The Maxwell-Stefan diffusion limit for a kinetic model of mixtures with general cross sections

Abstract : In this article, we derive the Maxwell-Stefan formalism from the Boltzmann equation for mixtures for general cross-sections. The derivation uses the Hilbert asymptotic method for systems at low Knudsen and Mach numbers. We also formally prove that the Maxwell-Stefan coecients can be linked to the direct linearized Boltzmann operator for mixtures. That allows to compute the values of the Maxwell-Stefan diusion coecients with explicit and simple formulae with respect to the cross-sections. We also justify the specic ansatz we use thanks to the so-called moment method.
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Laurent Boudin, Bérénice Grec, Vincent Pavan. The Maxwell-Stefan diffusion limit for a kinetic model of mixtures with general cross sections. Nonlinear Analysis: Theory, Methods and Applications, Elsevier, 2017, 159, pp.40-61. ⟨10.1016/j.na.2017.01.010⟩. ⟨hal-01303312⟩

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