Inertial nonequilibrium in strongly decelerated gas mixtures of disparate molecular weights

A Fokker-Planck kinetic equation is used to describe inertial nonequilibrium effects in a strongly decelerated dilute mixture of heavy molecules in a light bath. A "normal" (or diffusion) solution is found for the tractable case of the two-dimensional stagnation-point geometry allowing a hydrodynamical closure of the problem. Based on the ratio $\omega \tau$ between the heavy-species momentum-relaxation time $\tau$ and the flow time ${\omega }^{-1\mathrm{}}\left(\omega \equiv \frac{\mathrm{du}}{\mathrm{dx}}\right)$, this solution is valid for values of $\omega \tau$ up to ¼ and includes as a special case the Chapman-Enskog expressions which are valid only for very small values of $\omega \tau$ (less than 0.04). The corresponding diffusion velocity is nonlinear in the driving force $\omega$, although it satisfies the phenomenological linear-gradient flux laws. For $\omega \tau >\frac{1}{4}$ the flow is dominated by inertia and no diffusion solution exists. The model predicts velocity distribution functions not too far from the Maxwellian, but with a standard deviation (or temperature) larger along the deceleration direction than along the normal direction. This result leads to anisotropic diffusion in agreement with free-molecular-probe experiments in opposed jets of disparate mass mixtures. The predicted heavy-species translational temperature presents an unexpected minimum at the stagnation point in agreement with optical measurements in opposed jets. We conclude that the Fokker-Planck method is a good starting point to understand nonequilibrium flows prevailing in the separation nozzles used for the aerodynamic enrichment of ${}_{}{}^{235}{}_{}{}^{}\mathrm{U}$.