Showing papers on "Transport phenomena published in 1978"

High-field electronic conduction in insulators

Abstract: The quantum theory of electronic transport phenomena in large electric fields in highly dissipative media is critically examined. Serious conceptual problems and computational difficulties arise because neither the field nor the dissipation can be treated as a perturbation. We review a decade-old calculation of the velocity acquired by an electron in a finite electric field in a polar crystal and subsequent work which expanded our understanding of our method and results. A key feature of the earlier work was that in a single curve of electric field vs velocity, all the expected phenomena appeared, including a threshold field for producing hot electrons, in quantitative agreement with experiment, and a decreasing rate of energy loss with velocity for very fast electrons. A more recently studied problem, that of electron acceleration below the threshold field will be discussed. This problem is very important since such acceleration is the necessary precursor of ionization and breakdown. The physical significance of dissipation processes far from thermal equilibrium will also be mentioned.

A micromechanical derivation of Fick's law for interfacial diffusion of surfactant molecules

Abstract: A theory is presented for the diffusion of surfactant molecules, modeled as noninteracting Brownian spheres in proximity to, or straddling, the interface between two immiscible fluids. The spheres are assumed to be physicochemically inert except for the existence of short-range forces, which may be attractive and/or repulsive with respect to the interface. The number density of such particles is assumed small. Two alternative views of the diffusion process are presented; one, termed microscopic, in which variations in concentration are resolvable down to the scale l imposed by the short-range attractive or repulsive forces between the particles and the interface, and the other, termed macroscopic, in which variations are only discernible at the much larger scale, L , of gradients in the bulk surfactant concentration distribution, which are assumed to exist parallel to the interface. It is demonstrated that a rigorous theory can be developed, at the microscale , for prediction of the concentration profiles and diffusive flux of surfactant molecules parallel to the interface using only the well-established Stokes-Einstein theory of bulk-phase Brownian diffusion, and low Reynolds number hydrodynamics for the motion of a torque-free particle in close proximity, or straddling, a fluid-fluid interface. On the other hand, a macroscopic description of the same phenomena requires the introduction of new concepts, such as “adsorption” and “surface diffusion,” which are specifically associated with the interface, as seen from the macroscale of O ( L ). In the present paper, constitutive relationships for these macrosurface processes are derived in a rigorous manner from the more fundamental and complete microscopic description of the system. It is shown that Fick's law is applicable to surface diffusion, with the driving gradient based on a surface-excess concentration for surfactant particles. Furthermore, the surface diffusion coefficient is found to depend upon the Stokesian hydrodynamic resistance of a torque-free sphere translating parallel to the interface, as a function of the distance of its center from the interface, and upon the “adsorptive-potential” energy function which tends to cause the particles to accumulate there. Numerical values await the solution of the low Reynolds number hydrodynamics problem thereby posed, as well as the acquisition of knowledge relating to the potential energy function. Two examples of such potential energy functions are discussed for Brownian particles , one based upon a difference in area-specific, surface-free energies (i.e., solid/liquid interfacial tensions) for the two fluids, and the other on a simple density differential between the particle and the two fluids. Simple geometric models of surfactant molecules are also discussed in the context of potential energy functions for interaction between the molecules and the interface. The possibility of using such models in the analysis of other equilibrium and surface transport phenomena is pointed out.

The statistical mechanical theory of water transport through unsaturated soil: 1. The conservation laws

Abstract: The macroscopic differential equations of mass and momentum balance for water in a rigid unsaturated soil are derived from first principles by using the methods of statistical mechanics. The derivation begins with the development, at the molecular level, of expressions for the mass and linear momentum densities of water in a soil. The derivatives of these expressions with respect to the time then provide for local balance equations that are ensemble averaged and local volume averaged in order to produce the macroscopic balance equations. The resulting macroscopic equations agree with those derived for mass and linear momentum transport in a soil on the basis of the continuum theory of mixtures. The unified insight into mass transport processes afforded by a statistical mechanical theory as compared to one evolved from a solely macroscopic view is discussed.

The importance of convective mass transfer in the reduction of hematite

Abstract: The relative importance of transport phenomena, as opposed to chemical phenomena, in controlling the kinetics of hematite reduction has been debated for a long time. Recent measurements of gaseous diffusion coefficients in the porous iron and intermediate oxide layers produced by the reduction have shown that gaseous diffusion plays an increasingly important role, especially towards the end of the reaction. Convective mass transfer, however, is still assumed to play a negligible role, principally because of the way in which the reduction rate of hematite particles varies with the gas flow rate, and with the particle diameter. The established theories of convective mass transfer are used in this paper to show that the observed variations would occur whatever contribution convective mass transfer was making to controlling the reduction rate. The observed variations, therefore, give no indication as to the relative importance of convective mass transfer. This paper then, makes a quantitative comparison between the mass transfer rates necessary to sustain the reaction rates observed in recent hematite reduction experiments and the rates predicted by the established theories of mass transfer. This comparison shows that convective mass transfer can play a major role in controlling the reduction rate, although the relative magnitude of its contribution varies with particle size, and with reduction temperature.

