A rigorous derivation of multicomponent diffusion laws

TL;DR

This paper rigorously derives a multicomponent diffusion law for isothermal, inviscid gas mixtures, revealing a conservation-dissipation structure and resolving longstanding non-uniqueness issues in the field.

Contribution

It provides the first rigorous mathematical derivation of a multicomponent diffusion law that incorporates entropic variables and Onsager reciprocal relations.

Findings

Derivation of a conservation-dissipation structure for gas mixture equations

Resolution of non-uniqueness in multicomponent diffusion laws

The diffusion law involves entropic variables and satisfies Onsager reciprocal relations

Abstract

This article is concerned with the dynamics of a mixture of gases. Under the assumption that all the gases are isothermal and inviscid, we show that the governing equations have an elegant conservation-dissipation structure. With the help of this structure, a multicomponent diffusion law is derived mathematically rigorously. This clarifies a long-standing non-uniqueness issue in the field for the first time. The multicomponent diffusion law derived here takes the spatial gradient of an entropic variable as the thermodynamic forces and satisfies a nonlinear version of the Onsager reciprocal relations.