Numerical analysis of the shear flow of a binary mixture of hard-sphere gases over a plane wall

Abstract

The shear flow of a binary mixture of rarefied gases over a plane wall is investigated on the basis of the linearized Boltzmann equation for hard-sphere molecules with the diffuse reflection boundary condition. This fundamental problem in rarefied gas dynamics is analyzed numerically by a finite-difference method, in which the complicated collision integrals are computed by the extension to the case of a gas mixture of the method proposed by Sone, Ohwada, and Aoki [Phys. Fluids A 1, 363 (1989)]. As a result, the behavior of the mixture is clarified not only at the level of the macroscopic variables but also at the level of the velocity distribution function. In addition, an accurate formula of the shear-slip (viscous-slip) coefficient for arbitrary values of the concentration of a component gas is constructed by the use of the Chebyshev polynomial approximation.