Two-Fluid Model for the Structure of Neutral Shock Waves

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Abstract
Recent measurements indicate that the thickness of weak and moderate strength shocks (M < 2) is given accurately by the Navier-Stokes equations, whereas there is good reason to believe that the bimodal theory of Mott-Smith is a better description for strong shocks. It is therefore desirable to develop a theory that can account for shock structure at both large and small Mach number. Results of a promising two-fluid theory by Glansdorff are recomputed and the formulation is criticized. A modified two-fluid approach is developed, employing moments of the respective Boltzmann equations for each fluid, and employing an intermediate Maxwellian distribution function with a mean flow velocity and temperature at the center of the shock to account for irreversible particle transfer between the two fluids. Numerical solutions for rigid-sphere and inverse fifth molecules are given, and comparisons with other solutions and experimental data are made. The results are in substantial agreement with requirements at both large and small Mach number.