Resonant gas oscillation with evaporation and condensation

Resonant gas oscillation in a closed tube bounded by an oscillating plate and a vaporliquid interface is theoretically analyzed by applying the asymptotic theory to the ES-BGK Boltzmann equation for the case of M2≃Kn≪1 and a small evaporation coefficient α = O(Kn), where M and Kn are the typical Mach number and the Knudsen number, respectively. As a result, we derive a nonlinear integro-differential equation for determining the wave profile with the evaporation and condensation in the form including α.