical analysis shows that under the action of interfacial shearing, a recirculation structure may appear near the interface in the upper water layer. A higher mass transport velocity at the interface does not necessarily mean a higher discharge rate for a pseudo-plastic fluid mud.
NASA Astrophysics Data System (ADS)
Sojka, Paul E.; Rodrigues, Neil S.
2015-11-01
The current study investigates the drop characteristics of three Carboxymethylcellulose (CMC) sprays produced by the impingement of two liquid jets. The three water-based solutions used in this work (0.5 wt.-% CMC-7MF, 0.8 wt.-% CMC-7MF, and 1.4 wt.-% CMC-7MF) exhibited strong shear-thinning, non-Newtonian behavior - characterized by the Bird-Carreau rheological model. A generalized Bird-Carreau jet Reynolds number was used as the primary parameter to characterize the drop size and the drop velocity, which were measured using Phase Doppler Anemometry (PDA). PDA optical configuration enabled a drop size measurement range of approximately 2.3 to 116.2 μm. 50,000 drops were measured at each test condition to ensure statistical significance. The arithmetic mean diameter (D10) , Sauter mean diameter (D32) , and mass median diameter (MMD) were used as representative diameters to characterize drop size. The mean axial drop velocity Uz -mean along with its root-mean square Uz -rms were used to characterize drop velocity. Incredibly, measurements for all three CMC liquids and reference DI water sprays seemed to follow a single curve for D32 and MMD drop diameters in the high generalized Bird-Carreau jet Reynolds number range considered in this work (9.21E +03
NASA Technical Reports Server (NTRS)
Barr, A. C.; Pappalardo, R. T.
2004-01-01
Ice I exhibits a complex rheology at temperature and pressure conditions appropriate for the interiors of the ice I shells of Europa, Ganymede, and Callisto. We use numerical methods and existing parameterizations of the critical Rayleigh number to determine the conditions required to trigger convection in an ice I shell with the stress-, temperature- and grain size- dependent rheology measured in laboratory experiments by Goldsby and Kohlstedt [2001]. The critical Rayleigh number depends on the ice grain size and the amplitude and wavelength of temperature perturbation issued to an initially conductive ice I shell. If the shells have an assumed uniform grain size less than 0.4 mm, deformation during initial plume growth is accommodated by Newtonian volume diffusion. If the ice grain size is between 0.4 mm and 3 cm, deformation during plume growth is accommodated by weakly non-Newtonian grain boundary sliding, where the critical ice shell thickness for convection depends on the amplitude of temperature perturbation to the _0.5 power. If the ice grain size exceeds 2 cm, convection can not occur in the ice I shells of the Galilean satellites regardless of the amplitude or wavelength of temperature perturbation. If the grain size in a convecting ice I shell evolves to effective values greater than 2 cm, convection will cease. If the ice shell has a grain size large enough to permit flow by dislocation creep, the ice is too stiff to permit convection, even in the thickest possible ice I shell. Consideration of the composite rheology implies that estimates of the grain size in the satellites and knowledge of their initial thermal states are required when judging the convective instability of their ice I shells.
Universal inverse power-law distribution for temperature and rainfall in the UK region
NASA Astrophysics Data System (ADS)
Selvam, A. M.
2014-06-01
Meteorological parameters, such as temperature, rainfall, pressure, etc., exhibit selfsimilar space-time fractal fluctuations generic to dynamical systems in nature such as fluid flows, spread of forest fires, earthquakes, etc. The power spectra of fractal fluctuations display inverse power-law form signifying long-range correlations. A general systems theory model predicts universal inverse power-law form incorporating the golden mean for the fractal fluctuations. The model predicted distribution was compared with observed distribution of fractal fluctuations of all size scales (small, large and extreme values) in the historic month-wise temperature (maximum and minimum) and total rainfall for the four stations Oxford, Armagh, Durham and Stornoway in the UK region, for data periods ranging from 92 years to 160 years. For each parameter, the two cumulative probability distributions, namely cmax and cmin starting from respectively maximum and minimum data value were used. The results of the study show that (i) temperature distributions (maximum and minimum) follow model predicted distribution except for Stornowy, minimum temperature cmin. (ii) Rainfall distribution for cmin follow model predicted distribution for all the four stations. (iii) Rainfall distribution for cmax follows model predicted distribution for the two stations Armagh and Stornoway. The present study suggests that fractal fluctuations result from the superimposition of eddy continuum fluctuations.
Event-scale power law recession analysis: quantifying methodological uncertainty
NASA Astrophysics Data System (ADS)
Dralle, David N.; Karst, Nathaniel J.; Charalampous, Kyriakos; Veenstra, Andrew; Thompson, Sally E.
2017-01-01
The study of single streamflow recession events is receiving increasing attention following the presentation of novel theoretical explanations for the emergence of power law forms of the recession relationship, and drivers of its variability. Individually characterizing streamflow recessions often involves describing the similarities and differences between model parameters fitted to each recession time series. Significant methodological sensitivity has been identified in the fitting and parameterization of models that describe populations of many recessions, but the dependence of estimated model parameters on methodological choices has not been evaluated for event-by-event forms of analysis. Here, we use daily streamflow data from 16 catchments in northern California and southern Oregon to investigate how combinations of commonly used streamflow recession definitions and fitting techniques impact parameter estimates of a widely used power law recession model. Results are relevant to watersheds that are relatively steep, forested, and rain-dominated. The highly seasonal mediterranean climate of northern California and southern Oregon ensures study catchments explore a wide range of recession behaviors and wetness states, ideal for a sensitivity analysis. In such catchments, we show the following: (i) methodological decisions, including ones that have received little attention in the literature, can impact parameter value estimates and model goodness of fit; (ii) the central tendencies of event-scale recession parameter probability distributions are largely robust to methodological choices, in the sense that differing methods rank catchments similarly according to the medians of these distributions; (iii) recession parameter distributions are method-dependent, but roughly catchment-independent, such that changing the choices made about a particular method affects a given parameter in similar ways across most catchments; and (iv) the observed correlative relationship
Thermal convection of viscoelastic shear-thinning fluids
NASA Astrophysics Data System (ADS)
Albaalbaki, Bashar; Khayat, Roger E.; Ahmed, Zahir U.
2016-12-01
The Rayleigh-Bénard convection for non-Newtonian fluids possessing both viscoelastic and shear-thinning behaviours is examined. The Phan-Thien-Tanner (PTT) constitutive equation is implemented to model the non-Newtonian character of the fluid. It is found that while the shear-thinning and viscoelastic effects could annihilate one another for the steady roll flow, presence of both behaviours restricts the roll stability limit significantly compared to the cases when the fluid is either inelastic shear-thinning or purely viscoelastic with constant viscosity.
Power-law time distribution of large earthquakes.
Mega, Mirko S; Allegrini, Paolo; Grigolini, Paolo; Latora, Vito; Palatella, Luigi; Rapisarda, Andrea; Vinciguerra, Sergio
2003-05-09
We study the statistical properties of time distribution of seismicity in California by means of a new method of analysis, the diffusion entropy. We find that the distribution of time intervals between a large earthquake (the main shock of a given seismic sequence) and the next one does not obey Poisson statistics, as assumed by the current models. We prove that this distribution is an inverse power law with an exponent mu=2.06+/-0.01. We propose the long-range model, reproducing the main properties of the diffusion entropy and describing the seismic triggering mechanisms induced by large earthquakes.
Elastohydrodynamic analysis using a power law pressure-viscosity relation
NASA Technical Reports Server (NTRS)
Loewenthal, S. H.; Zaretsky, E. V.
1973-01-01
An isothermal elastohydrodynamic (EHD) inlet analysis of the Grubin type which considers a power law pressure-viscosity relation and a finite pressure at the inlet edge of the Hertzian contact zone was performed. Comparisons made with published X-ray EHD film thickness data for a synthetic paraffinic oil and when conventional EHD theory showed that the present theory exhibits a slightly stronger film thickness load dependence than do previous isothermal EHD theories but far less than that exhibited by the measured data.
Power laws, discontinuities and regional city size distributions
Garmestani, A.S.; Allen, C.R.; Gallagher, C.M.
2008-01-01
Urban systems are manifestations of human adaptation to the natural environment. City size distributions are the expression of hierarchical processes acting upon urban systems. In this paper, we test the entire city size distributions for the southeastern and southwestern United States (1990), as well as the size classes in these regions for power law behavior. We interpret the differences in the size of the regional city size distributions as the manifestation of variable growth dynamics dependent upon city size. Size classes in the city size distributions are snapshots of stable states within urban systems in flux. ?? 2008.
Analytical Limit Distributions from Random Power-Law Interactions
NASA Astrophysics Data System (ADS)
Zaid, Irwin; Mizuno, Daisuke
2016-07-01
Nature is full of power-law interactions, e.g., gravity, electrostatics, and hydrodynamics. When sources of such fields are randomly distributed in space, the superposed interaction, which is what we observe, is naively expected to follow a Gauss or Lévy distribution. Here, we present an analytic expression for the actual distributions that converge to novel limits that are in between these already-known limit distributions, depending on physical parameters, such as the concentration of field sources and the size of the probe used to measure the interactions. By comparing with numerical simulations, the origin of non-Gauss and non-Lévy distributions are theoretically articulated.
