Showing papers on "Transport phenomena published in 1977"

Simultaneous Heat, Mass, and Momentum Transfer in Porous Media: A Theory of Drying

Abstract: Publisher Summary The well-known transport equations for continuous media are used to construct a rational theory of simultaneous heat, mass, and momentum transfer in porous media. Several important assumptions regarding the structure of the gas–liquid system in a drying process are made that require theoretical or experimental confirmation. This chapter presents a general theory that provides a starting point for the construction of special theories so that various drying processes can be studied analytically without recourse to an enormous computational effort. It analyzes the motion of a liquid and its vapor through a rigid porous media. The development of the relevant volume averaged transport equations, which describe the drying process, is also focused. The transport of momentum in the gas phase and the laws of mechanics are applied to the drying process. The thermal energy equations are considered by forming the total thermal energy equation, and the problem of determining the mass average velocities in the gas and liquid phases are also discussed.

Transport phenomena in hydrothermal systems; cooling plutons

Abstract: The nature of heat and mass transport in plutonic environments has been described by partial differential equations and simulated by numerical approximation. A series of heuristic models based on these equations describes the general features of fluid circulation near an igneous intrusive body within the upper 10 km of the crust. Analysis indicates that fluid circulation is an inevitable consequence of magma emplacement. The magnitude of this circulation generates convective heat fluxes which predominate over conductive fluxes when host rock permeabilities exceed 1.0 nm/sup 2/. However, cooling rates for the pluton are not significantly shortened unless the pluton permeability is also greater than 1.0 nm/sup 2/. The geometries of circulation and isotherms are directly affected by variations in pluton size, depth, and permeability as well as permeability distribution in the host rock. The effect of fluid properties on heat and mass transport is striking. The style of circulation is controlled by coincident maxima of the isobaric thermal coefficient of expansion and heat capacity with the viscosity minima in the supercritical region of the H/sub 2/O system. Waters in intrusive systems are predicted to move several km in a few hundred thousand years. Temperature and pressure changes along the flowpaths producemore » changes in solvent properties. The fluid-rock interactions should generate diagnostic mineral assemblages and isotopic changes. Average fluid:rock mass ratios of 0.4 are realized over the permeable portions of the systems. The extent of circulation, and magnitude of convective heat flux over broad crustal regions and along plate boundaries may be much greater than suspected.« less

Transport phenomena in hydrothermal systems: the nature of porosity

Abstract: The porosity (P) of rock is described by: P-total = P-flow + P-diffusion + P-residual. Experimental results show that P-total of fractured rock in hydrothermal systems ranges from 0.2 to 0.01, and P-diffusion ranges from 0.001 to 0.00001. Data from the literature and from field studies of fractures indicate that P-flow is 0.001-0.00001. Consequently, the greater part of P-total in plutonic environments results from residual pores which are not interconnected to P-flow or P-diffusion. Permeability is a function of the abundance and geometry of continuous flow paths. Observations suggest that a planar fracture is a good first order approximation for fractures in plutonic environments. Analysis of aperture, abundance, and continuity suggests that permeabilities on the order of 1.0 nm/sup 2/ may be characteristic of large portions of the crust. The model proposed permits definition of the interface between circulating hydrothermal fluids and reactant minerals in a manner consistent with the physical phenomena and partial differential equations which describe the processes of advection-diffusion-reaction.

On thermodynamics and the nature of the second law

Abstract: The contents of this paper represent a new approach to continuum thermo­dynamics and are chiefly concerned with ( a ) a procedure for obtaining restrictions on constitutive equations, ( b ) an appropriate mathematical statement of the second law and ( c ) the nature of restrictions placed by the latter on thermo-mechanical behaviour of single phase continua. Our point of departure is the introduction of a balance of entropy and the use of the energy equation as an identity for all motions and all temperature distributions after the elimination of the external fields. This is in contrast to the approach adopted in most of the current literature on continuum ther­modynamics based on the use of the Clausius-Duhem inequality. In order to gain some insight into the nature of our procedure we first study the case of an elastic material, which includes that of an ideal fluid as a special case, before the consideration of the second law. We then go on to postu­late an inequality which reflects the fact that for every process associated with a dissipative material, a part of the mechanical work is always con­verted into heat and this cannot be withdrawn from the medium as mech­anical work. The restriction on the heat conduction vector is considered separately and is confined to equilibrium cases in which heat flow is steady. A restriction is also obtained for the internal energy when the body is in mechanical equilibrium subjected to spatially homogeneous temperature fields. Using the above approach, next we study the nature of thermodynamic restrictions on the thermo-mechanical response of a viscous fluid and simple materials with fading memory. A drawback to the Clausius-Duhem inequality is discussed by means of an example. For a class of rigid heat conductors in thermal equilibrium, the Clausius-Duhem inequality requires that if heat is added to the medium, the resulting spatially homogeneous temperature of the conductor decreases . Moreover, the in­-equality denies the possibility of propagation of heat in the conductor as a thermal wave with finite speed. The inequalities proposed in this paper do not suffer from these shortcomings.

