A three-phase flow model with two miscible phases

Abstract

The paper concerns the modelling of a compressible mixture of a liquid, its vapor and a gas. The gas and the vapor are miscible while the liquid is immiscible with the gaseous phases. This assumption leads to non symmetric constraints on the void fractions. We derive a three-phase three-pressure model endowed with an entropic structure. We show that interfacial pressures are uniquely defined and propose entropy-consistent closure laws for the source terms. Naturally one exhibits that the mechanical relaxation complies with Dalton’s law on the phasic pressures. Then the hyperbolicity and the eigenstructure of the homogeneous model are investigated and we prove that it admits a symmetric form leading to a local existence result. We also derive a barotropic variant which possesses similar properties.