Showing papers on "Transport phenomena published in 1986"
TL;DR: In this article, the authors present a systematic development of a continuum model of a porous medium and of transport processes occurring in it, and the concept of a Representative Elementary Volume (REV) as opposed to any arbitrary volume of averaging quantities at the micro-scale, is quantified.
Abstract: This is the first of two papers presenting a systematic development of a continuum model of a porous medium and of transport processes occurring in it. The concept of a Representative Elementary Volume (REV) as opposed to any arbitrary volume of averaging quantities at the micro-scale, is quantified. A universal criterion for selecting the size of an REV as a function of measurable characteristics of a porous medium and selected tolerance levels of estimation errors, is developed. The rules of spatial averaging are extended by including the effects of both the configuration of the solid matrix and of interphase transfer phenomena within an REV.
223 citations
TL;DR: In this paper, the second part of a series of two papers on the development of a general thermodynamic basis for the study of transport phenomena in porous media is presented, where the porous medium is modelled as a superposition of one solid continuum coexiting and interacting with an N-component fluid-phase continuum.
175 citations
TL;DR: In this paper, the averaging rules presented in Part 1 are employed in order to develop a general macroscopic balance equation and particular equations for mass, mass of a component, momentum and energy, all of a phase in a porous medium domain.
Abstract: In this second paper, the averaging rules presented in Part 1 are employed in order to develop a general macroscopic balance equation and particular equations for mass, mass of a component, momentum and energy, all of a phase in a porous medium domain. These balance equations involve averaged fluxes. Then macroscopic equations are developed for advective, dispersive and diffusive fluxes, all in terms of averaged state variables of the system. These are combined with the macroscopic balance equations to yield field equations that serve as the core of the mathematical models that describe the transport of extensive quantities in a porous medium domain.
134 citations
TL;DR: In this article, the first part of a series of two papers on the development of a general thermodynamic basis for the study of transport phenomena in a porous medium composed of a multi-component fluid flowing through a porous rock skeleton is presented.
102 citations
TL;DR: In this paper, a general solution of Fick's second law involving the near-surface diffusive resistance (NSDR) is given, and its particular solutions are considered for two limiting cases of bulk controlled and near surface controlled kinetics.
49 citations
TL;DR: In this article, a new formulation of an intertidal conservation equation is presented and examined in detail, showing that the mechanism for long-term transport of solutes is mainly convection due to the Lagrangian residual current in the interior of a tidal estuary.
Abstract: The transports of solutes and other tracers are fundamental to estuarine processes. The apparent transport mechanisms are convection by tidal current and current-induced shear effect dispersion for processes which take place in a time period of the order of a tidal cycle. However, as emphasis is shifted toward the effects of intertidal processes, the net transport is mainly determined by tide-induced residual circulation and by residual circulation due to other processes. The commonly used intertidal conservation equation takes the form of a convection-dispersion equation in which the convective velocity is the Eulerian residual current, and the dispersion terms are often referred to as the phase effect dispersion or, sometimes, as the “tidal dispersion.” The presence of these dispersion terms is merely the result of a Fickian type hypothesis. Since the actual processes are not Fickian, thus a Fickian hypothesis obscures the physical significance of this equation. Recent research results on residual circulation have suggested that long-term transport phenomena are closely related to the Lagrangian residual current or the Lagrangian residual transport. In this paper a new formulation of an intertidal conservation equation is presented and examined in detail. In a weakly nonlinear tidal estuary the resultant intertidal transport equation also takes the form of a convection-dispersion equation without the ad hoc introduction of phase effect dispersion in a form of dispersion tensor. The convective velocity in the resultant equation is the first-order Lagrangian residual current (the sum of the Eulerian residual current and the Stokes drift). The remaining dispersion terms are important only in higher-order solutions; they are due to shear effect dispersion and turbulent mixing. There exists a dispersion boundary layer adjacent to shoreline boundaries. An order of magnitude estimate of the properties in the dispersion boundary layer is given. The present treatment of intertidal transport processes is illustrated by an analytical solution for an amphidromic system and by a numerical application in South San Francisco Bay, California. The present formulation reveals that the mechanism for long-term transport of solutes is mainly convection due to the Lagrangian residual current in the interior of a tidal estuary. This result also points out the weakness in the tidal dispersion formulation, and explains the large variability of the observed values for tidal dispersion coefficients. Further research on properties of the dispersion boundary layer is needed.
