On the Macroscopic Boundary Conditions at the Interface for a Vapour-gas Mixture

Abstract

Motions of a binary gas mixture of a vapour and an inert gas in a general flow domain are investigated on the basis of kinetic theory in order to derive a set of macroscopic equations and the appropriate boundary conditions at the interface between the condensed phase and the gas phase. The analysis has been carried out based on the Boltzmann equation of BGK type subject to the diffuse-reflection condition for the distribution functions at the interface under the following situations: (i) the Knudsen number of the system defined by the ratio of the molecular mean free path of a vapour to a characteristic length of the system is small compared with unity; (ii) the deviation of the system from a certain stationary equilibrium state is small but is of the order of the Knudsen number In this case, the Reynolds number of the system is of order unity, because, in general, it is proportional to the ratio of the Mach number to the Knudsen number, where the Mach number is a measure of the magnitude of the deviation. The derived system of macroscopic equations and boundary conditions makes possible at the level of ordinary fluid dynamics the treatment of various flow problems of a binary gas mixture involving evaporation and condensation processes which require kinetic theory consideration, giving adequate description of the behaviour of a mixture and its component gases when the Reynolds number is finite. Although this macroscopic system is meant only for steady problems, the boundary conditions derived here may serve to provide appropriate conditions at the interface even for unsteady problems.