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

B. Anwasia; M. Bisi; F. Salvarani; A. J. Soares

doi:10.3934/krm.2020003

Article Contents

2020, Volume 13, Issue 1: 63-95. Doi: 10.3934/krm.2020003

This issue Previous Article A kinetic approach of the bi-temperature Euler model Next Article Hypocoercivity of linear kinetic equations via Harris's Theorem

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

1.
Universidade do Minho, Centro de Matemática, Campus de Gualtar, 4710-057 Braga, Portugal
2.
Università di Parma, Dipartimento di Scienze Matematiche, Fisiche e Informatiche, Parco Area delle Scienze 53/A, 43124 Parma, Italy
3.
Université Paris-Dauphine, PSL Research University, Ceremade, UMR CNRS, 75775 Paris, France
4.
Università degli Studi di Pavia, Dipartimento di Matematica, 27100 Pavia, Italy

^*Corresponding author: A. J. Soares
^*Corresponding author: A. J. Soares

Received: February 2019

Revised: July 2019

Published: February 2020

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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 general collision kernels and parameters of the kinetic model.

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Mathematics Subject Classification: Primary: 82C40, 35K57, 76R50; Secondary: 76P05, 80A30.

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