Hydrodynamic Theory of Multicomponent Diffusion and Thermal Diffusion in Multitemperature Gas Mixtures

Abstract

A phenomenological theory is developed for multicomponent diffusion, including thermal diffusion, in gas mixtures in which the components may have different temperatures. The theory is based on the hydrodynamic approach of Maxwell and Stefan, as extended and elaborated by Furry [1] and Williams [2]. The present development further extends these earlier treatments to multiple temperatures and multicomponent thermal diffusion. The resulting diffusion fluxes obey generalized Stefan-Maxwell relations which include the effects of ordinary, forced, pressure, and thermal diffusion. When thermal diffusion is neglected, these relations have the same form as the usual single-temperature ones, except that mole fractions are replaced by pressure fractions (i.e., ratios of partial pressures to total pressure). The binary ap.d thermal diffusion coefficients are given in terms of collision integrals. Single-temperature systems and binary systems are treated as special cases of the general theory. A self-consistent effective binary diffusion approximation for multitemperature systems is presented.

Basic knowledge on radiative and transport properties to begin in thermal plasmas modelling

“…Ghorui 116 and Colombo 117 compared the two theories and concluded that Devoto's approach (without coupling) was adequate to determine the electrical conductivity, the viscosity and the thermal conductivity of a nonequilibrium plasma even if the diffusion coefficients used in the expressions were obtained by the Ramshaw's approach. 123 Today, most of the works published seem to agree on the expressions to be used to calculate the viscosity, the electrical conductivity, the internal and translational thermal conductivities. The question especially concerns the calculation of one or two reactional thermal conductivities (and consequently the existence of a unique total thermal conductivity).…”

Multi-temperature Hydrodynamic Limit from Kinetic Theory in a Mixture of Rarefied Gases

“…Constitutive equations are needed for all fields which are relevant to single components of a species, in particular P i and q i , and for the collision contributions on the right sides, (14) and (16), that involve the specific distribution functions f i , and bear trace of their kinetic origin via the collision kernels affecting all integrals.…”

“…On the other hand, a multi-temperature approach naturally arises also in plasmas at high temperature [3], in the flow field around hypersonic vehicles at high altitude [15], as well as in several problems of aerothermodynamics [16,21]. In fact, a one-temperature gas flow description is not reliable in thermal non-equilibrium conditions when vibrational relaxations and possible chemical reactions proceed at the gas dynamic time scale, as widely investigated, especially by the Russian school [12].…”

A Selected Library of Transport Coefficients for Combustion and Plasma Physics Applications

“…There is a shortage of experimental data, and the traditional theory is so complex as to hinder its application by the nonspecialist, ttowevcr, Ramshaw has developed an approximate simplified theory [24] that has been incorporated into COYOTE. The first step is to estimate the collision cross section between molecules of types a and ~ as…”