Abstract:

Evaporation and condensation have been studied on the basis of the kinetic theory of gases fora long time. The time-independent evaporation or condensation flow of a vapor contact with a planar liquid surface has been formulated as a half-space boundary value problem of the Boltzmann equation, where the vapor at infinity is in an equilibrium state. The solution of the time-independent half-space problem is called the Knudsen layer correction for the fluid-dynamic-type solution of small Knudsen number flow, and the so-called slip boundary condition for the fluid-dynamic-type equations is determined simultaneously with the Knudsen layer correction (Sone 2007). In this talk, we consider a time-dependent half-space problem, where a simple wave (expansion wave) propagating in a steady condensation vapor flow is reflected at the interface, thereby leading to the transition from the condensation state to an evaporation state. We numerically solve the time-dependent boundary value problem of the Boltzmann-Krook-Welander equation (BGK model) and the complete condensation condition with a finite-difference method, and the numerical solution shows that the reflection wave is also a simple wave with the same entropy as that of the incident wave. The vapor pressure and vapor velocity of the reflection wave a redetermined by two equations for a Riemann invariant of the Euler equations and fora steady state solution of the Boltzmann equation. The vapor temperature near the interface is gradually updated by an advancing contact surface after the reflection wave has gone away.