Explicit model for a mixture of Eulerian fluids based on kinetic theory

Within extended thermodynamics, a mixture of non-reactive Eulerian fluids is described with the multi-velocity and multi-temperature system of Euler-like equations, consisting in conservation laws for mass densities and balance laws for momentum and energy densities of each mixture component. The source terms are of phenomenological nature and appear in the system due to the mutual interaction between species. The aim of this paper is to derive such a macroscopic model starting from the system of Boltzmann-like equations describing a mixture of both monatomic and polyatomic gases. The method relies on an exact maximum entropy principle and evaluation of the Boltzmann multi-species collision operators for the collision kernel used in a recent rigorous mathematical analysis. Based on the obtained highly non-linear momentum and energy production terms, we propose a non-linear closure for the phenomenological model in the case of multi-velocity/single-temperature and single-velocity/multi-temperature. For the multi-velocity and multi-temperature case, we propose a closure via linearization in the neighborhood of the mixture mean velocity and temperature.