Various hydrodynamic limits from a Boltzmann–BGK model for binary mixtures

Starting from a mixed Boltzmann–BGK model for binary gas mixtures, we formally derive 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 focus on the regime dominated by the whole collision phenomena; then, we consider the case of ε–mixtures of heavy and light species. In this latter case we assume, on one hand, a two–scale collision regime, with interactions within each component that constitute the dominant process, and, on the other hand, a three–scale regime, with dominant collisions within the heavier species and the slowest interactions occurring within the lighter one, leading to fluid–kinetic equations.