Stokesian locomotion in elastic fluids: Experiments
NASA Astrophysics Data System (ADS)
Zenit, Roberto; Lauga, Eric
2010-11-01
In many instances of biological relevance, self-propelled cells have to swim through non-Newtonian fluids. In order to provide fundamental understanding on the effect of such non-Newtonian stresses on locomotion, we have studied the motion an oscillating magnetic swimmer immersed in both Newtonian and non-Newtonian liquids at small Reynolds numbers. The swimmer is made with a small rare earth (Neodymium-Iron-Boron) magnetic rod (3 mm) to which a flexible tail was glued. This array was immersed in cylindrical container (50 mm diameter) in which the test fluid was contained. A nearly uniform oscillating magnetic field was created with a Helmholtz coil (R=200mm) and a AC power supply. For the Newtonian case, a 30,000 cSt silicon oil was used. In the non-Newtonian case, a fluid with nearly constant viscosity and large first normal stress difference (highly elastic) was used; this fluid was made with Corn syrup with a small amount of polyacrylamide. The swimming speed was measured, for different amplitudes and frequencies, using a digital image analysis. The objective of the present investigation is to determine whether the elastic effects of the fluid improve or not the swimming performance. Some preliminary results will be presented and discussed.
Influence of DBT reconstruction algorithm on power law spectrum coefficient
NASA Astrophysics Data System (ADS)
Vancamberg, Laurence; Carton, Ann-Katherine; Abderrahmane, Ilyes H.; Palma, Giovanni; Milioni de Carvalho, Pablo; Iordache, Rǎzvan; Muller, Serge
2015-03-01
In breast X-ray images, texture has been characterized by a noise power spectrum (NPS) that has an inverse power-law shape described by its slope β in the log-log domain. It has been suggested that the magnitude of the power-law spectrum coefficient β is related to mass lesion detection performance. We assessed β in reconstructed digital breast tomosynthesis (DBT) images to evaluate its sensitivity to different typical reconstruction algorithms including simple back projection (SBP), filtered back projection (FBP) and a simultaneous iterative reconstruction algorithm (SIRT 30 iterations). Results were further compared to the β coefficient estimated from 2D central DBT projections. The calculations were performed on 31 unilateral clinical DBT data sets and simulated DBT images from 31 anthropomorphic software breast phantoms. Our results show that β highly depends on the reconstruction algorithm; the highest β values were found for SBP, followed by reconstruction with FBP, while the lowest β values were found for SIRT. In contrast to previous studies, we found that β is not always lower in reconstructed DBT slices, compared to 2D projections and this depends on the reconstruction algorithm. All β values estimated in DBT slices reconstructed with SBP were larger than β values from 2D central projections. Our study also shows that the reconstruction algorithm affects the symmetry of the breast texture NPS; the NPS of clinical cases reconstructed with SBP exhibit the highest symmetry, while the NPS of cases reconstructed with SIRT exhibit the highest asymmetry.
Implitcation of a Power-Law Climate Response Function
NASA Astrophysics Data System (ADS)
Hébert, R.
2015-12-01
A study of global mean temperature is presented assuming that the climate response function to anthropogenic forcing is a power law. This general form allows for long-range dependancies with only 3 parameter while remaining within the linear forcing paradigm. This establish a one-to-one relation between the scaling exponent H and the ratio of the Transient Climate Response, TCR, and the Equilibrium Climate Sensitivity, ECS. The scaling exponent of the power law is estimated by a regression of temperature as a function of forcing and by a spectral analysis of the temperature and the forcing. We consider for the analysis 5 different datasets of historical global mean temperature and 100 CMIP5 RCP runs distributed among the 4 scenarios. We find that the error function for the estimate on historical temperature is very wide and thus, many scaling exponent can be used without meaningful changes in the fit residuals of historical temperatures; their response in the year 2100 on the other hand, is very broad. CMIP5 runs allow a narrower estimate of H which can then be used to estimate the ECS by dividing the TCR estimated from the historical data.
Power Laws in Real Estate Prices during Bubble Periods
NASA Astrophysics Data System (ADS)
Ohnishi, Takaaki; Mizuno, Takayuki; Shimizu, Chihiro; Watanabe, Tsutomu
How can we detect real estate bubbles? In this paper, we propose making use of information on the cross-sectional dispersion of real estate prices. During bubble periods, prices tend to go up considerably for some properties, but less so for others, so that price inequality across properties increases. In other words, a key characteristic of real estate bubbles is not the rapid price hike itself but a rise in price dispersion. Given this, the purpose of this paper is to examine whether developments in the dispersion in real estate prices can be used to detect bubbles in property markets as they arise, using data from Japan and the U.S. First, we show that the land price distribution in Tokyo had a power-law tail during the bubble period in the late 1980s, while it was very close to a lognormal before and after the bubble period. Second, in the U.S. data we find that the tail of the house price distribution tends to be heavier in those states which experienced a housing bubble. We also provide evidence suggesting that the power-law tail observed during bubble periods arises due to the lack of price arbitrage across regions.
Power-law distributions from additive preferential redistributions
NASA Astrophysics Data System (ADS)
Ree, Suhan
2006-02-01
We introduce a nongrowth model that generates the power-law distribution with the Zipf exponent. There are N elements, each of which is characterized by a quantity, and at each time step these quantities are redistributed through binary random interactions with a simple additive preferential rule, while the sum of quantities is conserved. The situation described by this model is similar to those of closed N -particle systems when conservative two-body collisions are only allowed. We obtain stationary distributions of these quantities both analytically and numerically while varying parameters of the model, and find that the model exhibits the scaling behavior for some parameter ranges. Unlike well-known growth models, this alternative mechanism generates the power-law distribution when the growth is not expected and the dynamics of the system is based on interactions between elements. This model can be applied to some examples such as personal wealths, city sizes, and the generation of scale-free networks when only rewiring is allowed.
Beyond the power law: Uncovering stylized facts in interbank networks
NASA Astrophysics Data System (ADS)
Vandermarliere, Benjamin; Karas, Alexei; Ryckebusch, Jan; Schoors, Koen
2015-06-01
We use daily data on bilateral interbank exposures and monthly bank balance sheets to study network characteristics of the Russian interbank market over August 1998-October 2004. Specifically, we examine the distributions of (un)directed (un)weighted degree, nodal attributes (bank assets, capital and capital-to-assets ratio) and edge weights (loan size and counterparty exposure). We search for the theoretical distribution that fits the data best and report the "best" fit parameters. We observe that all studied distributions are heavy tailed. The fat tail typically contains 20% of the data and can be mostly described well by a truncated power law. Also the power law, stretched exponential and log-normal provide reasonably good fits to the tails of the data. In most cases, however, separating the bulk and tail parts of the data is hard, so we proceed to study the full range of the events. We find that the stretched exponential and the log-normal distributions fit the full range of the data best. These conclusions are robust to (1) whether we aggregate the data over a week, month, quarter or year; (2) whether we look at the "growth" versus "maturity" phases of interbank market development; and (3) with minor exceptions, whether we look at the "normal" versus "crisis" operation periods. In line with prior research, we find that the network topology changes greatly as the interbank market moves from a "normal" to a "crisis" operation period.
Steele, Catriona M; James, David F; Hori, Sarah; Polacco, Rebecca C; Yee, Clemence
2014-06-01
Thickened liquids are frequently used in the management of oropharyngeal dysphagia. Previous studies suggest that compression of a liquid bolus between the tongue and the palate in the oral phase of swallowing serves a sensory function, enabling the tuning of motor behavior to match the viscosity of the bolus. However, the field lacks information regarding healthy oral sensory discrimination ability for small differences in liquid viscosity. We undertook to measure oral viscosity discrimination ability for five non-Newtonian xanthan gum-thickened liquids in the nectar- and honey-thick range. Xanthan gum concentration ranged from 0.5 to 0.87 % and increased by an average of 0.1 % between stimuli in the array. This translated to an average apparent viscosity increase of 0.2-fold between adjacent stimuli at 50 reciprocal seconds (/s). A triangle test paradigm was used to study stimulus discrimination in 78 healthy adults in two, sex-balanced age cohorts. Participants were provided 5-ml samples of liquids in sets of three; one liquid differed in xanthan gum concentration from the other two. Participants were required to sample the liquid orally and indicate which sample was perceived to have a different viscosity. A protocol of 20 sets (60 samples) allowed calculation of the minimum difference in xanthan gum concentration detected accurately. On average, participants were able to accurately detect a 0.38-fold increase in xanthan-gum concentration, translating to a 0.67-fold increase in apparent viscosity at 50/s. The data did not suggest the existence of a nonlinear point boundary in apparent viscosity within the range tested. No differences in viscosity discrimination were found between age cohorts or as a function of sex. The data suggest that for xanthan gum-thickened liquids, there may be several increments of detectably different viscosity within the ranges currently proposed for nectar- and honey-thick liquids. If physiological or functional differences in
Deviation from power law of the global seismic moment distribution
NASA Astrophysics Data System (ADS)
Serra, Isabel; Corral, Álvaro
2017-01-01
The distribution of seismic moment is of capital interest to evaluate earthquake hazard, in particular regarding the most extreme events. We make use of likelihood-ratio tests to compare the simple Gutenberg-Richter power-law (PL) distribution with two statistical models that incorporate an exponential tail, the so-called tapered Gutenberg-Richter (Tap) and the truncated gamma, when fitted to the global CMT earthquake catalog. Although the Tap distribution does not introduce any significant improvement of fit respect the PL, the truncated gamma does. Simulated samples of this distribution, with parameters β = 0.68 and mc = 9.15 and reshuffled in order to mimic the time occurrence of the order statistics of the empirical data, are able to explain the temporal heterogeneity of global seismicity both before and after the great Sumatra-Andaman earthquake of 2004.
Optimized dynamical decoupling for power-law noise spectra
Pasini, S.; Uhrig, G. S.
2010-01-15
We analyze the suppression of decoherence by means of dynamical decoupling in the pure-dephasing spin-boson model for baths with power law spectra. The sequence of ideal pi pulses is optimized according to the power of the bath. We expand the decoherence function and separate the canceling divergences from the relevant terms. The proposed sequence is chosen to be the one minimizing the decoherence function. By construction, it provides the best performance. We analytically derive the conditions that must be satisfied. The resulting equations are solved numerically. The solutions are very close to the Carr-Purcell-Meiboom-Gill sequence for a soft cutoff of the bath while they approach the Uhrig dynamical-decoupling sequence as the cutoff becomes harder.