47 citations
TL;DR: In this article, the retention characteristics of UF membranes are de-lined through comparison of the combined viscous flow and frictional model with the Ferry-Faxen equation, and the molecular weight cutoff curves at varying pressure levels can be determined and by comparing with the model an average pore radius can be calculated.
Abstract: Retention characteristics of UF membranes are de— lineated through comparison of the combined viscous flow and frictional model with the Ferry—Faxen equation. The molecular weight cut—off concept is discussed using calculations of how sharp cut-off curves one can expect of UF membranes with uniform pore sizes and how heteroporosity will affect such curves. Experimental retention—flux curves for different macromolecules have been measured. From these data the molecular weight cutoff curves at varying pressure levels can be determined and by comparing with the model an average pore radius can be calculated. Permeate flux is often more or less pressure independent, which has been explained by a gel layer formation at the membrane surface. However, recently it has been shown that for many types of macromolecules it is rather an osmotic pressure of the concentrated boundary layer, which is responsible for the special flux-pressure relationship.
37 citations
TL;DR: In this paper, the symmetry-breaking nonequilibrium phase transitions from phase-locked coherent to phase-lagged differentiated behavior of the two subsystems were investigated, and the structural change of the system flow from stable morphogenesis to boiling-type turbulence was investigated.
Abstract: Originally designed to account for the main phenomena of symmetry-breaking morphogenesis, the well-known Rashevsky-Turing theory is a prototype model of many different synergetic systems in nature. The simplest version of Turing's model can be realized by a two-cellular symmetrical reaction-diffusion system, consisting of two cross-inhibitorily coupled, potentially oscillating two-variable subsystems (4-D flow). We present numerical evidence of symmetry-breaking nonequilibrium phase transitions from “phase-locked” coherent to “phase-lagged” differentiated behavior of the two subsystems. We further investigate the structural change of the system flow from stable morphogenesis to boiling-type turbulence. Finally, we present experimental evidence that the spatiotemporal nonlinear behavior of impurity-impact-ionization-induced avalanche breakdown in semiconducting germanium can be described qualitatively by the present 4-D reaction-diffusion model.
20 citations
TL;DR: In this article, the theory of collective phenomena in quantum Maxwellian gases is surveyed in a simple and readily assimilated form, and possible experimental studies are outlined, with particular attention devoted to weakly-damped spin waves.
Abstract: The concept of the quantum gas is introduced and illustrated by numerous examples. The fundamentals of the theory of collective phenomena in quantum Maxwellian gases are surveyed in a simple and readily assimilated form, and possible experimental studies are outlined. Particular attention is devoted to weakly-damped spin waves. The spectrum of these waves is calculated and the magnetic susceptibility generalized. The results obtained are compared with experimental data on spin waves in gaseous H,3He,and 3He–4He quantum solutions. It is shown that, at low temperatures, spin-polarized Boltzmann gases exhibit longrange spin correlations which fall off as r-1 at large distances. The equations of spin dynamics are solved for arbitrary temperatures and degrees of polarization, both in the weakly damped and diffusion regimes. The thermodynamics of spin-polarized gases and some of the features of transport phenomena are examined. Paramagnetic resonance and other collective effects in binary quantum gases are discussed. Magnetic and structural thermodynamic phase transitions in binary Maxwellian gases are predicted. Collective phenomena in semimagnetic semiconductors and analogous effects in the spectroscopy of Rydberg atoms and levitating electrons are discussed.
18 citations
TL;DR: In this article, the potential applicability of fractal concepts to various aspects of transport phenomena in heterogeneous porous media is discussed, and three examples of phenomena where a fractal approach should prove illuminating are presented.
