A mass diffusion effect in gas dynamics equations

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.

22 pages, updated the derivation of the Boltzmann collision operator, corrected some typos