Macroscopic equations for inert gas mixtures in different hydrodynamic regimes

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 e-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.