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 coefficients can be linked to the direct linearized Boltzmann operator for mixtures. That allows to compute the values of the Maxwell–Stefan diffusion coefficients with explicit and simple formulae with respect to the cross-sections. We also justify the specific ansatz we use thanks to the so-called moment method.
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