The mechanism of water transport in membranes.

Abstract: Biological membranes, lipid membranes and organic polymer membranes have some chemical similarities. All can transport water and it is likely that the molecular transport processes have some common features in the three types of system. Polymer membranes, being stable and strong, can be subjected to more varied and intensive study than can either lipid or biological membranes. Furthermore, the structures, dimensions and molecular organization of polymer membranes, which are very simple compared with their biological counterparts, can be characterized in some detail. It is already a reasonable objective to analyse transport phenomena in polymer membranes in terms of the molecular processes likely to occur in media of known structure. If the level of understanding in this area could be improved it might become possible to make some confident deductions about structure in lipid and biological membranes from observations on their transport properties. This review is intended to assess the current situation regarding the interpretation of flux data in structural terms and, perhaps, to encourage further developments. Although observations on transport processes are made by observing changes in the bulk phases in contact with the membrane, it is the processes within the membrane that are under study. The mathematical formulation of membrane transport must be designed to emphasize the role of the membrane as a phase in which irreversible processes are occurring. This requires the determination of diffusion coefficients, concentrations, activity coefficients and their profiles within the membrane. The concentration and activity of water in a membrane are studied through equilibrium absorption isotherms. These vary widely in form with the chemical structure and organization in polymer membranes. Almost nothing detailed is known about sorption by lipid membranes. Most flow processes are studied between pairs of aqueous solutions that contain solutes which may also be able to permeate the membrane. The possibility of several irreversible processes occurring simultaneously in the membrane can best be handled through the formalism of non-equilibrium thermodynamics. This formulation provides also a convenient method of introducing pressure and osmotic pressure as driving forces in addition to that of simple Fickian diffusion flow. A bridge between the phenomenological coefficients of thermodynamics and molecular processes can be built only on a model system. By regarding the membrane as intrinsically homogeneous and isotropic the frictional model can be applied in which steady flow is represented by a balance between thermodynamic driving forces and frictional retarding forces among the various flowing components and the membrane. A case of particular interest arises where the solute is an isotopically labelled species of water. The number of independent frictional coefficients in the two-component system is reduced from three to two. They can be determined from measurements of the tracer diffusion coefficient and the hydrodynamic or osmotic permeability of the membrane. This has been done for two sets of polymer membranes: highly hydrated hydrogels and moderately hydrated cellulose acetates. The membranes were prepared so as to be as nearly homogeneous as possible and it was found that the frictional co-efficients observed were consistent with the homogeneous model theory. By applying a form of argument which has several times been used to diagnose the existence of pores in biological and lipid membranes, it was possible to deduce from the data on the synthetic membranes that they too transport water in, sometimes quite large, pores. This conclusion would be at variance with their known structures and shows that the argument is unsound when it is used as a criterion for the presence or absence of pores. It is clear also that the argument is valid only when applied to a homogeneous system and so would not be valid if applied to a system that were truly porous but also transported water through the matrix material supporting the pores.

Charge pulse studies of transport phenomena in bilayer membranes

Abstract: A charge pulse technique has been applied to studies of transport phenomena in bilayer membranes. The membrane capacitance can be rapidly charged (in less than a microsecond). The charge then decays through the membrane's conductive mechanism-no current flows through the solution or external circuitry. The resulting voltage decay is thus a manifestation of membrane and boundary layer phenomena only. There are a number of advantages to this approach over conventional voltage or currentclamp techniques: the rise-time of the voltage perturbation is not limited by the time constant deriving from the membrane capacitance and solution resistance, thus permitting study of extremely rapid rate processes; the membrane is exposed to high voltage for relatively short times and thus can be subjected to higher voltages without breakdown; the steady-state current-voltage behavior of the membrane can be deduced from a single charge pulse experiment; the charge (and therefore the integral of the ion flux through the membrane) is monitored allowing detection of rate processes too rapid to follow directly. In this paper we present what is primarily a steady-state analysis of actin (non-, mon-, din-, trin-)-mediated transport of ammonium ion and valinomycin-mediated transport of cesium and potassium ions through glycerol monooleate bilayers. We introduce the concept of the “intercept discrepancy”, a method for measuring charge lost through extremely rapid rate processes. Directly observable pre-steady-state phenomena are also discussed but will be the main subject of part II.

