# On the Maxwell-Stefan diffusion limit for a reactive mixture of polyatomic gases in non-isothermal setting

## TL;DR

This paper derives a Maxwell-Stefan diffusion model for reactive polyatomic gas mixtures with internal energy, in a non-isothermal setting, based on kinetic theory and asymptotic analysis.

## Contribution

It introduces a new mathematical model coupling Maxwell-Stefan diffusion with chemical reactions and temperature evolution for polyatomic gases, derived from kinetic equations.

## Key findings

- Derived Maxwell-Stefan equations for reactive mixtures with internal energy.
- Obtained expressions for reaction and diffusion coefficients from kinetic parameters.
- Established the model in a non-isothermal, reactive context.

## Abstract

In this article we deduce a mathematical model of Maxwell-Stefan type for a reactive mixture of polyatomic gases with a continuous structure of internal energy. The equations of the model are derived in the diffusive limit of a kinetic system of Boltzmann equations for the considered mixture, in the general non-isothermal setting. The asymptotic analysis of the kinetic system is performed under a reactive-diffusive scaling for which mechanical collisions are dominant with respect to chemical reactions. The resulting system couples the Maxwell-Stefan equations for the diffusive fluxes with the evolution equations for the number densities of the chemical species and the evolution equation for the temperature of the mixture. The production terms due to the chemical reaction and the Maxwell-Stefan diffusion coefficients are moreover obtained in terms of the collisional kernels and parameters of the kinetic model.