Kinetic theory of recondensation in a binary gas mixture with arbitrary Knudsen numbers

Abstract

A rigorous solution of the problem of recondensation between two surfaces with arbitrary Knudsen numbers is possible only on the basis of a consecutive kinetic consideration. For the single-component case, this problem was solved in [1] using the BGK model of the collision integral in the kinetic equation. In [2], for the same purpose, the method of moments for “Maxwellian∝ molecules was used. The case of a binary mixture, in which one of the components is a noncondensing gas was discussed in [3, 4]. Under these circumstances, in [3], a single-relaxation lumped model was used for each component; the model did not reflect many of the properties of the exact collision integral. A more rigorous model (the collision integral in the Hamel form) was applied in [4]. Here there was written a system of integral equations for the hydrodynamic quantities, and its numerical solution is examined in several specific partial cases. In the present article, the problem of recondensation in a binary mixture is treated by the method of moments for “Maxwellian∝ molecules. For the case of small relative difference in the temperature of the surfaces, analytical expressions are obtained for the rates of mass transfer and the heat fluxes, making it possible to shed light on the principal special characteristics of the process of recondensation in a binary mixture.