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

TL;DR

This paper formally derives an isentropic two-phase flow model from the multi-species Boltzmann equation by analyzing the zero Knudsen number limit in a resonant collision regime, including volume fraction evolution.

Contribution

It provides a rigorous asymptotic derivation of a multi-velocity, multi-pressure two-phase model from kinetic theory, explicitly computing model coefficients.

Findings

Derivation of a multi-velocity, multi-pressure two-phase model

Explicit computation of macroscopic model coefficients

Inclusion of volume fraction evolution in the model

Abstract

Starting from the multi-species Boltzmann equation for a gas mixture, we propose the formal derivation of the isentropic two-phase flow model introduced in [Romenski, E., and Toro, E. F., Comput. Fluid Dyn. J., 13 (2004)]. We examine the asymptotic limit as the Knudsen numbers approach zero, in a regime characterized by resonant intra-species collisions, where interactions between particles of the same species dominate. This specific regime leads to a multi-velocity and multi-pressure 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