Shock-wave structure in binary mixtures of chemically inert perfect gases

Abstract

Starting with expressions for viscous stress, heat flux and diffusion flux, we formulate a continuum theory for steady flow of a binary mixture of chemically inert perfect gases through a normal shock of arbitrary strength. For shocks of vanishing strength, a solution by series expansion in Grad's (1952) shcok-strength parameter gives a result essentially the same as found previously by Dyakov (1954). For stronger shocks a straightforward numerical integration, quite analogous to that useful in the simpler pure-gas problem, is laid out.The resulting problem has eight parameters: shock strength, ratio of specific heats, ration of bulk viscosity to shear viscosity, Prandtl number, Schmidt number, thermal diffusion factor, molecular mass ratio, and initial mixture concentration. A dozen examples were worked out on a simple desk calculator to exhibit the influence of some of these parameters. They involve the gas pairs argon40–argon36, argon–neon, argon–helium, and xenon–helium.In discussing the results, special attention is paid to the degree of success with which the weak-shock theory may be extrapolated to arbitrary shock strength, and to the question of the accuracy of the Navier-Stokes approximation for a mixture of gases of very different molecular weights.