Kinetic theory analysis of the two-surface problem of a vapor–vapor mixture in the continuum limit

Abstract

A steady flow of a vapor–vapor mixture between two parallel plane condensed phases for small Knudsen numbers is investigated on the basis of the kinetic theory of gases. By a systematic asymptotic analysis of the Boltzmann equation, it is shown that there are two distinct types of behavior of the mixture: the Euler-type behavior and the convection-diffusion-type behavior. Both types of behavior are confirmed numerically for the Boltzmann equation by the direct simulation Monte Carlo method and for the model Boltzmann equation proposed by Garzó, Santos, and Brey by the standard finite-difference method. Finally, the continuum limit (Kn=0₊) is considered, and it is shown that the ghost effect that some of the gas rarefaction effects still have an influence in the continuum limit manifests itself in the case of the convection-diffusion-type. This result shows that the infinitesimal jump of pressure at the surface of the condensed phase must be taken into account correctly for the description of the behavior of the vapors in the continuum limit.