On the Maxwell-Stefan diffusion limit for a mixture of monatomic gases

TL;DR

This paper derives explicit expressions for binary diffusion coefficients in Maxwell-Stefan equations from multi-species Boltzmann equations for monatomic gases under certain assumptions, advancing the theoretical understanding of gas mixture diffusion.

Contribution

It provides a formal derivation of Maxwell-Stefan diffusion coefficients directly from Boltzmann equations for monatomic gases, under specific analytic and cutoff assumptions.

Findings

Explicit formulas for binary diffusion coefficients obtained

Connection established between Boltzmann and Maxwell-Stefan models

Theoretical framework for gas mixture diffusion clarified

Abstract

Multi-species Boltzmann equations for gaseous mixtures, with analytic cross sections and under Grad's angular cutoff assumption, are considered under diffusive scaling. In the limit, we formally obtain an explicit expression for the binary diffusion coefficients in the Maxwell-Stefan equations.