Two-temperature fluid models for a polyatomic gas based on kinetic theory for nearly resonant collisions

A polyatomic ideal gas with weak interaction between the translational and internal modes is considered. For the purpose of describing the behavior of such a gas, a Boltzmann equation is proposed in the form that the collision integral is a linear combination of inelastic and elastic (or resonant) collisions, and its basic properties are discussed. Then, in the case where the elastic collisions are dominant, fluid dynamic equations of Euler and Navier–Stokes type including two temperatures, i.e., translational and internal temperatures, as well as relaxation terms are systematically obtained by means of the Chapman–Enskog expansion. The obtained equations are different depending on the degree of weakness of the interaction between the translational and internal modes.