Temperature, pressure, and concentration jumps for a binary mixture of vapors on a plane condensed phase: Numerical analysis of the linearized Boltzmann equation

The half-space problem of the temperature, pressure, and concentration jumps for a binary mixture of vapors is investigated on the basis of the linearized Boltzmann equation for hard-sphere molecules with the complete condensation condition. First, the problem is shown to be reduced to three elemental ones: the problem of the jumps caused by the net evaporation or condensation, that caused by the gradient of temperature, and that caused by the gradient of concentration. Then, the latter two are investigated numerically in the present contribution because the first problem has already been studied [Yasuda, Takata, and Aoki, Phys. Fluids 17, 047105 (2005)]. The numerical method is a finite-difference one, in which the complicated collision integrals are computed by the extension of the method proposed by Sone, Ohwada, and Aoki [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 are constructed for arbitrary values of the concentration of the background reference state by the use of the Chebyshev polynomial approximation. The solution of the corresponding problem of a vapor-gas mixture and that of the temperature-jump problem on a simple solid wall are also obtained as special cases of the present problem.