Half-space problem of the nonlinear Boltzmann equation for weak evaporation and condensation of a binary mixture of vapors

Abstract

The half-space problem of evaporation and condensation of a binary mixture of vapors is investigated on the basis of the kinetic theory of gases. Assuming the Mach number of the normal component of the flow is small, a solution of the Boltzmann equation that varies slowly in the scale of the molecular mean-free-path (slowly varying solution) is introduced. Then a fluid-dynamic system that describes the behavior of the slowly varying solution is derived by a systematic asymptotic analysis. The analytical expression of the conditions allowing steady evaporation or condensation is derived from that system. We analyze the qualitative difference between the conditions in the evaporation and condensation cases: four conditions are needed in the former case while only one condition is required in the latter case. The present paper extends a earlier contribution of the first author for the BGK-type model equation [S. Takata, Half-space problem of weak evaporation and condensation of a binary mixture of vapors, in: Capitelli M. (Ed.), Rarefied Gas Dynamics, AIP, New York, 2005, pp. 503–508] to the Boltzmann equation. The extension is achieved by considering the linear stability of the far field in the case of evaporation and the H theorem, the monotonic decrease of the flux of Boltzmann's H function, in the case of condensation.