A mass diffusion effect in gas dynamics equations

TL;DR

This paper introduces a theoretical correction to classical gas dynamics equations accounting for a mass diffusion effect, derived from homogenization limits of molecular interactions, with estimates for various gases and models.

Contribution

It proposes a new mass diffusion correction in gas dynamics equations based on homogenization theory and computes diffusion coefficients for different molecular interaction models.

Findings

Mass diffusion effect appears as a homogenization correction.

Diffusion coefficients estimated for Euler, Navier-Stokes, Grad equations.

Applicable to monatomic and polyatomic gases.

Abstract

In the current work we propose a theory for an additional mass diffusion effect in the conventional gas dynamics equations. We find that this effect appears as a homogenization time limit correction, when the deterministic interaction process of the real gas molecules is replaced with a simplified random interaction process for consistency with the Boltzmann equation. For the simplified random interaction processes represented by either a hard sphere random scattering model, or by a model which employs the Lennard-Jones potential for random molecular deflections, we compute the estimates of the corrective diffusion coefficient in the Euler, Navier-Stokes and Grad equations for some monatomic and polyatomic gases.