On the Maxwell-Stefan approach to multicomponent diffusion

2010/07/11 by Dieter Bothe, Bothe, Dieter
Computer Science · Mathematics · Physics and Astronomy · #76R50 #76T30 #92E20 #Advanced Mathematical Modeling in Engineering #Analysis of PDEs (math.AP) #Differential Equations and Numerical Methods #FOS: Mathematics #FOS: Physical sciences #Fluid Dynamics (physics.flu-dyn) #Gas Dynamics and Kinetic Theory #Primary 35K59 #Secondary 35Q35 #math.AP #msc:35K59 #msc:35Q35 #msc:76R50 #msc:76T30 #msc:92E20 #physics.flu-dyn

paper · pdf · doi:10.48550/arxiv.1007.1775

Based on a talk given at the Conference on Nonlinear Parabolic Problems in Bedlewo, Mai 2009

arxiv created 2010/07/11 · openalex publication_date 2010/07/11 · arxiv updated 2010/07/13 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We consider the system of Maxwell-Stefan equations which describe multicomponent diffusive fluxes in non-dilute solutions or gas mixtures. We apply the Perron-Frobenius theorem to the irreducible and quasi-positive matrix which governs the flux-force relations and are able to show normal ellipticity of the associated multicomponent diffusion operator. This provides local-in-time wellposedness of the Maxwell-Stefan multicomponent diffusion system in the isobaric, isothermal case.

Related

• Existence analysis of Maxwell-Stefan systems for multicomponent mixtures
• On the structure of continuum thermodynamical diffusion fluxes -- A novel closure scheme and its relation to the Maxwell-Stefan and the Fick-Onsager approach
• Analysis of an incompressible Navier-Stokes-Maxwell-Stefan system
• Perturbative Cauchy theory for a flux-incompressible Maxwell-Stefan system
• Heat-conducting, compressible mixtures with multicomponent diffusion: construction of a weak solution