Abstract: We present an overview of the potential applicability of fractal concepts to various aspects of transport phenomena in heterogeneous porous media. Three examples of phenomena where a fractal approach should prove illuminating are presented. In the first example we consider pore level heterogeneities as typified by pore surface roughness. We suggest that roughness may be usefully modelled by fractal curves and surfaces and also cite experimental evidence for regarding pores as fractals. In the second example we consider a fractal network approach to modelling large-scale heterogeneities. The presence of features on all length scales in simple fractal models should capture the essential role played by the presence of heterogeneities on many scales in natural reservoirs. Studies of transport phenomena in such models may yield valuable insights into the problems of macroscopic dispersion. The final example concerns dispersion in multiphase flow. Here the fractal character is attributed to the distribution of the fluid phases rather than the porous medium itself. Again studies of transport phenomena in simple fractal models should help to clarify various problems associated with the corresponding phenomena in real reservoirs.
17 citations
TL;DR: In this paper, fast relaxations of the electron temperature profile during pellet injection or disruptions, and its readjustment during additional heating are described, and a global picture for both phenomena is proposed.
Abstract: Fast relaxations of the electron temperature profile during pellet injection or disruptions, and its readjustment during additional heating are described. A global picture for both phenomena is proposed.
TL;DR: In this article, a qualitative model of the steady state material transport has been developed to describe these effects and to explain the particular properties of glow discharge optical emission spectroscopy (GDOES) mentioned above.
TL;DR: Theoretical models based both on the general transport equations and on the Nernst-Planck equations are presented in this paper, where experiments and calculations for the binary system NaCl-H2O with trace ions Li+ and K+ were performed.
Abstract: The transport of trace ions added to a binary electrolyte system through a porous membrane during countercurrent electrolysis has been studied both theoretically and experimentally. Theoretical models based both on the general transport equations and on the Nernst-Planck equations are presented. Experiments and calculations for the binary system NaCl-H2O with trace ions Li+ and K+ were performed. The theoretical model was able to predict the transport phenomena fairly well.
01 Jan 1986
TL;DR: The role of fractal structures in physics is reviewed in this article, where the various structures can be classified by different types of fractAL dimensionalities (dF, dl, dH) and it is shown explicitely how relevant physical laws (diffusion, biased diffusion, and phonon density of states) are changed on fractal structure.
Abstract: The role of fractal structures in physics is reviewed. Several examples of fractal structures in physics are discussed, and it is shown how the various structures can be classified by different types of fractal dimensionalities (dF, dl, dH). Spreading phenomena leading to 0131 0141 fractal structures as well as transport phenomena on fractal substrates are discussed, and it is shown explicitely how relevant physical laws (diffusion, biased diffusion, and phonon density of states) are changed on fractal structures.
TL;DR: In this paper, the basic laws and assumptions describing multicomponent mass transport in capillaries, and their use in building the models of mass transfer in porous media, are discussed, and physical principles of measurement techniques designed to determine the parameters of the models and to relate them both to the properties of the transferring species and to the porous structure of a pellet.
Abstract: The current studies concerning the interactions between chemical and physical phenomena in a porous catalyst pellet have been reviewed, with particular attention given to the following problems: 3 (1) discussion of the basic laws and assumptions describing multicomponent mass transport in capillaries, and their use in building the models of mass transfer in porous media; (2) presentation of the physical principles of measurement techniques designed to determine the parameters of the models and to relate them both to the properties of the transferring species and to the porous structure of a pellet; (3) theoretical analysis of the mass and energy transport in a porous catalyst pellet for a multicomponent and multireaction system and the experimentelle Uberprufung der Theorie.
TL;DR: In this article, the boundary between bubble flow and churn turbulent flow regimes can be predicted analytically and analytical solutions for both coalescing and non-coalescing liquids are presented.
Abstract: In bubble column reactors, flow regime characteristics significantly influence hydrodynamic and transport phenomena. It is shown that the boundary between the bubble flow and the churn turbulent flow regimes can be predicted analytically. Analytical solutions for both coalescing and non-coalescing liquids are presented. The validity of the analytical expressions is illustrated by comparing the calculated values of the transition velocities to the observed ones in the literature. Finally, the limitations of this technique are pointed out.