Power-law creep and residual stresses in carbopol microgels
NASA Astrophysics Data System (ADS)
Lidon, Pierre; Manneville, Sebastien
We report on the interplay between creep and residual stresses in carbopol microgels. When a constant shear stress σ is applied below the yield stress σc, the strain is shown to increase as a power law of time, γ (t) =γ0 +(t / τ) α , with and exponent α ~= 0 . 38 that is strongly reminiscent of Andrade creep in hard solids. For applied shear stresses lower than some characteristic value of about σc / 10 , the microgels experience a more complex creep behavior that we link to the existence of residual stresses and to weak aging of the system after preshear. The influence of the preshear protocol, of boundary conditions and of microgel concentration on residual stresses is investigated. We discuss our results in light of previous works on colloidal glasses and other soft glassy systems.
Power-law weighted networks from local attachments
NASA Astrophysics Data System (ADS)
Moriano, P.; Finke, J.
2012-07-01
This letter introduces a mechanism for constructing, through a process of distributed decision-making, substrates for the study of collective dynamics on extended power-law weighted networks with both a desired scaling exponent and a fixed clustering coefficient. The analytical results show that the connectivity distribution converges to the scaling behavior often found in social and engineering systems. To illustrate the approach of the proposed framework we generate network substrates that resemble steady state properties of the empirical citation distributions of i) publications indexed by the Institute for Scientific Information from 1981 to 1997; ii) patents granted by the U.S. Patent and Trademark Office from 1975 to 1999; and iii) opinions written by the Supreme Court and the cases they cite from 1754 to 2002.
Deviation from power law of the global seismic moment distribution
Serra, Isabel; Corral, Álvaro
2017-01-01
The distribution of seismic moment is of capital interest to evaluate earthquake hazard, in particular regarding the most extreme events. We make use of likelihood-ratio tests to compare the simple Gutenberg-Richter power-law (PL) distribution with two statistical models that incorporate an exponential tail, the so-called tapered Gutenberg-Richter (Tap) and the truncated gamma, when fitted to the global CMT earthquake catalog. Although the Tap distribution does not introduce any significant improvement of fit respect the PL, the truncated gamma does. Simulated samples of this distribution, with parameters β = 0.68 and mc = 9.15 and reshuffled in order to mimic the time occurrence of the order statistics of the empirical data, are able to explain the temporal heterogeneity of global seismicity both before and after the great Sumatra-Andaman earthquake of 2004. PMID:28053311
Power-law rheology controls aftershock triggering and decay
Zhang, Xiaoming; Shcherbakov, Robert
2016-01-01
The occurrence of aftershocks is a signature of physical systems exhibiting relaxation phenomena. They are observed in various natural or experimental systems and usually obey several non-trivial empirical laws. Here we consider a cellular automaton realization of a nonlinear viscoelastic slider-block model in order to infer the physical mechanisms of triggering responsible for the occurrence of aftershocks. We show that nonlinear viscoelasticity plays a critical role in the occurrence of aftershocks. The model reproduces several empirical laws describing the statistics of aftershocks. In case of earthquakes, the proposed model suggests that the power-law rheology of the fault gauge, underlying lower crust, and upper mantle controls the decay rate of aftershocks. This is verified by analysing several prominent aftershock sequences for which the rheological properties of the underlying crust and upper mantle were established. PMID:27819355
Power-law rheology controls aftershock triggering and decay
NASA Astrophysics Data System (ADS)
Zhang, Xiaoming; Shcherbakov, Robert
2016-11-01
The occurrence of aftershocks is a signature of physical systems exhibiting relaxation phenomena. They are observed in various natural or experimental systems and usually obey several non-trivial empirical laws. Here we consider a cellular automaton realization of a nonlinear viscoelastic slider-block model in order to infer the physical mechanisms of triggering responsible for the occurrence of aftershocks. We show that nonlinear viscoelasticity plays a critical role in the occurrence of aftershocks. The model reproduces several empirical laws describing the statistics of aftershocks. In case of earthquakes, the proposed model suggests that the power-law rheology of the fault gauge, underlying lower crust, and upper mantle controls the decay rate of aftershocks. This is verified by analysing several prominent aftershock sequences for which the rheological properties of the underlying crust and upper mantle were established.
Power-law resistivity, magnetic relaxation and ac susceptibility
Gilchrist, J.; van der Beek, C.J.
1994-07-01
The nonlinear diffusion of magnetic flux into a superconducting sample can be studied by measuring the relaxation of the magnetisation after application of a step field or by measuring the ac susceptibility, {chi}{sub 1} and its third harmonic, {chi}{sub 3}, or preferably both methods covering different time scales. Each has been analysed recently for a field-cooled sample of a material whose creep activation energy depends logarithmically on current density, J corresponding to a power-law relation between electric field, E and J. Here, results are compared, using a universal scaling depth. Maximum {chi}{sub 1}{double_prime} {vert_bar}{chi}{sub 3}{vert_bar} and values occur, and also the magnetisation has relaxed to half its initial value when the scaling depth is comparable to the sample half-thickness.
Deviations from uniform power law scaling in nonstationary time series
NASA Technical Reports Server (NTRS)
Viswanathan, G. M.; Peng, C. K.; Stanley, H. E.; Goldberger, A. L.
1997-01-01
A classic problem in physics is the analysis of highly nonstationary time series that typically exhibit long-range correlations. Here we test the hypothesis that the scaling properties of the dynamics of healthy physiological systems are more stable than those of pathological systems by studying beat-to-beat fluctuations in the human heart rate. We develop techniques based on the Fano factor and Allan factor functions, as well as on detrended fluctuation analysis, for quantifying deviations from uniform power-law scaling in nonstationary time series. By analyzing extremely long data sets of up to N = 10(5) beats for 11 healthy subjects, we find that the fluctuations in the heart rate scale approximately uniformly over several temporal orders of magnitude. By contrast, we find that in data sets of comparable length for 14 subjects with heart disease, the fluctuations grow erratically, indicating a loss of scaling stability.
Brain Network Dynamics Adhere to a Power Law
Tomasi, Dardo G.; Shokri-Kojori, Ehsan; Volkow, Nora D.
2017-01-01
The temporal dynamics of complex networks such as the Internet are characterized by a power scaling between the temporal mean and dispersion of signals at each network node. Here we tested the hypothesis that the temporal dynamics of the brain networks are characterized by a similar power law. This realization could be useful to assess the effects of randomness and external modulators on the brain network dynamics. Simulated data using a well-stablished random diffusion model allowed us to predict that the temporal dispersion of the amplitude of low frequency fluctuations (ALFF) and that of the local functional connectivity density (lFCD) scale with their temporal means. We tested this hypothesis in open-access resting-state functional magnetic resonance imaging datasets from 66 healthy subjects. A robust power law emerged from the temporal dynamics of ALFF and lFCD metrics, which was insensitive to the methods used for the computation of the metrics. The scaling exponents (ALFF: 0.8 ± 0.1; lFCD: 1.1 ± 0.1; mean ± SD) decreased with age and varied significantly across brain regions; multimodal cortical areas exhibited lower scaling exponents, consistent with a stronger influence of external inputs, than limbic and subcortical regions, which exhibited higher scaling exponents, consistent with a stronger influence of internal randomness. Findings are consistent with the notion that external inputs govern neuronal communication in the brain and that their relative influence differs between brain regions. Further studies will assess the potential of this metric as biomarker to characterize neuropathology. PMID:28261049
Collective motion of microswimmers in viscoelastic fluids
NASA Astrophysics Data System (ADS)
Li, Gaojin; Ardekani, Arezoo
2015-11-01
The dynamics of suspension of self-propelled microorganisms show fascinating hydrodynamic phenomena, such as, large scale swarming motion, locally correlated motion, enhanced particle diffusion, and enhanced fluid mixing. Even though many studies have been conducted in a Newtonian fluid, the collective motion of microorganisms in non-Newtonian fluids is less understood. The non-Newtonian fluid rheological properties, such as viscoelasticity and shear-dependent viscosity in saliva, mucus and biofilm, significantly affect the swimming properties and hydrodynamic interaction of microorganisms. In this work, we use direct numerical simulation to investigate the collective motion of rod-like swimmers in viscoelastic fluids. Two swimming types, pusher and puller, are investigated. The background viscoelastic fluid is modeled using an Oldroyd-B constitutive equation. This work is supported by NSF CBET-1445955 and Indiana CTSI TR001108.
Power-law cross-correlations estimation under heavy tails
NASA Astrophysics Data System (ADS)
Kristoufek, Ladislav
2016-11-01
We examine the performance of six estimators of the power-law cross-correlations-the detrended cross-correlation analysis, the detrending moving-average cross-correlation analysis, the height cross-correlation analysis, the averaged periodogram estimator, the cross-periodogram estimator and the local cross-Whittle estimator-under heavy-tailed distributions. The selection of estimators allows to separate these into the time and frequency domain estimators. By varying the characteristic exponent of the α-stable distributions which controls the tails behavior, we report several interesting findings. First, the frequency domain estimators are practically unaffected by heavy tails bias-wise. Second, the time domain estimators are upward biased for heavy tails but they have lower estimator variance than the other group for short series. Third, specific estimators are more appropriate depending on distributional properties and length of the analyzed series. In addition, we provide a discussion of implications of these results for empirical applications as well as theoretical explanations.
Power law distributions and dynamic behaviour of stock markets
NASA Astrophysics Data System (ADS)
Richmond, P.
