# American Institute of Mathematical Sciences

August  2018, 11(4): 821-858. doi: 10.3934/krm.2018033

## On the Chapman-Enskog asymptotics for a mixture of monoatomic and polyatomic rarefied gases

 1 CEA-CESTA, 15 avenue des sablières, CS 60001 33116 Le Barp Cedex, France 2 University of Parma, Dept. of Mathematics, Physics and Computer Sciences, Parco Area delle Scienze 53/A, I-43124 Parma, Italy 3 University of Bordeaux, CNRS, Bordeaux INP, IMB, UMR 5251, F-33400 Talence, France 4 University Paris Diderot, Sorbonne Paris Cité, Institut de Mathématiques de Jussieu - Paris Rive Gauche, UMR 7586, CNRS, Sorbonne Universités, UPMC Univ. Paris 06, F-75013, Paris, France

* Corresponding author: L. Desvillettes

Received  August 2017 Revised  November 2017 Published  April 2018

In this paper, we propose a formal derivation of the Chapman-Enskog asymptotics for a mixture of monoatomic and polyatomic gases. We use a direct extension of the model devised in [8,16] for treating the internal energy with only one continuous parameter. This model is based on the Borgnakke-Larsen procedure [6]. We detail the dissipative terms related to the interaction between the gradients of temperature and the gradients of concentrations (Dufour and Soret effects), and present a complete explicit computation in one case when such a computation is possible, that is when all cross sections in the Boltzmann equation are constants.

Citation: Céline Baranger, Marzia Bisi, Stéphane Brull, Laurent Desvillettes. On the Chapman-Enskog asymptotics for a mixture of monoatomic and polyatomic rarefied gases. Kinetic & Related Models, 2018, 11 (4) : 821-858. doi: 10.3934/krm.2018033
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