Application of irreversible thermodynamics to transport in self-complexing electrolytes

Abstract: The study of transport in self-complexed aqueous electrolytes, particularly those of the metal halides, has been pursued since the middle of last century. In 1859 Hittorf observed negative transport numbers for cadmium in concentrated solutions of cadmium chloride and cadmium iodide and for zinc in concentrated solutions of zinc chloride and zinc iodide. These results have been verified by subsequent work. Arrhenius, in 1902, noted the requirement of negative complexes of cadmium to explain such effects and expected a number of such to exist in solution. McBain, surveying the effects of complexes and hydrolysis in 1907, concluded that the concentrations of simple uncomplexed ions would be negligibly small when such anomalous transport phenomena were observed. The effect of complexing is less dramatic for electrical conductance and diffusivity of these salts, but both are lower than would be expected if the salts were dissociated.This paper is concerned with the more quantitative explanation and prediction of such data, using as a basis the theory of irreversible thermodynamics. Any predictive treatment will require a knowledge of the concentrations of free ions and complexes in solution, together with their corresponding mobilities. The theory of irreversible thermodynamics requires in addition that kinetic coupling interactions between these species be recognised. The Onsager mobility coefficients of the binary electrolyte have been determined experimentally for a number of these self-complexed salts. These are shown to be functions of the more fundamental direct mobilities of the free ions and complexes, together with their coupling coefficients, one with another, in all possible combinations.The experimentally derived binary coefficients are shown to have an anomalous concentration dependence, varying in degree according to the degree of complexation of the salt. Choosing aqueous cadmium iodide, which is the most complexed of the group IIB halides, predictive calculations have been made which reproduce the observed concentration dependencies of the binary coefficients, electrical conductance, transport number and salt diffusivity. The method employs Pikal's restatement of Onsager limiting law theory in macroscopic irreversible thermodynamic terms.Additional data on cadmium isotopic diffusion in cadmium iodide are presented. There too, anomalous behaviour is observed, particularly an initial maximum in diffusion coefficient. An extension of the theoretical method to include isotopic experiments is presented and once more, using Pikal's basic treatment these isotopic diffusion features are reproduced. In both cases the predictive capability of theory is limited by the concentration limits for Onsager theory.

Scattering of Electrons by the Deformation Potential in Doped InSb

Abstract: An analysis of the experimental data for InSb and of the theoretical considerations used for the determination of the deformation potential constant of the conduction band ϵl is made. It is shown that the correctly calculated value of |ϵ1| is about 30 eV. The small values of |ϵ1| obtained in some works by observing transport phenomena in the hot electron region at lattice temperatures of 4.2 K in samples with electron densities n from 1015 to lo17 cm−3 for which the Boltzmann transport equation is valid, are caused by a distortion of the bottom of the conduction band due to fluctuations of the impurity potential. [Russian Text Ignored]

Variational thermodynamics of viscous compressible heat-conducting fluids

Abstract: A new variational principle of virtual dissipation generalizing d'Alembert's principle to nonlinear irreversible thermodynamics is applied to compressible heat- conducting fluids with Newtonian and non-Newtonian viscosity. The principle is applied in the context of Eulerian formalism where the flow is described with reference to a fixed coordinate system. New concepts of entropy displacement and mass displacement are used as well as a new definition of the chemical potential which avoids the usual ambi- guities of the classical thermodynamic approach. The variational principle is used to derive a novel, form of field differential equations for the coupled fluid dynamics and convective heat transfer.

Parameters of the exponential-six potential model for neon

Abstract: On the basis of our experimental data for the isotropic thermal diffusion factor and the more recent data for the transport phenomena and the second virial of pressure, we propose for neon the new set of parameters α = 15.5, ϵ/k = 46.6±0.9 K and rm = 3.030 A for the exponential-six potential model. For accurate theoretical comparisons, however, the model is unable to correlate transport and equilibrium properties with a unique set of parameters as well as the experiments over large temperature ranges.

Pseudothermoosmosis in a Composite Membrane System

Abstract: A composite membrane system, constituted by two cellulose membranes and an aqueous solution of poly(ethylene oxide) (liquid membrane), was used to investigate the transport phenomena occurring when a thermal difference was applied. At the steady state, pressures were measured (ca. 6.0×105 dyn cm−2) far higher than those reached in ordinary thermoosmosis experiments. In order to explain these unusual effects a model was proposed in which the contribution of the polymeric liquid membrane was taken into account. The thermodynamics of irreversible processes was used to derive the composite membrane phenomenological equations containing both the classical thermoosmosis and the thermal diffusion as particular cases. In this paper the observed phenomena were indicated as “pseudothermoosmosis.” The flow of matter, phenomenological coefficients and heat of transport were also measured. For the activation energy a value of 3.91 kcal mol−1 was found, indicating the diffusive nature of the solvent flow through the composite membrane.

Thermodynamics of Transport

Abstract: Since thermodynamics deals with properties of matter and laws which can be understood without knowledge of the inner structure of matter, it is of great utility in the exploration of unknown physicochemical mechanisms of transport phenomena. Although thermodynamics itself does not describe the microscopic details of transport mechanisms, it shows which of the various hypothetical mechanisms are thermodynamically permissible. An admirable “Introduction to Thermodynamics” was written by Spanner (1964) and is recommended in this connection. Only a brief summary of the most important implications of thermodynamics in the field of transport is presented here.