Chapter 3 Sound Propagation and Kinetic Coefficients in Superfluid 3He

Abstract: Publisher Summary This chapter reviews the theories of sound propagation and of a number of transport phenomena in the superfluid phases of 3He (helium). The ultrasound propagation have played an important role in identifying the nature of correlations in the ordered phases of liquid 3He, complementing and corroborating the information obtained in NMR (nuclear magnetic resonance) experiments. The measurements of ultrasound absorption in 3He-A and 3He-B have revealed the existence of a new type of collective modes, never observed in nature before, which is closely associated with the tensor as opposed to scalar or vector character of the order. Both sound propagation and transport properties are of interest in that they provide information on the energy spectrum of elementary excitations and their interaction, probing in particular anisotropic properties. Systematic measurements of sound propagation as a function of temperature, pressure, and frequency may be used to determine (1) the gap parameter as a function of temperature and pressure, (2) the quasi-particle lifetime on the Fermi surface in the normal state as a function of pressure, (3) the collision integral parameter , as a function of pressure, (4) the collective mode structure in the A- and B-phases and, thereby the symmetry of these states.

Numerical analysis of flow behaviour of highly viscous fluid in agitated vessel

Abstract: A numerical algorithm of two-dimensional laminar flow in an agitated vessel is established and the numerical results of the power input, the stream line and the velocity profiles for paddle and anchor impellers of various sizes are compared with the experimental ones. Both results are in good agreement with each other and it is concluded that the flow pattern in an agitated vessel with large-width impeller is almost two-dimensional. It is also shown that the characteristic velocity and length defined for the analogy expression of the transport phenomena at the agitated vessel wall by the authors are very useful for the local similarity of momentum transfer at and near the vessel wall for small-size impeller of d/D<0.6 in high ReG range.

Transport phenomena in laminar flow of blood.

Abstract: Recently it has been shown experimentally that transport of heat and gas (specifically oxygen and helium) are augmented in the laminar flow of aqueous suspensions of polystyrene spheres 50 and 150 micrometer in diameter. In this report, data on heat and gas transport are correlated. Application of this correlation to flowing blood leads to the following conclucions. There is no significant augmentation of oxygen and heat transport in flowing blood even at shear rates much higher than physiological shear rates; an observation which is in accord with the experimental results. The augmentation of the diffusion coefficient of plasma proteins in flowing blood, though not very high, appears to be measurable. Of the total measured augmentation of about 6000--30 000% in platelet diffusivity in flowing blood, quoted from the literature, about 500% is attributable from this correlation to fluid mechanical forces, and the balance is hypothetically attributed to other forces (electrical or biochemical) present in blood.

Point of inversion in electro-osmosis and phase transformation of Onsager coefficients

Abstract: In an earlier paper concerning membrane phenomena it was shown that in isotonic systems the driving force of the flux of water is the electro-osmotic pressure and not the electric potential. As the electro-osmotic pressure vanishes in the point of the inversion where cD=cF, i.e., the concentration of the Donnan ions equals the concentration of the fixed ions, the flux of water vanishes independently of the electric potential. This behaviour was proved experimentally in the case of electro-osmosis. Moreover it was shown, that the diffusion potential in binary isotopic osmosis and the external electric potential in electro-osmosis lead to the same result.The different behaviour of the transport phenomena in a solution and a membrane results from constraints which give raise to a modification of the Onsager-coefficients. The transformation principles of these coefficients are derived.

Electrochemical Method for Dynamic Measurements in Two-Phase Flow

Abstract: Two phase flows have a great importance in engineering sciences for which transport phenomena are essential such as in petroleum, nuclear and chemical engineering, so a more precise study of these flows is very needed. Knowledge of wall shear stress is of great interest for elaboration of valuable models particularly in pressure drop prediction. This work gives results of friction obtained in bubble and plug flow using an electrochemical technique: the polarography (1), (2).

Transport phenomena in MHD generators: Effect of boundary layers

Abstract: An investigation of the effect of velocity/temperature boundary layers on the conductivity and the power output of an MHD generator has been presented in this paper; the analysis is based on the Boltzmann transfer equation. It is seen that the conductivity and the mean power output per unit volume of an MHD generator becomes considerably reduced because of the presence of the velocity and temperature boundary layers. The power output is found to decrease sharply with boundary‐layer thickness for low values of the thickness and levels off at larger thicknesses.

Transport Phenomena in Heterogeneous Media

Abstract: Classical work on transport in heterogeneous media is reviewed to show the broad interest in it as well as the specific need for a thorough treatment of a more comprehensive model. Such a model is presented and it consists of a random distribution of one or more dispersed phases in a continuous phase. Both the stab and spherical geometry are also considered. Both the transient and steady state transport solutions are developed for each of three different cases. The equivalent diffusivities are extracted from the steady state solutions. Applications are considered to illustrate the validity of the work. It is emphasized that the flux Ji for phase i can be complex as discussed elsewhere in the literature and all of this without any detraction from the exposition presented. It is also pointed out that this exposition is apparently the first to establish the connection between a realistic model, its transient solutions and its steady state solutions from which the equivalent diffusivities have been extracted. In the case of dead-end pores the results suggest application to experimental data to serve as a precision test for the presence and amount of dead-end pores. The advantages of testing under steady state conditions are discussed in detail. An appropriate diffusion cell design is referenced. The results can be useful in the research and design of barrier materials, catalysts, etc.

The analysis of relaxation time constant population distributions in dielectric materials

Abstract: Charge transport phenomena in complex dielectric media are frequently characterised by distributed relaxation times and associated activation energy spectra. The population distribution of such relaxation phenomena may be determined via isothermal observations of associated rate processes or by variable temperature (tempering) observations. The author shows how power law and logarithmic power law initial relaxation time population distributions lead to analytically simple forms for reaction rates under both isothermal and tempering conditions. It is thus indicated how measured relaxation rate data can be used to deduce arbitrary population distributions.