Evaporation and condensation of a binary mixture of vapors on a plane condensed phase: Numerical analysis of the linearized Boltzmann equation

Abstract

Half-space problem of evaporation and condensation of a binary mixture of vapors is investigated on the basis of the linearized Boltzmann equation for hard-sphere molecules with the complete condensation condition. The problem is analyzed numerically by a finite-difference method, in which the complicated collision integrals are computed by the extension of the method proposed by Y. Sone, T. Ohwada, and K. Aoki [“Temperature jump and Knudsen layer in a rarefied gas over a plane wall: Numerical analysis of the linearized Boltzmann equation for hard-sphere molecules,” Phys. Fluids A 1, 363 (1989)] to the case of a gas mixture. As a result, the behavior of the mixture is clarified not only at the level of the macroscopic quantities but also at the level of the velocity distribution function. In addition, accurate formulas of the temperature, pressure, and concentration jumps caused by the evaporation and condensation are constructed for arbitrary values of the concentration of the background reference state by the use of the Chebyshev polynomial approximation.