The Maxwell–Stefan diffusion limit for a kinetic model of mixtures with general cross sections. (August 2017)

• Record Type: Journal Article
• Authors: Boudin, Laurent; Grec, Bérénice; Pavan, Vincent
• Is Part Of: Nonlinear analysis. Volume 159(2017)
• Page Start: 40
• Page End: 61
• Publication Date: 2017-08
• Subjects: Boltzmann equation for mixtures -- Maxwell–Stefan diffusion coefficients; Mathematical analysis -- Periodicals; Functional analysis -- Periodicals; Nonlinear theories -- Periodicals; Analyse mathématique -- Périodiques; Analyse fonctionnelle -- Périodiques; Théories non linéaires -- Périodiques; Functional analysis; Mathematical analysis; Nonlinear theories; Periodicals; Electronic journals; 515.7248
• DOI: 10.1016/j.na.2017.01.010
• Languages: English
• ISSNs: 0362-546X

Abstract

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.