06 Jan 1986
TL;DR: In this article, the authors studied the pressure fluctuations in the interaction region oif a two-dimensional compression flow and established that the frequency of the unsteadiness is of the same order as the bursting frequency of upstream boundary layer and that this frequency is independent of the downstream separated flow.
Abstract: The present study of the pressure fluctuations in the interaction region oif a two-dimensionals compression flow established that the frequency of the shock-wave unsteadiness is of the same order as the bursting frequency of the upstream boundary layer and that this frequency is independent of the downstream separated flow. The conditional-sampling technique developed herein is capable of separating phenomena due to shock-wave oscillations from those due to transport phenomena of turbulence. The results show that turbulence as inferred from wall-pressure fluctuations may be significantly amplified approaching the shock.
25 Apr 1986
TL;DR: In this paper, a computer model for characterizing reacting flows through coal char beds is presented, which are related to the underground coal gasification conditions in terms of combustion and multi-component chemical reactions that take place inside beds of coal char.
Abstract: A computer model for characterizing reacting flows through packed beds is presented. These flows are related to the underground coal gasification conditions in terms of combustion and multi-component chemical reactions that take place inside beds of coal char. Time-dependent, two-dimensional (including axisymmetrical) partial differential equations (PDE's) describing conservation of mass, species, momentum, and the thermal energy are formulated. These PDE's are then recast into a set of ordinary differential equations (ODE's) with time as independent variable. The resulting ODE's are solved by applying a method-of-lines (MOL) technique to multi-component flows through packed char beds. The present formulation considers: the transport phenomena at the wall; various transient flow cases; multiple reactions and species; a wide range of options on the boundary conditions: temperature-dependent physical parameters; and rezoning capabilities. A numerical code called GSF has been developed, and computer runs have been performed to verify various aspects of the physical models as well as the numerical approach taken in the present analysis. These include favorable agreements with available analytical solutions for simple, one-dimensional flows and two-dimensional non-isotropic heat transfer to a wall. For more complicated flow situations for which there are no analytical solutions, good agreements have also been obtained between themore » results of the present method and those of alternative numerical methods. The code has been applied to several physical situations bearing on the underground coal gasification processes, i.e., wall drying, wall regression during gasification, and water injection into a gasifying bed. Preliminary results demonstrate that the present numerical modeling approach shows promise as a first step in describing the transient thermophysical phenomena taking place inside packed beds. 35 refs., 19 figs.« less
TL;DR: In this article, it is shown that one solution for the electric field parallel to the fibre direction leads to an expression for composite conductivity at cryogenic and higher temperatures, and a solution for normal electric field is normal to the fiber direction.
Abstract: The Boltzmann equation and its solutions are cental to the development of microscopic models describing the longitudinal and transverse electrical conductivity of metal matrix and in situ composites. Such solutions are needed to describe electron and phonon scattering and transport phenomena in the matrix due to the presence of a second filamentary phase, and to describe electrical conductivity at cryogenic and higher temperatures. In this paper, we derive solutions to the Boltzmann equation in the relaxation time approximation in cylindrical coordinates. It is shown that one solution for the electric field parallel to the fibre direction leads to an expression for composite conductivity at cryogenic and higher temperatures. We also present a solution for the case in which the electric field is normal to the fibre direction.
01 Jan 1986
TL;DR: In this article, photoelectrochemical cells are distinguished by the use of a semiconductor-electrolyte interface to create the necessary junction for use as a photovoltaic device.
Abstract: Photoelectrochemical cells are distinguished by the use of a semiconductor-electrolyte interface to create the necessary junction for use as a photovoltaic device.1-8 This chapter presents a description of this device from an electrochemical engineering viewpoint. The traditional chemical engineering fundamentals of transport phenomena, reaction kinetics, thermodynamics, and system design provide a useful foundation for the study of semiconducting devices. The motivation for the study of photoelectrochemical cells is discussed, and a physical description of the cell features is presented. A tutorial on the mechanism of cell operation is presented which includes descriptions of the phenomena of band-bending and straightening, the effect of interfacial phenomena, and current flow. Mathematical relationships are developed which describe this system, and the influence of cell design is discussed.
