Low-Speed Transport of Gas Mixtures in Long Cylindrical Tubes According to the BGK Model

Abstract

The interior flow of a binary gas mixture at all densities is analyzed by means of the BGK kinetic theory. A single long cylinder which is often considered part of an ensemble employed to model flow and dispersion of gases in porous media is considered. A linearization that is appropriate for describing low-speed isothermal flow and is necessary to yield linear constitutive relationships provides a pair of integro-differential equations. The formal integration of this set results in two simultaneous nonsymmetric linear integral equations. Two trial functions are chosen to illustrate the utility of the Bubnov–Galerkin method to obtain expressions for the axial flux of each species. Uniform-pressure counter diffusion and the Kramers–Kistemaker effect are considered as specific examples. High- and low-density limiting cases are evaluated analytically using trial functions with optimally chosen coefficients. The flat velocity profiles predict the ratio of the average axial fluxes to be inversely proportional to the ratio of the square roots of the molecular weights for constant pressure diffusion at low and high pressures. The parabolic velocity profile describes the Kramers–Kistemaker effect exactly at low pressures and agrees well with the “dusty-gas” model at the high-pressure limit.