Showing papers on "Transport phenomena published in 1972"

Coupled problems of thermoviscoelasticity

Abstract: The author derives a heat flux equation with allowance for the dissipation of internal forces on the basis of the fundamental equations of continuum mechanics and the thermodynamics of irreversible processes.

Electronic properties of selenium-tellurium melts

Abstract: The electronic transport phenomena of SeTe melts are analyzed with two models of density of states. At low temperatures ( T ∗ ) a semiconducting behaviour is observed and we calculate activation energies involved in conducting and thermopower when only hole transport is taken into account. The optical absorption results give the width of optical gap and its temperature dependence. At high temperatures ( T > T ∗ ) a metallic conduction, with a short mean free path occurs so that a pseudogap and onset of localization near the Fermi level are likely when the Mott's criterion is satisfied. The observation of switching phenomena in liquid Se-rich alloys strengthens the analogy with amorphous semiconductors.

Membrane Transport Against the External Driving Force Due to Mass Transfer-Reaction Coupling

Abstract: Coupling between chemical reactions and transport phenomena can cause the substrate concentration at the surface of a membrane to be lower on the substrate-rich side than the substrate-lean side. Thus, the diffusing flux inside the membrane may be counter to the overall external concentration driving force. Graphical solutions of various steady states of such membranes are presented.

Conduction electron scattering by critical fluctuations

Abstract: A recent mushrooming of activity has resulted in the solution of several riddles centered on the observed transport coefficient anomalies (e.g., in the resistivity, thermal conductivity and the thermoelectric effect) resulting from conduction electron scattering by critical spin fluctuations. While the emphasis in this review will be on metallic magnetic systems, reference will also be made to the recent experimental work on critical transport properties in metallic order‐disorder systems and binary liquid metals which display miscibility gaps. The temperature dependence of the resistivity in the vicinity of the critical point, which seems to exhibit universal behavior in a variety of metallic systems, is understood semi‐quantitatively within the framework of the de Gennes‐Friedel‐Fisher‐Langer model; whereas, the understanding of other transport phenomena such as thermal conductivity and thermoelectric power resides at a more primitive level. It appears that the measurement of electron transport properties can provide information about critical fluctuations which is either inaccessible or difficult to extract from other experiments.

Breakdown of superfluidity for cylinders in saturated liquid helium ii

Abstract: In the past few years. studies of boiling and vaporization have been extended to liquid helium temperatures above the λ point (T λ = 2.172°K) in liquid He I and below the λ point in liquid He II. The phase change in ordinary liquid He I is consistent, in essential details, with the boiling conditions of other classical liquids. Liquid He II. however, is a superfluid, whose thermohydrodynamic behavior [1,2] is radically different from classical liquids. For instance, nucleate boiling is suppressed because of the excellent heat transport capability of He II. Without boiling, heat from an immersed dissipative solid (e.g., a horizontal cylinder as shown in the insert of Fig. 1) is transported through the liquid He II bath to the upper liquid—vapor interface where vapor is pumped off to maintain the bath temperature below T λ . After a certain limiting peak heat flux has been exceeded, however, boiling similar to classical film boiling initiates, i.e., an insulating vapor film forms adjacent to the heater surface, which lowers the heat transfer rate substantially. This type of boiling sets in, after breakdown of superfluidity, when the local thermodynamic state has reached saturation conditions of vapor liquid equilibrium (temperature T* and pressure P* as noted in Fig. 1). This transport limit of liquid He II near a heated single solid appears, for the present, to be predictable only for a few ideal situations (upper bound). Therefore, a number of experiments have been carried out in recent years to determine the superfluidity breakdown at the peak flux for several configurations. In particular, studies with horizontal cylinders (Table I) showed that the peak heat flux depends on the cylinder diameter D, the bath temperature T, and the submersion depth H (Fig. 1). No detailed consistent account of these effects has been given so far. Very recent work [3–5], however, suggests that a large variety of He II transport phenomena may be accounted for within a common thermohydrodynamic frame of reference for He II. Along this line of approach the present study was conducted to eliminate the lack of a theoretical account for the liquid impedance which opposes entropy transport near a single dissipative horizontal cylinder in a large pool of He II. The next section of the paper considers the pertinent thermohydrodynamic conditions and similarity rules. This theory includes special power law approximations. Subsequently, the experimental data (Table I) are compared with the power laws. The data agree satisfactorily with the theory within the data scatter encountered during the experiments.

