Center of mass velocity during diffusion: Comparisons of fluid and kinetic models

We examine the diffusion process between two ideal gases mixing across an initial discontinuity by comparing fluid and kinetic model results and find several similarities between ideal gases and plasma transport. Binary diffusion requires a net zero species mass flux in the Lagrange frame to assure momentum conservation in collisions. Diffusion between ideal gases is often assumed to be isobaric and isothermal which requires constant molar density. We show this condition exists only in the lab frame at late times (many collision times) after a pressure transient relaxes. The sum of molar flux across an initial discontinuity is non-zero for species of differing atomic masses resulting in a pressure perturbation. The results show three phases of mixing: a pressure discontinuity forms across the initial interface (times of a few collisions), pressure perturbations propagate away from the mix region (time scales of an acoustic transit) and at late times characteristic of the diffusion process, the pressure relaxes leaving a non-zero center of mass flow velocity. The center of mass velocity associated with the outward propagating pressure waves is required to conserve momentum in the rest frame. Implications are considered in multi-species diffusion numerics and in applications.