TL;DR: In this article, the local interactions between strong temperature gradients, rapid polymerization, temperature/conversion-dependent transport properties and elongated velocity profiles have been analyzed for different thermal conditions.
01 Jan 1986
TL;DR: The most important effects of gravity are the impossibility of levitating a fluid mass isolated from solid surfaces and the consequences of buoyancy-driven-convection caused by gradients of temperature and concentration in the fluid as mentioned in this paper.
Abstract: Probably the most alluring prospect of performing experiments in a low-gravity environment is the ability of freeing an experiment from the action of the earth’s gravity, which although constant and of known direction, has pronounced effects on the processing of fluids and gases. The most important effects of gravity are the impossibility of levitating a fluid mass isolated from solid surfaces and the consequences of buoyancy-driven-convection caused by gradients of temperature and concentration in the fluid. It was recognized over a decade ago that the large reductions in gravity possible aboard an orbital spacecraft will remove these two effects and lead to new experiments and, possibly, to the development of new methods for processing materials. In conjunction with the enormous interest in experimental research in a low-gravity environment, many new analyses have been reported that add to the understanding of transport phenomena both on earth and in space relevant to the design and intepretation of these experiments.
TL;DR: In this paper, a new method combining analytical and numerical solutions is presented for analyzing coupled transport phenomena between multiple regions, which is applied to simulate heat transfer from hot laminar forced downward convection in a parallel plate duct to external natural convection through a finite section of one wall.
Abstract: A new method which combines analytical and numerical solutions is presented for analyzing coupled transport phenomena between multiple regions. The method was applied to simulate heat transfer from hot laminar forced downward convection in a parallel plate duct to external natural convection through a finite section of one wall. Obtained numerical results showed that the longitudinal wall conduction markedly relaxed the thermal interaction between the two convection systems. Experiments were also performed, using conducting walls made of aluminum, stainless steel and granite. Predicted temperature profiles agreed well with the experimental data.
TL;DR: In this article, a physical analysis is given and the mathematical properties and conditions of applicability of the equations of hydrodynamics of multitemperature and multivelocity gas mixtures are indicated and the momentum and energy equations are given for the whole mixture as well as the equations describing the velocity and temperature separation of the mixture components.
TL;DR: In this article, the authors analyzed thermal behavior and heat transport phenomena in electrolytic reactors via the governing equations of appropriate models, such as the continuous-flow stirred tank electrochemical reactor (CSTER) and plug-flow electrochemical reaction (PFER).
Abstract: Thermal behaviour and heat transport phenomena occurring in electrolytic reactors are analysed via the governing equations of appropriate models. Applications of the continuous-flow stirred tank electrochemical reactor (CSTER) and plug-flow electrochemical reactor (PFER) models to estimate temperature profiles in electrolysers are discussed.
01 Jan 1986
TL;DR: In this paper, a review of transport phenomena in two-dimensional electronic systems in high magnetic fields is given, where the authors show that the quantum Hall effect can be observed in such systems.
Abstract: The discovery of the quantum Hall effect in 1980 has demonstrated the importance of two-dimensional electronic systems for application and fundamental research. In this paper a review of some transport phenomena in such systems in high magnetic fields is given.
01 Jan 1986
TL;DR: In this article, the design of observers for processes involving transport phenomena with time-varying transportation velocity is considered, and the observed systems are modelled by first-order bilinear partial differential equations of the hyperbolic type.
Abstract: The design of observers for processes involving transport phenomena with time-varying transportation velocity is considered. The observed systems are modelled by first-order bilinear partial differential equations of the hyperbolic type. Using geometric techniques, the asymptotic reconstruction of sets of linear functionals of the state is examined, yielding existence criteria and design procedures for finite-dimensional exact and approximate observers. Attention is paid to both cases of distributed measurements and of point measurements.