Higher-order Maxwell-Stefan model of diffusion

• Main Authors: Grec, Bérénice, Simic, Srboljub
• Format: Journal Article
• Language: English
• Published: 15-05-2023
• Subjects: Mathematics - Analysis of PDEs
• DOI: 10.48550/arxiv.2305.08412

The paper studies a higher-order diffusion model of Maxwell-Stefan kind. The
model is based upon higher-order moment equations of kinetic theory of
mixtures, which include viscous dissipation in the model. Governing equations
are analyzed in a scaled form, which introduces the proper orders of magnitude
of each term. In the socalled diffusive scaling, the Mach and Knudsen numbers
are assumed to be of the same small order of magnitude. In the asymptotic limit
when the small parameter vanishes, the model exhibits a coupling between the
species' partial pressure gradients, which generalizes the classical model.
Scaled equations also lead to a higher-order model of diffusion with correction
terms in the small parameter. In that case, the viscous tensor is determined by
genuine balance laws.