Relevant Transport Equations Research Articles

A mathematical model of the middle and high latitude ionosphere

A time-dependent three-dimensional model of the middle and high latitude ionosphere is described. The density distributions of six ion species (NO+, N 2 + , N 2 + , O+, N+, He+) and the electron and ion temperatures are obtained from a numerical solution of the appropriate continuity, momentum and energy equations. The equations are solved as a function of height for an inclined magnetic field atE andF region altitudes. The three-dimensional nature of the model is obtained by following flux tubes of plasma as they convect or corotate through a moving neutral atmosphere. The model takes account of field-aligned diffusion, cross-field electrodynamic drifts, thermospheric winds, polar wind escape, energy-dependent chemical reactions, neutral composition changes, ion production due to solar EUV radiation and auroral precipitation, thermal conduction, diffusion-thermal heat flow and local heating and cooling processes. The model also takes account of the offset between the geomagnetic and geographic poles. A complete description of the ionospheric model is given, including a derivation of the relevant transport equations, formulas for all of the chemical and physical processes contained in the model, a discussion of the numerical technique, and a description of the required model inputs. The effects that various chemical and physical processes have on the ionosphere are also illustrated.

Conduction processes in oxide solid electrolytes

The quasi-chemical description of the defect structure in an oxide solid electrolyte is considered. It is shown how variations in the environment give rise to variations in the concentrations of defects which participate in the conduction processes of the oxide. Relevant transport equations that describe conduction processes which occur in oxide solid electrolytes are developed.

Thin films and wetting transitions in binary fluid mixtures

The objective of this study is to assess the impact of a dense-phase treatment on the hydrodynamic description of granular, binary mixtures relative to a previous dilute-phase treatment. Two theories were considered for this purpose. The first, proposed by Garzó and Dufty (GD) [Phys. Fluids 14, 146 (2002)], is based on the Boltzmann equation which does not incorporate finite-volume effects, thereby limiting its use to dilute flows. The second, proposed by Garzó, Hrenya and Dufty (GHD) [Phys. Rev. E 76, 31303 and 031304 (2007)], is derived from the Enskog equation which does account for finite-volume effects; accordingly this theory can be applied to moderately dense systems as well. To demonstrate the significance of the dense-phase treatment relative to its dilute counterpart, the ratio of dense (GHD) to dilute (GD) predictions of all relevant transport coefficients and equations of state are plotted over a range of physical parameters (volume fraction, coefficients of restitution, material density ratio, diameter ratio, and mixture composition). These plots reveal the deviation between the two treatments, which can become quite large (> 100%) even at moderate values of the physical parameters. Such information will be useful when choosing which theory is most applicable to a given situation, since the dilute theory offers relative simplicity and the dense theory offers improved accuracy. It is also important to note that several corrections to original GHD expressions are presented here in the form of a complete, self-contained set of relevant equations.

The Temperature Dependence of the Properties of Electrolyte Solutions. I. A Semi‐Phenomenological Approach to an Electrolyte Theory Including Short Range Forces

AbstractPair distribution functions f,ij(r1, r2) of a symmetrical ionophoric electrolyte compound Y Cz+ Az‐ in solution are determined with the help of a semi‐phenomenological method permitting to avoid a truncated series expansion of the Boltzmann factor exp [ — eo zj ψ i(r) k T] of Coulomb ion‐ion interaction in the vicinity of the i ion and to introduce the mean potential of short range forces. The appropriate chemical potential of the electrolyte component μY(p, T) and the relevant transport equations, especially of electrolyte conductance, are given. The concept of ion association is discussed within the framework of this approach.

Quantum transport equations for vibrating isotopically disordered crystals

A transport equation approach is developed for the linear response of the electron-phonon system in a vibrating isotopically disordered crystal to a frequency dependent electric field. The smallness of the mutual differences of the various masses is taken into account to derive a microscopic set of equations for the phonon and electron distribution functions. Applying an appropriate averaging technique, we obtain a set of equations from which the relevant macroscopic transport equation and hence physical quantities, such as the electrical conductivity, may be derived.

Molecular Sieve Studies of Interacting Protein Systems: XI. ISOMERIZING SOLUTES

Abstract The behavior of isomerizing solutes on molecular sieve columns has been studied theoretically and experimentally. Solutions of the relevant transport equations predict the shape and movement of solute zones for such systems. An experimental investigation of one such system has been carried out: the reversible unfolding of hen egg lysozyme. Results of this study clearly illustrate the effects of finite reaction kinetics on the shapes of solute profiles. To elucidate the influence of chromatographic parameters on the solute profiles, numerical simulations have also been carried out based on the theoretical expressions derived. From these investigations some guidelines have been formulated to aid the design of optimal chromatographic systems for study of isomerizing proteins. In general the technique is best applied to systems with rate constants less than 3 hour-1.

A mechanistic theory of hydrogen embrittlement of steels

AbstractConsideration of the relation between the cohesive energy and the surface free energy leads to the inference that dissolved hydrogen reduces the maximum cohesive resistive force of which the iron lattice is capable. This forms the basis of a mechanistic model for the velocity of hydrogen‐induced crack propagation in steels. The crack grows when the local tensile elastic stress normal to the plane of the crack equals the local maximum cohesive force per unit area as reduced by the large concentration of hydrogen drawn there by the effect of elastic stress on the chemical potential of hydrogen. The velocity of the growth is given by the solution of the relevant transport equation for the accumulation of hydrogen. Although quantifiable in principle the theory remains implicit because of current ignorance of the needed functional relationships, but some qualitative predictions and insights are possible, as well as the specification of important experiments.

Path Variable Formulation of the Hot Carrier Problem

A theoretical treatment of transport phenomena in strong electric fields is presented. Instead of the Legendre polynomial expansion of the distribution function usually employed in solving the transport equation, we transform the Boltzmann equation to a coordinate system determined by the collision-free trajectories of the particles and formulate an integral equation for the distribution function. This method is applied to hot carriers in nonpolar semiconductors, where the relevant transport equation is then reduced to a one-dimensional integral equation. This equation is solved numerically and energy distributions are calculated for $n$- and $p$-type germanium. The calculations for heavy holes in germanium demonstrate the non-Maxwellian nature of the distribution function as well as its strong displacement in momentum space, and are in excellent agreement with experiment. The energy distributions for electrons show weaker deviations from Maxwellian and smaller ratios of drift to rms velocity, this being due to the weaker coupling to optical phonons for electrons as compared to holes.