2001-04-01
A simple agent model is introduced by analogy with the mean field approach to the Ising model for a magnetic system. Our model is characterised by a generalised Langevin equation = F ϕ + G ϕ t where t is the usual Gaussian white noise, i.e.: t t' = 2Dδ t-t' and t = 0. Both the associated Fokker Planck equation and the long time probability distribution function can be obtained analytically. A steady state solution may be expressed as P ϕ = exp{ - Ψ ϕ - ln G(ϕ)} where Ψ ϕ = - F/ G dϕ and Z is a normalization factor. This is explored for the simple case where F ϕ = Jϕ + bϕ2 - cϕ3 and fluctuations characterised by the amplitude G ϕ = ϕ + ɛ when it readily yields for ϕ>>ɛ, a distribution function with power law tails, viz: P ϕ = exp{ 2bϕ-cϕ2 /D}. The parameter c ensures convergence of the distribution function for large values of ϕ. It might be loosely associated with the activity of so-called value traders. The parameter J may be associated with the activity of noise traders. Output for the associated time series show all the characteristics of familiar financial time series providing J < 0 and D | J|.
The speed–curvature power law in Drosophila larval locomotion
2016-01-01
We report the discovery that the locomotor trajectories of Drosophila larvae follow the power-law relationship between speed and curvature previously found in the movements of human and non-human primates. Using high-resolution behavioural tracking in controlled but naturalistic sensory environments, we tested the law in maggots tracing different trajectory types, from reaching-like movements to scribbles. For most but not all flies, we found that the law holds robustly, with an exponent close to three-quarters rather than to the usual two-thirds found in almost all human situations, suggesting dynamic effects adding on purely kinematic constraints. There are different hypotheses for the origin of the law in primates, one invoking cortical computations, another viscoelastic muscle properties coupled with central pattern generators. Our findings are consistent with the latter view and demonstrate that the law is possible in animals with nervous systems orders of magnitude simpler than in primates. Scaling laws might exist because natural selection favours processes that remain behaviourally efficient across a wide range of neural and body architectures in distantly related species. PMID:28120807
Evaluation of detection model performance in power-law noise
NASA Astrophysics Data System (ADS)
Burgess, Arthur E.
2001-06-01
Two alternative forced-choice (2AFC) nodule detection performances of a number of model observers were evaluated for detection of simulated nodules in filtered power-law (1/f3) noise. The models included the ideal observer, the channelized Fisher-Hotelling (FH) model with two different basis function sets, the non-prewhitening matched filter with an eye filter (NPWE), and the Rose model with no DC response (RoseNDC). Detectability of the designer nodule signal was investigated. It has equation s((rho) )equalsA*Rect((rho) /2)(1-(rho) 2)v, where (rho) is a normalized distance (r/R), R is the nodule radius and A is signal amplitude. The nodule profile can be changed (designed) by changing the value of v. For example, the result is a sharp-edged, flat-topped disc for v equal to zero and the projection of a sphere for v equal to 0.5. Human observer experiments were done with nodules based on v equal to 0, 0.5 and 1.5. For the v equal to 1.5 case, human results could be well fitted using a variety of models. The human CD diagram slopes were -0.12, +0.27 and +0.44 for v equal to 0, 0.5 and 1.5 respectively.
There is More than a Power Law in Zipf
Cristelli, Matthieu; Batty, Michael; Pietronero, Luciano
2012-01-01
The largest cities, the most frequently used words, the income of the richest countries, and the most wealthy billionaires, can be all described in terms of Zipf’s Law, a rank-size rule capturing the relation between the frequency of a set of objects or events and their size. It is assumed to be one of many manifestations of an underlying power law like Pareto’s or Benford’s, but contrary to popular belief, from a distribution of, say, city sizes and a simple random sampling, one does not obtain Zipf’s law for the largest cities. This pathology is reflected in the fact that Zipf’s Law has a functional form depending on the number of events N. This requires a fundamental property of the sample distribution which we call ‘coherence’ and it corresponds to a ‘screening’ between various elements of the set. We show how it should be accounted for when fitting Zipf’s Law. PMID:23139862
Reciprocity and the Emergence of Power Laws in Social Networks
NASA Astrophysics Data System (ADS)
Schnegg, Michael
Research in network science has shown that many naturally occurring and technologically constructed networks are scale free, that means a power law degree distribution emerges from a growth model in which each new node attaches to the existing network with a probability proportional to its number of links (= degree). Little is known about whether the same principles of local attachment and global properties apply to societies as well. Empirical evidence from six ethnographic case studies shows that complex social networks have significantly lower scaling exponents γ ~ 1 than have been assumed in the past. Apparently humans do not only look for the most prominent players to play with. Moreover cooperation in humans is characterized through reciprocity, the tendency to give to those from whom one has received in the past. Both variables — reciprocity and the scaling exponent — are negatively correlated (r = -0.767, sig = 0.075). If we include this effect in simulations of growing networks, degree distributions emerge that are much closer to those empirically observed. While the proportion of nodes with small degrees decreases drastically as we introduce reciprocity, the scaling exponent is more robust and changes only when a relatively large proportion of attachment decisions follow this rule. If social networks are less scale free than previously assumed this has far reaching implications for policy makers, public health programs and marketing alike.
Steady flow for shear thickening fluids in domains with unbounded sections
NASA Astrophysics Data System (ADS)
Dias, Gilberlandio J.
2017-02-01
We solve the stationary Stokes and Navier-Stokes equations for non-Newtonian incompressible fluids with shear dependent viscosity in domains with outlets containing unbounded cross sections, in the case of shear thickening viscosity. The flux assumes arbitrary given values and the growth of the cross sections are analyzed under different convergence hypotheses, inclusive the growth of Dirichlet's integral of the velocity field is deeply related the convergence hypotheses of such sections. We extend the results of the section 4 of [12, Ladyzhenskaya and Solonnikov] (for Newtonian fluids) to non-Newtonian fluids using the techniques found in [3, Dias and Santos].
Pulsatile flow with heat transfer of dusty magnetohydrodynamic Ree-Eyring fluid through a channel
NASA Astrophysics Data System (ADS)
Shawky, Hameda Mohammed
2009-08-01
The flow due to the pulsatile pressure gradient of dusty non-Newtonian fluid with heat transfer in a channel is considered. The system is stressed by an external magnetic field. The non-Newtonian fluid under consideration is obeying the rheological equation of state due to Ree-Eyring’s stress-strain relation. The equations of momentum and energy have been solved by using Lightill method. The velocity and temperature distributions of the two phase of the dusty fluid are obtained. The effects of various physical parameters of distributions the problem on these distributions are discussed and illustrated graphically through a set of figure.
Power-law tail probabilities of drainage areas in river basins
Veitzer, S.A.; Troutman, B.M.; Gupta, V.K.
2003-01-01
The significance of power-law tail probabilities of drainage areas in river basins was discussed. The convergence to a power law was not observed for all underlying distributions, but for a large class of statistical distributions with specific limiting properties. The article also discussed about the scaling properties of topologic and geometric network properties in river basins.
NASA Astrophysics Data System (ADS)
Chen, Yanguang
2015-03-01
The difference between the inverse power function and the negative exponential function is significant. The former suggests a complex distribution, while the latter indicates a simple distribution. However, the association of the power-law distribution with the exponential distribution has been seldom researched. This paper is devoted to exploring the relationships between exponential laws and power laws from the angle of view of urban geography. Using mathematical derivation and numerical experiments, I reveal that a power-law distribution can be created through a semi-moving average process of an exponential distribution. For the distributions defined in a one-dimension space (e.g. Zipf's law), the power exponent is 1; while for those defined in a two-dimension space (e.g. Clark's law), the power exponent is 2. The findings of this study are as follows. First, the exponential distributions suggest a hidden scaling, but the scaling exponents suggest a Euclidean dimension. Second, special power-law distributions can be derived from exponential distributions, but they differ from the typical power-law distributions. Third, it is the real power-law distributions that can be related with fractal dimension. This study discloses an inherent link between simplicity and complexity. In practice, maybe the result presented in this paper can be employed to distinguish the real power laws from spurious power laws (e.g. the fake Zipf distribution).
Numerical tools for obtaining power-law representations of heavy-tailed datasets
NASA Astrophysics Data System (ADS)
Mansfield, Marc L.
2016-01-01
Many empirical datasets have highly skewed, non-Gaussian, heavy-tailed distributions, dominated by a relatively small number of data points at the high end of the distribution. Consistent with their role as stable distributions, power laws have frequently been proposed to model such datasets. However there are physical situations that require distributions with finite means. Such situations may call for power laws with high-end cutoffs. Here, I present a maximum-likelihood technique for determining an optimal cut-off power law to represent a given dataset. I also develop a new statistical test of the quality of fit. Results are demonstrated for a number of benchmark datasets. Non-power-law datasets can frequently be represented by power laws, but this is a trivial result unless the dataset spans a broad domain. Nevertheless, I demonstrate that there are non-power-law distributions, including broad log-normal distributions, whose tails can be fit to power laws over many orders of magnitude. Therefore, caution is called for whenever power laws are invoked to represent empirical data. Supplementary material in the form of one pdf file available from the Journal web page at: http://dx.doi.org/10.1140/epjb/e2015-60452-3
Power law distribution in high frequency financial data? An econometric analysis
NASA Astrophysics Data System (ADS)
Todorova, Lora; Vogt, Bodo
2011-11-01
Power law distributions are very common in natural sciences. We analyze high frequency financial data from XETRA and the NYSE using maximum likelihood estimation and the Kolmogorov-Smirnov statistic to test whether the power law hypothesis holds also for these data. We find that the universality and scale invariance properties of the power law are violated. Furthermore, the returns of Daimler Chrysler and SAP traded simultaneously on both exchanges follow a power law at one exchange, but not at the other. These results raise some questions about the no-arbitrage condition. Finally, we find that an exponential function provides a better fit for the tails of the sample distributions than a power law function.
Chimera patterns induced by distance-dependent power-law coupling in ecological networks.