Chemical Fluid Mechanics

Abstract: The theory of fluid mechanics can be profitably applied to chemistry by simply noting that many fluids are substances. Certain equations of fluid mechanics then become the counterparts of equations in the theory of the chemical thermodynamics of systems at constant temperature. Consequently, some of the most valuable parts of this theory may, for some purposes, also be regarded as a part of elementary physics completely independent of thermodynamics.

Transport phenomena in neutral and ionized gases

Abstract: Transport processes in gases are examined from both the point of view of non-equilibrium thermodynamics and kinetic theory. Thermodynamics is used to establish concise representations of the general properties of transport coefficients, and in particular, it is shown how the redundancy of Onsager relations in systems with geometrical symmetries can be removed by using the theory of irreducible tensorial sets. The Boltzmann equation for fully and partially ionized gases is solved by a polynomial expansion of the distribution function, and expressions for transport coefficients are obtained in terms of the inverse of certain infinite-dimensional matrices. In the case of fully-ionized gases, it is shown that the approximations associated with the Fokker-Planck equation are accurate as long as the deviation from equilibrium is not substantial. Partially-ionized gases are considered under significantly nonequilibrium conditions brought about by application of an electric field. A new expression is obtained for ion mobility, and comparison is made with the earlier theories of Wannier and Kihara. For electrons, it is shown by way of direct numerical calculations that approximation of the distribution function by the first two terms of an expansion in Legendre polynomials is satisfactory even when the deviation from Maxwellian is substantial. Anisotropic diffusion of ions and electrons in an electric field is also examined, and expressions are derived for longitudinal and transverse diffusion coefficients both via solution of the Boltzmann equation and through thermodynamic analysis.

Transport Equations of Multicomponent Systems of Polyatomic Molecules. II

Abstract: The treatment of the transport phenomena starting with the Liouville equation was first given by Irving and Kirkwood [J. Chem. Phys. 18, 817 (1950)] for a one‐component system composed of point molecules. The theory has been extended by Bearman and Kirkwood [J. Chem. Phys. 28, 136 (1957)] to multiple‐component point‐molecule systems and by Dahler [J. Chem. Phys. 30, 1447 (1959)] to a one‐component system of diatomic molecules. In the present work, the theory is extended to a multicomponent system composed of polyatomic molecules. The theory treats the translational, rotational, and vibrational motions of fluids but not the electronic motion. From the Liouville equation, the equations of continuity and of linear momentum, angular momentum, and energy transport are developed. The one‐particle and pair densities, involving the one‐particle and the two‐particle distribution functions are expanded in powers of a parameter measuring the small deviations from the state of local thermodynamic equilibrium, but the calculations extend only to the first order in the gradients of the particle densities and temperature. From the general transport equations, the phenomenological equations involving transport coefficients are obtained. These coefficients are formally determined in terms of the laws of intermolecular interaction and of the assumed dependence of the distribution functions on the gradients of the particle densities and of temperature.

On the Quantum Theory of Electrical Transport in a Uniform Magnetic Field

Abstract: The Boltzmann equation of electrical transport in a uniform magnetic field has been very successful in describing a variety of transport phenomena in metals and semiconductors and has yielded important information concerning the electronic structure of these materials. However, textbooks usually do not derive the Boltzmann equation, whereas the quantum mechanical derivations which have appeared in the literature are either very complex or are based on a particular gauge describing the magnetic field. It is the purpose of this note to describe a very simple quantum mechanical derivation of the field terms of the Boltzmann equation. This derivation does not depend on the initial choice of gauge, since use is made of a gauge-independent density matrix formalism. The effect of scattering is taken into account phenomenologically. The derivation is carried out for free electrons as well as for Bloch electrons.

Transport phenomena in zonal centrifuge rotors IV. Stability of isopycnic banding

Abstract: A small perturbation analysis is carried out to determine the stability criteria of an equilibrium method in a zonal centrifugation run. It is found that the stability is related to the width of the isopycnic band, which can be expressed in terms of various diffusitivities between the particles and a gradient solution, a profile of gradient solution, particle size, and rotational speed of a rotor. The results unify the previous observations in sedimentation and the theoretical analysis for diffusion phenomena under one gravitational field.

