Macroscopic equations for inert gas mixtures in different hydrodynamic regimes

Abstract

Starting from a BGK model for gas mixtures involving sums of relaxation operators, we formally derive Euler and Navier–Stokes equations in different regimes, in the asymptotic limit for proper Knudsen number, with explicit computation of the transport coefficients of viscosity and thermal conductivity. First, we consider a regime dominated by the whole collision phenomena; then, we focus on the case of ɛ−mixtures of heavy and light species, assuming accordingly that the collisions within each component constitute the dominant process. In this latter case we show that the two-scale collision regime leads to a multi-velocity and multi-temperature hydrodynamic description, which emphasizes the distinctive features of each constituent.