Banerjee, Tanmoy; Dutta, Partha Sharathi; Zakharova, Anna; Schöll, Eckehard
2016-09-01
This paper reports the occurrence of several chimera patterns and the associated transitions among them in a network of coupled oscillators, which are connected by a long-range interaction that obeys a distance-dependent power law. This type of interaction is common in physics and biology and constitutes a general form of coupling scheme, where by tuning the power-law exponent of the long-range interaction the coupling topology can be varied from local via nonlocal to global coupling. To explore the effect of the power-law coupling on collective dynamics, we consider a network consisting of a realistic ecological model of oscillating populations, namely the Rosenzweig-MacArthur model, and show that the variation of the power-law exponent mediates transitions between spatial synchrony and various chimera patterns. We map the possible spatiotemporal states and their scenarios that arise due to the interplay between the coupling strength and the power-law exponent.
Do wealth distributions follow power laws? Evidence from ‘rich lists’
NASA Astrophysics Data System (ADS)
Brzezinski, Michal
2014-07-01
We use data on the wealth of the richest persons taken from the 'rich lists' provided by business magazines like Forbes to verify if the upper tails of wealth distributions follow, as often claimed, a power-law behaviour. The data sets used cover the world's richest persons over 1996-2012, the richest Americans over 1988-2012, the richest Chinese over 2006-2012, and the richest Russians over 2004-2011. Using a recently introduced comprehensive empirical methodology for detecting power laws, which allows for testing the goodness of fit as well as for comparing the power-law model with rival distributions, we find that a power-law model is consistent with data only in 35% of the analysed data sets. Moreover, even if wealth data are consistent with the power-law model, they are usually also consistent with some rivals like the log-normal or stretched exponential distributions.
NASA Astrophysics Data System (ADS)
Echeverria, J. C.; Rodriguez, E.; Aguilar-Cornejo, M.; Alvarez-Ramirez, J.
2016-10-01
In many instances, the fluctuation function obtained from detrended fluctuation analysis (DFA) cannot be described by a uniform power-law function along scales. In fact, the manifestation of crossover scales may reflect the simultaneous action of different stochastic mechanisms displayed predominantly within certain scale ranges. This note proposes the use of a linear combination of power-law functions for adjusting DFA data. The idea is that each power-law function recast the dominance of certain stochastic mechanisms (e.g., the mean-reversion and long-term trends) at specific scale domains. Different values of the scaling exponents are numerically estimated by means of a nonlinear least-squares fitting of power-law functions. Examples of crude oil market and heart rate variability are discussed with some detail for illustrating the advantages of taking a linear combination of power-law functions for describing scaling behavior from DFA.
Chimera patterns induced by distance-dependent power-law coupling in ecological networks
NASA Astrophysics Data System (ADS)
Banerjee, Tanmoy; Dutta, Partha Sharathi; Zakharova, Anna; Schöll, Eckehard
2016-09-01
This paper reports the occurrence of several chimera patterns and the associated transitions among them in a network of coupled oscillators, which are connected by a long-range interaction that obeys a distance-dependent power law. This type of interaction is common in physics and biology and constitutes a general form of coupling scheme, where by tuning the power-law exponent of the long-range interaction the coupling topology can be varied from local via nonlocal to global coupling. To explore the effect of the power-law coupling on collective dynamics, we consider a network consisting of a realistic ecological model of oscillating populations, namely the Rosenzweig-MacArthur model, and show that the variation of the power-law exponent mediates transitions between spatial synchrony and various chimera patterns. We map the possible spatiotemporal states and their scenarios that arise due to the interplay between the coupling strength and the power-law exponent.
POWER-LAW TEMPLATE FOR INFRARED POINT-SOURCE CLUSTERING
Addison, Graeme E.; Dunkley, Joanna; Hajian, Amir; Das, Sudeep; Hincks, Adam D.; Page, Lyman A.; Staggs, Suzanne T.; Viero, Marco; Bond, J. Richard; Devlin, Mark J.; Reese, Erik D.; Halpern, Mark; Scott, Douglas; Hlozek, Renee; Marriage, Tobias A.; Spergel, David N.; Moodley, Kavilan; Wollack, Edward
2012-06-20
We perform a combined fit to angular power spectra of unresolved infrared (IR) point sources from the Planck satellite (at 217, 353, 545, and 857 GHz, over angular scales 100 {approx}< l {approx}< 2200), the Balloon-borne Large-Aperture Submillimeter Telescope (BLAST; 250, 350, and 500 {mu}m; 1000 {approx}< l {approx}< 9000), and from correlating BLAST and Atacama Cosmology Telescope (ACT; 148 and 218 GHz) maps. We find that the clustered power over the range of angular scales and frequencies considered is well fitted by a simple power law of the form C{sup clust}{sub l}{proportional_to}l{sup -n} with n = 1.25 {+-} 0.06. While the IR sources are understood to lie at a range of redshifts, with a variety of dust properties, we find that the frequency dependence of the clustering power can be described by the square of a modified blackbody, {nu}{sup {beta}} B({nu}, T{sub eff}), with a single emissivity index {beta} = 2.20 {+-} 0.07 and effective temperature T{sub eff} = 9.7 K. Our predictions for the clustering amplitude are consistent with existing ACT and South Pole Telescope results at around 150 and 220 GHz, as is our prediction for the effective dust spectral index, which we find to be {alpha}{sub 150-220} = 3.68 {+-} 0.07 between 150 and 220 GHz. Our constraints on the clustering shape and frequency dependence can be used to model the IR clustering as a contaminant in cosmic microwave background anisotropy measurements. The combined Planck and BLAST data also rule out a linear bias clustering model.
Power law olivine crystal size distributions in lithospheric mantle xenoliths
NASA Astrophysics Data System (ADS)
Armienti, P.; Tarquini, S.
2002-12-01
Olivine crystal size distributions (CSDs) have been measured in three suites of spinel- and garnet-bearing harzburgites and lherzolites found as xenoliths in alkaline basalts from Canary Islands, Africa; Victoria Land, Antarctica; and Pali Aike, South America. The xenoliths derive from lithospheric mantle, from depths ranging from 80 to 20 km. Their textures vary from coarse to porphyroclastic and mosaic-porphyroclastic up to cataclastic. Data have been collected by processing digital images acquired optically from standard petrographic thin sections. The acquisition method is based on a high-resolution colour scanner that allows image capturing of a whole thin section. Image processing was performed using the VISILOG 5.2 package, resolving crystals larger than about 150 μm and applying stereological corrections based on the Schwartz-Saltykov algorithm. Taking account of truncation effects due to resolution limits and thin section size, all samples show scale invariance of crystal size distributions over almost three orders of magnitude (0.2-25 mm). Power law relations show fractal dimensions varying between 2.4 and 3.8, a range of values observed for distributions of fragment sizes in a variety of other geological contexts. A fragmentation model can reproduce the fractal dimensions around 2.6, which correspond to well-equilibrated granoblastic textures. Fractal dimensions >3 are typical of porphyroclastic and cataclastic samples. Slight bends in some linear arrays suggest selective tectonic crushing of crystals with size larger than 1 mm. The scale invariance shown by lithospheric mantle xenoliths in a variety of tectonic settings forms distant geographic regions, which indicate that this is a common characteristic of the upper mantle and should be taken into account in rheological models and evaluation of metasomatic models.
Exponential and power-law mass distributions in brittle fragmentation
NASA Astrophysics Data System (ADS)
Åström, J. A.; Linna, R. P.; Timonen, J.; Møller, Peder Friis; Oddershede, Lene
2004-08-01
Generic arguments, a minimal numerical model, and fragmentation experiments with gypsum disk are used to investigate the fragment-size distribution that results from dynamic brittle fragmentation. Fragmentation is initiated by random nucleation of cracks due to material inhomogeneities, and its dynamics are pictured as a process of propagating cracks that are unstable against side-branch formation. The initial cracks and side branches both merge mutually to form fragments. The side branches have a finite penetration depth as a result of inherent damping. Generic arguments imply that close to the minimum strain (or impact energy) required for fragmentation, the number of fragments of size s scales as s-(2D-1)/Df1(-(2/λ)Ds)+f2(-s0-1(λ+s1/D)D) , where D is the Euclidean dimension of the space, λ is the penetration depth, and f1 and f2 can be approximated by exponential functions. Simulation results and experiments can both be described by this theoretical fragment-size distribution. The typical largest fragment size s0 was found to diverge at the minimum strain required for fragmentation as it is inversely related to the density of initially formed cracks. Our results also indicate that scaling of s0 close to this divergence depends on, e.g., loading conditions, and thus is not universal. At the same time, the density of fragment surface vanishes as L-1 , L being the linear dimension of the brittle solid. The results obtained provide an explanation as to why the fragment-size distributions found in nature can have two components, an exponential as well as a power-law component, with varying relative weights.
Power-Law Template for IR Point Source Clustering
NASA Technical Reports Server (NTRS)
Addison, Graeme E.; Dunkley, Joanna; Hajian, Amir; Viero, Marco; Bond, J. Richard; Das, Sudeep; Devlin, Mark; Halpern, Mark; Hincks, Adam; Hlozek, Renee; Marriage, Tobias A.; Moodley, Kavilan; Page, Lyman A.; Reese, Erik D.; Scott, Douglass; Spergel, David N.; Staggs,Suzanne T.; Wollack, Edward
2011-01-01
We perform a combined fit to angular power spectra of unresolved infrared (IR) point sources from the Planck satellite (at 217,353,545 and 857 GHz, over angular scales 100 < I < 2200), the Balloonborne Large-Aperture Submillimeter Telescope (BLAST; 250, 350 and 500 microns; 1000 < I < 9000), and from correlating BLAST and Atacama Cosmology Telescope (ACT; 148 and 218 GHz) maps. We find that the clustered power over the range of angular scales and frequencies considered is well fit by a simple power law of the form C_l\\propto I(sup -n) with n = 1.25 +/- 0.06. While the IR sources are understood to lie at a range of redshifts, with a variety of dust properties, we find that the frequency dependence of the clustering power can be described by the square of a modified blackbody, nu(sup beta) B(nu,T_eff), with a single emissivity index beta = 2.20 +/- 0.07 and effective temperature T_eff= 9.7 K. Our predictions for the clustering amplitude are consistent with existing ACT and South Pole Telescope results at around 150 and 220 GHz, as is our prediction for the effective dust spectral index, which we find to be alpha_150-220 = 3.68 +/- 0.07 between 150 and 220 GHz. Our constraints on the clustering shape and frequency dependence can be used to model the IR clustering as a contaminant in Cosmic Microwave Background anisotropy measurements. The combined Planck and BLAST data also rule out a linear bias clustering model.
