Nonlinear resonant gas oscillation accompanied with evaporation and condensation

Resonant gas oscillation in a closed tube bounded by an oscillating plate and a vapor-liquid interface is theoretically analyzed by applying the asymptotic theory to the ES-BGK Boltzmann equation for the case of MP ∼ Kn ≪ 1 and a small evaporation coefficient α = O(Kn), where MP and Kn are the Mach number of the plate 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 including α. We numerically solve the integro-differential equation with the method of Fourier series, and obtain a parameter plane for shock formation conditions and also the prediction of critical condition for shock formation.