On the distribution of current generation in porous gas electrodes

Abstract: In the active layer of porous gas electrodes, the spatial distribution of energy generation is determined by several interacting factors, e.g. pore statistics, distribution of active sites, and a set of correlated transport equations. After a short introduction to the problem, it is shown that the transport phenomena can, in this case, be treated in a very simplified manner. In particular, the specific electron resistance can be neglected. Restriction of gas supply can be described by a formalistic gas resistanceρ g. Thus, the interaction of the different transport parameters can be treated by considering purely electrical models. The relative magnitudes of the different parameters, in the case under study, are of such an order that finally it is only necessary to consider two of them: the specific ionic resistivity of the porous electrode filled partly with liquid electrolyte, and a special parameterp which describes the overvoltage in the region between gaseous phase and electrolyte. As a result, the spatial distribution of current generation can be indicated in the form of analytical expressions and diagrams. One also obtains values of the penetration depth of current generation which do not disagree with practical experience.

Thermochemical nonequilibrium in atomic hydrogen at elevated temperatures

Abstract: A numerical study of the nonequilibrium flow of atomic hydrogen in a cascade arc was performed to obtain insight into the physics of the hydrogen cascade arc. A rigorous mathematical model of the flow problem was formulated, incorporating the important nonequilibrium transport phenomena and atomic processes which occur in atomic hydrogen. Realistic boundary conditions, including consideration of the wall electrostatic sheath phenomenon, were included in the model. The governing equations of the asymptotic region of the cascade arc were obtained by writing conservation of mass and energy equations for the electron subgas, an energy conservation equation for heavy particles and an equation of state. Finite-difference operators for variable grid spacing were applied to the governing equations and the resulting system of strongly coupled, stiff equations were solved numerically by the Newton-Raphson method.

Chemical relaxation in a viscous shock

Abstract: We consider the flow of a nonequilibrium dissociating diatomic gas in a normal compression shock with account for viscosity and heat conductivity. The distribution of gas parameters in the flow is found by numerically solving the Navier-Stokes and chemical kinetics equations. The greatest difficulty in numerical integration comes from the singular points of this system at which the initial conditions are given. These points lead to instability of the numerical results when the problem is solved by standard numerical methods. An integration method is proposed that yields stable numerical results-continuous profiles of the distribution of the basic gas parameters in the shock are obtained. We consider steady one-dimensional flow in which the gas passes from equilibrium state 1 to another equilibrium state 2, which has higher values for temperature, density, and pressure. Such a flow is termed a normal compression shock. The parameter distribution in normal shock for nonequilibrium chemical processes has usually been calculated [1–3] without account for the transport phenomena (viscosity, heat conduction, and diffusion). The presence of an infinitely thin shock front perpendicular to the flow velocity direction was postulated. It was assumed that the flow is undisturbed ahead of the shock front. The gas parameters (velocity, density, and temperature) change discontinuously across the shock front, but the gas composition does not change. The composition change due to reactions takes place behind the shock front. The gas parameter distribution behind the front was calculated by solving the system of gasdynamic and chemical kinetics equations using the initial values determined from the Hugoniot conditions at the front to state 2 far downstream. Several studies (for example, [4, 5]) do account for transport phenomena in calculating parameter distribution in a compression shock, but not for nonequilibrium chemical reactions. These problems are solved by integrating the Navier-Stokes equations continuously from state 1 in the oncoming flow to state 2 downstream. We present a solution to the problem of normal compression shock in nonequilibrium dissociating oxygen with account for viscosity and heat conduction using the Navier-Stokes equations.

Hochtemperaturgasdynamik (High Temperature Gas Dynamics)

Abstract: : An introduction to the field of high temperature gas flows without transport phenomena, electromagnetic phenomena and external forces is presented. The difference between such a flow and the corresponding flow of an ideal gas of constant specific heats comes from internal changes in the fluid. If these changes form a reversible process, the high temperature gas flow as well as the corresponding flow of an ideal gas of constant specific heats belong to the general class of flows of a physically homogeneous medium. The article yields a first understanding of the field and informs about important applications. It describes the real gas model adopted in this article, and various concepts of thermodynamic equilibrium are explained. The close relationship and fundamental differences are demonstrated by means of suitable flow patterns.