Power-Law Template for Infrared Point-Source Clustering
NASA Technical Reports Server (NTRS)
Addison, Graeme E; Dunkley, Joanna; Hajian, Amir; Viero, Marco; Bond, J. Richard; Das, Sudeep; Devlin, Mark J.; Halpern, Mark; Hincks, Adam D; Hlozek, Renee; Marriage, Tobias A.; Moodley, Kavilan; Page, Lyman A.; Reese, Erik D.; Scott, Douglas; Spergel, David N.; Staggs, Suzanne T.; Wollack, Edward
2012-01-01
We perform a combined fit to angular power spectra of unresolved infrared (IR) point sources from the Planck satellite (at 217, 353, 545, and 857 GHz, over angular scales 100 approx < l approx < 2200), the Balloon-borne Large-Aperture Submillimeter Telescope (BLAST; 250, 350, and 500 micron; 1000 approx < l approx < 9000), and from correlating BLAST and Atacama Cosmology Telescope (ACT; 148 and 218 GHz) maps. We find that the clustered power over the range of angular scales and frequencies considered is well fitted by a simple power law of the form C(sup clust)(sub l) varies as l (sub -n) with n = 1.25 +/- 0.06. While the IR sources are understood to lie at a range of redshifts, with a variety of dust properties, we find that the frequency dependence of the clustering power can be described by the square of a modified blackbody, ?(sup Beta)B(?, T(sub eff) ), with a single emissivity index Beta = 2.20 +/- 0.07 and effective temperature T(sub eff) = 9.7 K. Our predictions for the clustering amplitude are consistent with existing ACT and South Pole Telescope results at around 150 and 220 GHz, as is our prediction for the effective dust spectral index, which we find to be alpha(sub 150-220) = 3.68 +/- 0.07 between 150 and 220 GHz. Our constraints on the clustering shape and frequency dependence can be used to model the IR clustering as a contaminant in cosmic microwave background anisotropy measurements. The combined Planck and BLAST data also rule out a linear bias clustering model.
NASA Astrophysics Data System (ADS)
Pnueli, David; Gutfinger, Chaim
1997-01-01
This text is intended for the study of fluid mechanics at an intermediate level. The presentation starts with basic concepts, in order to form a sound conceptual structure that can support engineering applications and encourage further learning. The presentation is exact, incorporating both the mathematics involved and the physics needed to understand the various phenomena in fluid mechanics. Where a didactical choice must be made between the two, the physics prevails. Throughout the book the authors have tried to reach a balance between exact presentation, intuitive grasp of new ideas, and creative applications of concepts. This approach is reflected in the examples presented in the text and in the exercises given at the end of each chapter. Subjects treated are hydrostatics, viscous flow, similitude and order of magnitude, creeping flow, potential flow, boundary layer flow, turbulent flow, compressible flow, and non-Newtonian flows. This book is ideal for advanced undergraduate students in mechanical, chemical, aerospace, and civil engineering. Solutions manual available.
Electrorheological Fluids: Aerospace Applications
NASA Technical Reports Server (NTRS)
Parmar, D. S.; Eftekhari, A.; Belvin, K. W.; Singh, J. J.
1996-01-01
Electrorheological fluids (ERF) are an intriguing class of non-Newtonian industrial fluids. They consist of fine dielectric particles suspended in liquids of low dielectric constants. The objectives of this research were to select a particulate system such that: (1) its density can be varied to match that of the selected liquid, and (2) the dielectric constant of the particles and the liquids should be such that the critical fields needed for asymptotic increase in viscosity are less than or equal to 10 KV/cm. Synthetic Zeolite particles were selected as the solute/suspensions. Octoil oil was selected as the solvent. The results are summarized here.
Traction in elastohydrodynamic line contacts for two synthesized hydrocarbon fluids
NASA Technical Reports Server (NTRS)
Trachman, E. G.; Cheng, H. S.
1973-01-01
The paper describes the disk machine designed and constructed for the investigation of the traction in elastohydrodynamic line contacts for two synthesized hydrocarbon fluids. The results of this experimental study are presented and compared with the theoretical predictions of traction according to the thermal and non-Newtonian theory recently presented by the authors.
AEGIS: A MULTIWAVELENGTH STUDY OF SPITZER POWER-LAW GALAXIES
Park, S. Q.; Barmby, P.; Willner, S. P.; Ashby, M. L. N.; Fazio, G. G.; Georgakakis, A.; Ivison, R. J.; Konidaris, N. P.; Rosario, D. J.; Nandra, K.
2010-07-10
This paper analyzes a sample of 489 Spitzer/Infrared Array Camera (IRAC) sources in the Extended Groth Strip (EGS), whose spectral energy distributions fit a red power law (PL) from 3.6 to 8.0 {mu}m. The median redshift for sources with known redshifts is (z) = 1.6. Though all or nearly all of the sample galaxies are likely to be active galactic nuclei (AGNs), only 33% were detected in the EGS X-ray survey (AEGIS-X) using 200 ks Chandra observations. The detected sources are X-ray luminous with L {sub X}>10{sup 43} erg s{sup -1} and moderately to heavily obscured with N {sub H}>10{sup 22} cm{sup -2}. Stacking the X-ray-undetected sample members yields a statistically significant X-ray signal, suggesting that they are on average more distant or more obscured than sources with X-ray detections. The ratio of X-ray to mid-infrared fluxes suggests that a substantial fraction of the sources undetected in X-rays are obscured at the Compton-thick level, in contrast to the X-ray-detected sources, all of which appear to be Compton thin. For the X-ray-detected PL sources with redshifts, an X-ray luminosity L {sub X} {approx} 10{sup 44} erg s{sup -1} marks a transition between low-luminosity, blue sources dominated by the host galaxy to high-luminosity, red PL sources dominated by nuclear activity. X-ray-to-optical ratios, infrared variability, and 24 {mu}m properties of the sample are consistent with the identification of infrared PL sources as active nuclei, but a rough estimate is that only 22% of AGNs are selected by the PL criteria. Comparison of the PL selection technique and various IRAC color criteria for identifying AGNs confirms that high-redshift samples selected via simple IRAC colors may be heavily contaminated by starlight-dominated objects.
Scale Invariance in Landscape Evolution Models Using Stream Power Laws
NASA Astrophysics Data System (ADS)
Kwang, J. S.; Parker, G.
2014-12-01
Landscape evolution models (LEM) commonly utilize stream power laws to simulate river incision with formulations such as E = KAmSn, where E is a vertical incision rate [L/T], K is an erodibility constant [L1-2m/T], A is an upstream drainage area [L2], S is a local channel gradient [-], and m and n are positive exponents that describe the basin hydrology. In our reduced complexity model, the landscape approached equilibrium by balancing an incision rate with a constant, uniform, vertical rock uplift rate at every location in the landscape. From our simulations, for a combination of m and n, the landscape exhibited scale invariance. That is, regardless of the size and scale of the basin, the relief and vertical structure of the landscape remained constant. Therefore, the relief and elevation profile of the landscape at equilibrium were only dependent on the coefficients for erodibility and uplift and an equation that described how upstream area, A, increased as the length of a stream increased. In our analytical 1D models, we utilized two equations that described upslope area, (a) A = Bl, where B is the profile width [L], and l is the stream length from the ridge [L] and (b) A = Clh, Hack's Law, where C is a constant [L2-h] and h is a positive exponent. With these equations, (a) m = n and (b) hm = n resulted in scale invariance. In our numerical 2D models, the relationship between A and l was inherent in the actual structure of the drainage network. From our numerical 2D results, scale invariance occurred when 2m = n. Additionally, using reasonable values from the literature for exponents, n, m and h, resulted in singularities at the ridges in the landscape, which caused truncation error. In consequence, the elevation of the ridge increased as the number of grid cells in the domain increased in the numerical model, and the model was unable to converge. These singularities at the ridges appeared when (a) m ≥ n and (b) hm ≥ n in the analytical model and 2m ≥ n in
Simple inflationary quintessential model. II. Power law potentials
NASA Astrophysics Data System (ADS)
de Haro, Jaume; Amorós, Jaume; Pan, Supriya
2016-09-01
The present work is a sequel of our previous work [Phys. Rev. D 93, 084018 (2016)] which depicted a simple version of an inflationary quintessential model whose inflationary stage was described by a Higgs-type potential and the quintessential phase was responsible due to an exponential potential. Additionally, the model predicted a nonsingular universe in past which was geodesically past incomplete. Further, it was also found that the model is in agreement with the Planck 2013 data when running is allowed. But, this model provides a theoretical value of the running which is far smaller than the central value of the best fit in ns , r , αs≡d ns/d l n k parameter space where ns, r , αs respectively denote the spectral index, tensor-to-scalar ratio and the running of the spectral index associated with any inflationary model, and consequently to analyze the viability of the model one has to focus in the two-dimensional marginalized confidence level in the allowed domain of the plane (ns,r ) without taking into account the running. Unfortunately, such analysis shows that this model does not pass this test. However, in this sequel we propose a family of models runs by a single parameter α ∈[0 ,1 ] which proposes another "inflationary quintessential model" where the inflation and the quintessence regimes are respectively described by a power law potential and a cosmological constant. The model is also nonsingular although geodesically past incomplete as in the cited model. Moreover, the present one is found to be more simple compared to the previous model and it is in excellent agreement with the observational data. In fact, we note that, unlike the previous model, a large number of the models of this family with α ∈[0 ,1/2 ) match with both Planck 2013 and Planck 2015 data without allowing the running. Thus, the properties in the current family of models compared to its past companion justify its need for a better cosmological model with the successive
Blinking in quantum dots: The origin of the grey state and power law statistics
NASA Astrophysics Data System (ADS)
Ye, Mao; Searson, Peter C.
