A consistent non-linear Fokker-Planck model for a gas mixture of polyatomic molecules

TL;DR

This paper develops a consistent non-linear Fokker-Planck model for a multi-species gas mixture with polyatomic molecules, capturing energy transfer and equilibrium properties.

Contribution

It introduces a novel kinetic Fokker-Planck framework for polyatomic gas mixtures with internal energy degrees of freedom, ensuring physical consistency and equilibrium characterization.

Findings

Model conserves total momentum and energy.

Ensures positivity of temperatures.

Equilibrium states are characterized as Maxwell distributions with equal temperatures.

Abstract

We consider a multi component gas mixture with translational and internal energy degrees of freedom without chemical reactions assuming that the number of particles of each species remains constant. We will illustrate the derived model in the case of two species, but the model can be generalized to multiple species. The two species are allowed to have different degrees of freedom in internal energy and are modeled by a system of kinetic Fokker-Planck equations featuring two interaction terms to account for momentum and energy transfer between the species. We prove consistency of our model: conservation properties, positivity of the temperatures, H-theorem and we characterize the equilibrium as two Maxwell distributions where all temperatures coincide.