Formal derivation of an isentropic two-phase flow model from the multispecies Boltzmann equation

Starting from the multispecies Boltzmann equation for a gas mixture, we propose the formal derivation of the isentropic two-phase flow model introduced in E. Romenski, D. Drikakis, and E. Toro [J. Sci. Comput. 42, 68 (2010)]. We examine the asymptotic limit as the Knudsen numbers approach zero, in a regime characterized by resonant intraspecies collisions, where interactions between particles of the same species dominate. This specific regime leads to a multivelocity and multipressure hydrodynamic model, enabling the explicit computation of the coefficients for the two-phase macroscopic model. Our derivation also accounts for the inclusion of the evolution of the volume fraction, which is a key variable in many macroscopic multiphase models.