2011-09-01
Quantum dot (QD) blinking is characterized by switching between an “on” state and an “off” state, and a power-law distribution of on and off times with exponents from 1.0 to 2.0. The origin of blinking behavior in QDs, however, has remained a mystery. Here we describe an energy-band model for QDs that captures the full range of blinking behavior reported in the literature and provides new insight into features such as the gray state, the power-law distribution of on and off times, and the power-law exponents.
Auditory Power-Law Activation Avalanches Exhibit a Fundamental Computational Ground State
NASA Astrophysics Data System (ADS)
Stoop, Ruedi; Gomez, Florian
2016-07-01
The cochlea provides a biological information-processing paradigm that we are only beginning to understand in its full complexity. Our work reveals an interacting network of strongly nonlinear dynamical nodes, on which even a simple sound input triggers subnetworks of activated elements that follow power-law size statistics ("avalanches"). From dynamical systems theory, power-law size distributions relate to a fundamental ground state of biological information processing. Learning destroys these power laws. These results strongly modify the models of mammalian sound processing and provide a novel methodological perspective for understanding how the brain processes information.
On the origin of power-law X-ray spectra of active galactic nuclei
NASA Technical Reports Server (NTRS)
Schlosman, I.; Shaham, J.; Shaviv, G.
1984-01-01
In the present analytical model for a power law X-ray continuum production in active galactic nuclei, the dissipation of turbulent energy flux above the accretion disk forms an optically thin transition layer with an inverted temperature gradient. The emitted thermal radiation has a power law spectrum in the 0.1-100 keV range, with a photon energy spectral index gamma of about 0.4-1.0. Thermal X-ray contribution from the layer is 5-10 percent of the total disk luminosity. The gamma value of 0.75 is suggested as a 'natural' power law index for Seyfert galaxies and QSOs.
Auditory Power-Law Activation Avalanches Exhibit a Fundamental Computational Ground State.
Stoop, Ruedi; Gomez, Florian
2016-07-15
The cochlea provides a biological information-processing paradigm that we are only beginning to understand in its full complexity. Our work reveals an interacting network of strongly nonlinear dynamical nodes, on which even a simple sound input triggers subnetworks of activated elements that follow power-law size statistics ("avalanches"). From dynamical systems theory, power-law size distributions relate to a fundamental ground state of biological information processing. Learning destroys these power laws. These results strongly modify the models of mammalian sound processing and provide a novel methodological perspective for understanding how the brain processes information.
The double power law in human collaboration behavior: The case of Wikipedia
NASA Astrophysics Data System (ADS)
Kwon, Okyu; Son, Woo-Sik; Jung, Woo-Sung
2016-11-01
We study human behavior in terms of the inter-event time distribution of revision behavior on Wikipedia, an online collaborative encyclopedia. We observe a double power law distribution for the inter-editing behavior at the population level and a single power law distribution at the individual level. Although interactions between users are indirect or moderate on Wikipedia, we determine that the synchronized editing behavior among users plays a key role in determining the slope of the tail of the double power law distribution.
The logarithmic and power law behaviors of the accelerating, turbulent thermal boundary layer
NASA Astrophysics Data System (ADS)
Castillo, Luciano; Hussain, Fazle
2017-02-01
Direct numerical simulation of spatially evolving thermal turbulent boundary layers with strong favorable pressure gradient (FPG) shows that the thermal fluctuation intensity, θ' + and the Reynolds shear stress, u'v'¯+ exhibit a logarithmic behavior spanning the meso-layer (e.g., 50 ≤y+≤170 ). However, the mean thermal profile is not logarithmic even in the zero pressure gradient (ZPG) region; instead, it follows a power law. The maxima of u' 2 ¯+ and v'θ'¯+ change little with the strength of acceleration, while v'+, w'+, and u'v'¯+ continue to decay in the flow direction. Furthermore, θ'+ and u'θ'¯+ surprisingly experience changes from constants in ZPG to sharp rises in the FPG region. Such behavior appears to be due to squashing of the streaks which decreases the streak flank angle below the critical value for "transient growth" generation of streamwise vortices, shutting down production [W. Schoppa and F. Hussain, "Coherent structure generation near-wall turbulence," J. Fluid Mech. 453, 57-108 (2002)]. The streamwise vortices near the wall, although shrink because of stretching, simultaneously, also become weaker as the structures are progressively pushed farther down to the more viscous region near the wall. While the vortical structures decay rapidly in accelerating flows, the thermal field does not—nullifying the myth that both the thermal and velocity fields are similar.
Intermittent Flow In Yield Stress Fluids Slows Down Chaotic Mixing
NASA Astrophysics Data System (ADS)
Boujlel, Jalila; Wendell, Dawn; Gouillart, Emmanuelle; Pigeonneau, Franck; Jop, Pierre; Laboratoire Surface du Verre et Interfaces Team
2013-11-01
Many mixing situations involve fluids with non-Newtonian properties: mixing of building materials such as concrete or mortar are based on fluids that have shear- thinning rheological properties. Lack of correct mixing can waste time and money, or lead to products with defects. When fluids are stirred and mixed together at low Reynolds number, the fluid particles should undergo chaotic trajectories to be well mixed by the so-called chaotic advection resulting from the flow. Previous work to characterize chaotic mixing in many different geometries has primarily focused on Newtonian fluids. First studies into non-Newtonian chaotic advection often utilize idealized mixing geometries such as cavity flows or journal bearing flows for numerical studies. Here, we present experimental results of chaotic mixing of yield stress fluids with non-Newtonian fluids using rod-stirring protocol with rotating vessel. We describe the various steps of the mixing and determine their dependence on the fluid rheology and speeds of rotation of the rods and the vessel. We show how the mixing of yield-stress fluids by chaotic advection is reduced compared to the mixing of Newtonian fluids and explain our results, bringing to light the relevant mechanisms: the presence of fluid that only flows intermittently, a phenomenon enhanced by the yield stress, and the importance of the peripheral region. This result is confirmed via numerical simulations.
Pressurized fluid damping of nanoelectromechanical systems.
Svitelskiy, Oleksiy; Sauer, Vince; Liu, Ning; Cheng, Kar-Mun; Finley, Eric; Freeman, Mark R; Hiebert, Wayne K
2009-12-11
Interactions of nanoscale structures with fluids are of current interest both in the elucidation of fluid dynamics at these small scales, and in determining the ultimate performance of nanoelectromechanical systems outside of vacuum. We present a comprehensive study of nanomechanical damping in three gases (He, N2, CO2), and liquid CO2. Resonant dynamics in multiple devices of varying size and frequency is measured over 10 decades of pressure (1 mPa-20 MPa) using time-domain stroboscopic optical interferometry. The wide pressure range allows full exploration of the regions of validity of Newtonian and non-Newtonian flow damping models. Observing free molecular flow behavior extending above 1 atm, we find a fluid relaxation time model to be valid throughout, but not beyond, the non-Newtonian regime, and a Newtonian flow vibrating spheres model to be valid in the viscous limit.
Fitting power-laws in empirical data with estimators that work for all exponents
Hanel, Rudolf; Corominas-Murtra, Bernat; Liu, Bo; Thurner, Stefan
2017-01-01
Most standard methods based on maximum likelihood (ML) estimates of power-law exponents can only be reliably used to identify exponents smaller than minus one. The argument that power laws are otherwise not normalizable, depends on the underlying sample space the data is drawn from, and is true only for sample spaces that are unbounded from above. Power-laws obtained from bounded sample spaces (as is the case for practically all data related problems) are always free of such limitations and maximum likelihood estimates can be obtained for arbitrary powers without restrictions. Here we first derive the appropriate ML estimator for arbitrary exponents of power-law distributions on bounded discrete sample spaces. We then show that an almost identical estimator also works perfectly for continuous data. We implemented this ML estimator and discuss its performance with previous attempts. We present a general recipe of how to use these estimators and present the associated computer codes. PMID:28245249
Charged Noncommutative Wormhole Solutions via Power-Law f(T) Models
NASA Astrophysics Data System (ADS)
Rani, Shamaila; Jawad, Abdul; Bilal Amin, M.
2016-10-01
In this paper, we explore static spherically symmetric charged wormhole solutions in extended teleparallel gravity taking power-law f(T) models. We consider noncommutative geometry under Lorentzian distribution. In order to obtain matter components, we develop field equations using effective energy-momentum tensor for non-diagonal tetrad. We explore solutions by considering various viable power-law f(T) models, which also include teleparallel gravity case. The violation of energy conditions obtain by exotic matter to form wormhole solutions in teleparallel case while, physical acceptable wormhole solutions exist for charged noncommutative wormhole solutions for some cases of power-law models. The effective energy-momentum tensor and charge are responsible for the violation of the energy conditions. Also, we check the equilibrium condition for these solutions. The equilibrium condition meets for the teleparallel case and some power-law solutions while remaining solutions are either in less equilibrium or in disequilibrium situation.
Stochastic model of Zipf's law and the universality of the power-law exponent.
