Using a kinetic BGK model to determine transport coefficients of gas mixtures

TL;DR

This paper uses a kinetic BGK model to derive transport coefficients for gas mixtures, providing a method to estimate diffusion, viscosity, heat conductivity, and thermal diffusion parameters from microscopic models.

Contribution

It introduces a Chapman-Enskog expansion of a kinetic model with adjustable parameters to accurately determine multiple transport coefficients in gas mixtures.

Findings

The model captures three key transport coefficients.

Extensions proposed for the ellipsoidal statistical model.

Potential for improved accuracy in gas mixture simulations.

Abstract

We consider a non reactive two component gas mixture. In a macroscopic description of a gas mixture we expect four physical coefficients characterizing the physical behaviour of the gases to appear. These are the diffusion coefficient, the viscosity coefficient, the heat conductivity and the thermal diffusion parameter in the Navier-Stokes equations. We present a Chapman-Enskog expansion of a kinetic model for gas mixtures by Klingenberg, Pirner and Puppo, 2017 that has three free parameters in order to capture three of these four physical coefficients. In addition, we propose several possible extensions to an ellipsoidal statistical model for gas mixtures in order to capture the fourth coefficient.