Heavy gas relaxation in a light gas shock wave at small Prandtl number

The shock wave structure of a binary mixture with very different molecular weights is analyzed using a two-fluid theory in the limit of small Prandtl (Pr) number of the light gas. In particular, the case in which both the density ratio and Λ=Pr/δSc are order unity or below is considered, where δ≪1 is the molecular mass ratio and Sc is the Schmidt number. Approximate analytical solutions are given for weak, and for moderately strong, shock waves. In the former case the solution is continuous, while in the latter case the light gas shock exhibits a discontinuity and the heavy gas relaxes towards the final equilibrium state.