Yamamoto, Ken
2014-04-01
We propose a stochastic model of Zipf's law, namely a power-law relation between rank and size, and clarify as to why a specific value of its power-law exponent is quite universal. We focus on the successive total of a multiplicative stochastic process. By employing properties of a well-known stochastic process, we concisely show that the successive total follows a stationary power-law distribution, which is directly related to Zipf's law. The formula of the power-law exponent is also derived. Finally, we conclude that the universality of the rank-size exponent is brought about by symmetry between an increase and a decrease in the random growth rate.
Fitting power-laws in empirical data with estimators that work for all exponents.
Hanel, Rudolf; Corominas-Murtra, Bernat; Liu, Bo; Thurner, Stefan
2017-01-01
Most standard methods based on maximum likelihood (ML) estimates of power-law exponents can only be reliably used to identify exponents smaller than minus one. The argument that power laws are otherwise not normalizable, depends on the underlying sample space the data is drawn from, and is true only for sample spaces that are unbounded from above. Power-laws obtained from bounded sample spaces (as is the case for practically all data related problems) are always free of such limitations and maximum likelihood estimates can be obtained for arbitrary powers without restrictions. Here we first derive the appropriate ML estimator for arbitrary exponents of power-law distributions on bounded discrete sample spaces. We then show that an almost identical estimator also works perfectly for continuous data. We implemented this ML estimator and discuss its performance with previous attempts. We present a general recipe of how to use these estimators and present the associated computer codes.
Convex and concave successions of power-law decays in small-angle scattering
NASA Astrophysics Data System (ADS)
Anitas, E. M.
2016-08-01
The small-angle scattering (SAS) structure factor from a new model of a 3D deterministic fractal in which the relative positions and the number of structural units vary with fractal iteration number is calculated. It is shown that, depending on the relative positions of scattering units inside the fractal, we can obtain various types of power-law successions, such as: convex/concave - when the absolute value of the scattering exponent of the first power-law decay is higher/smaller than that of the subsequent power- law decay, or any combination of them (i.e. convex-concave or concave-convex). The obtained results can explain experimental SAS (neutron or X-rays) data which are characterized by a succession of power-law decays of arbitrary length.
Sato, Aki-Hiro
2004-04-01
Autoregressive conditional duration (ACD) processes, which have the potential to be applied to power law distributions of complex systems found in natural science, life science, and social science, are analyzed both numerically and theoretically. An ACD(1) process exhibits the singular second order moment, which suggests that its probability density function (PDF) has a power law tail. It is verified that the PDF of the ACD(1) has a power law tail with an arbitrary exponent depending on a model parameter. On the basis of theory of the random multiplicative process a relation between the model parameter and the power law exponent is theoretically derived. It is confirmed that the relation is valid from numerical simulations. An application of the ACD(1) to intervals between two successive transactions in a foreign currency market is shown.
NASA Astrophysics Data System (ADS)
Sato, Aki-Hiro
2004-04-01
Autoregressive conditional duration (ACD) processes, which have the potential to be applied to power law distributions of complex systems found in natural science, life science, and social science, are analyzed both numerically and theoretically. An ACD(1) process exhibits the singular second order moment, which suggests that its probability density function (PDF) has a power law tail. It is verified that the PDF of the ACD(1) has a power law tail with an arbitrary exponent depending on a model parameter. On the basis of theory of the random multiplicative process a relation between the model parameter and the power law exponent is theoretically derived. It is confirmed that the relation is valid from numerical simulations. An application of the ACD(1) to intervals between two successive transactions in a foreign currency market is shown.
Exploring the effect of power law social popularity on language evolution.
Gong, Tao; Shuai, Lan
2014-01-01
We evaluate the effect of a power-law-distributed social popularity on the origin and change of language, based on three artificial life models meticulously tracing the evolution of linguistic conventions including lexical items, categories, and simple syntax. A cross-model analysis reveals an optimal social popularity, in which the λ value of the power law distribution is around 1.0. Under this scaling, linguistic conventions can efficiently emerge and widely diffuse among individuals, thus maintaining a useful level of mutual understandability even in a big population. From an evolutionary perspective, we regard this social optimality as a tradeoff among social scaling, mutual understandability, and population growth. Empirical evidence confirms that such optimal power laws exist in many large-scale social systems that are constructed primarily via language-related interactions. This study contributes to the empirical explorations and theoretical discussions of the evolutionary relations between ubiquitous power laws in social systems and relevant individual behaviors.
Tunable power law in the desynchronization events of coupled chaotic electronic circuits
Oliveira, Gilson F. de Lorenzo, Orlando di; Chevrollier, Martine; Passerat de Silans, Thierry; Oriá, Marcos; Souza Cavalcante, Hugo L. D. de
2014-03-15
We study the statistics of the amplitude of the synchronization error in chaotic electronic circuits coupled through linear feedback. Depending on the coupling strength, our system exhibits three qualitatively different regimes of synchronization: weak coupling yields independent oscillations; moderate to strong coupling produces a regime of intermittent synchronization known as attractor bubbling; and stronger coupling produces complete synchronization. In the regime of moderate coupling, the probability distribution for the sizes of desynchronization events follows a power law, with an exponent that can be adjusted by changing the coupling strength. Such power-law distributions are interesting, as they appear in many complex systems. However, most of the systems with such a behavior have a fixed value for the exponent of the power law, while here we present an example of a system where the exponent of the power law is easily tuned in real time.
Apparent Power-Law Behavior of Conductance in Disordered Quasi-One-Dimensional Systems
NASA Astrophysics Data System (ADS)
Rodin, Aleksandr; Fogler, Michael
2011-03-01
Observation of power-law dependence of conductance on temperature and voltage has been reported for a wide variety of low-dimensional systems(nano-wires, nano-tubes, and conducting polymers). This behavior has been attributed to the Luttinger liquid effects expected in a pure one-dimensional wire. However, the systems studied were neither one-dimensional nor defect-free. Using numerical simulations we show that the power-law behavior can arise from variable-range hopping in an ensemble of non-interacting disordered wires connected in parallel. This power-law behavior holds in restricted ranges of voltage and temperature, typical of experimental situations. Physically, it comes from rare, but highly conducting hopping paths that appear by chance in some members of the ensemble. The power-law exponents and their dependence on system parameters are consistent with the great majority of available empirical data. Supported by Grant NSF DMR-0706654.
An Analytical Model of Wave-Induced Longshore Current Based on Power Law Wave Height Decay.
1988-01-01
34I ANALYtTICAL MODEL OF NAVE-INDUCED LON6SHORE CURRENT BASED ON PONE* LAW.. (U) COASTAL ENG INEERING RESEAKNH CENTER VICKSBURG NS J N SMITH ET AL...j . - .L .V . : ; * AN ANALYTICAL MODEL OF WAVE-INDUCED ~ z * LONGSHORE CURRENT BASED ON POWER LAW * - WAVE HEIGHT DECAY by Jane McKee...I_ I IF 31592 11. TITLE (Include Security Classfication) • An Analytical Model of Wave-Induced Longshore Current Based on Power Law . Wave
Analytical study of solitons in the fiber waveguide with power law nonlinearity
NASA Astrophysics Data System (ADS)
Mirzazadeh, Mohammad; Ekici, Mehmet; Zhou, Qin; Sonmezoglu, Abdullah
2017-01-01
This work deals with the existence of exact soliton solutions in fiber waveguide with power law nonlinearity. The propagation equation that is the resonant dispersive nonlinear Schrödinger's equation with power law nonlinearity is studied by three analytical methods. The integration tools are the extended trial equation method, exp(-Φ(ξ)) -expansion method and extended G‧ / G - expansion method. The presented results show that analytical optical solitons can exist in this setting.
Conductivity scaling in supercritical percolation of nanoparticles--not a power law.
Li, Jiantong; Östling, Mikael
2015-02-28
The power-law behavior widely observed in supercritical percolation systems of conductive nanoparticles may merely be a phenomenological approximation to the true scaling law not yet discovered. In this work, we derive a comprehensive yet simple scaling law and verify its extensive applicability to various experimental and numerical systems. In contrast to the power law which lacks theoretical backing, the new scaling law is explanatory and predictive, and thereby helpful to gain more new insights into percolation systems of conductive nanoparticles.
Power-Law Dynamics of Membrane Conductances Increase Spiking Diversity in a Hodgkin-Huxley Model
Teka, Wondimu; Stockton, David; Santamaria, Fidel
2016-01-01
We studied the effects of non-Markovian power-law voltage dependent conductances on the generation of action potentials and spiking patterns in a Hodgkin-Huxley model. To implement slow-adapting power-law dynamics of the gating variables of the potassium, n, and sodium, m and h, conductances we used fractional derivatives of order η≤1. The fractional derivatives were used to solve the kinetic equations of each gate. We systematically classified the properties of each gate as a function of η. We then tested if the full model could generate action potentials with the different power-law behaving gates. Finally, we studied the patterns of action potential that emerged in each case. Our results show the model produces a wide range of action potential shapes and spiking patterns in response to constant current stimulation as a function of η. In comparison with the classical model, the action potential shapes for power-law behaving potassium conductance (n gate) showed a longer peak and shallow hyperpolarization; for power-law activation of the sodium conductance (m gate), the action potentials had a sharp rise time; and for power-law inactivation of the sodium conductance (h gate) the spikes had wider peak that for low values of η replicated pituitary- and cardiac-type action potentials. With all physiological parameters fixed a wide range of spiking patterns emerged as a function of the value of the constant input current and η, such as square wave bursting, mixed mode oscillations, and pseudo-plateau potentials. Our analyses show that the intrinsic memory trace of the fractional derivative provides a negative feedback mechanism between the voltage trace and the activity of the power-law behaving gate variable. As a consequence, power-law behaving conductances result in an increase in the number of spiking patterns a neuron can generate and, we propose, expand the computational capacity of the neuron. PMID:26937967