Shock-induced instability of dual-layer dilute gas-particle mixture

We investigate the two-dimensional shock-induced instability of a dual-layer gas- particle (DLGP) mixture, with particle volume fractions on the order of 10-3 and moderate mass loading at the initial time. We elucidate the mechanism underlying the instability in the DLGP mixture using vorticity budgets, wave system analysis, and particle dynamics. The mechanism is distinct from that in the dual-layer gas (DLG) mixture. In the DLG mixture, the shock-induced instability is driven by the baroclinic vorticity. By contrast, in the DLGP mixture, the vorticity budgets suggest that the instability is not triggered by the baroclinic vorticity, because its contribution is negligible. Instead, the shock-induced instability in the DLGP mixture is induced by the pressure perturbation near the perturbed interface. The particle dynamics show that the velocity difference in particles near the perturbed interface is driven by the velocity difference in gas through the drag force. Thus, the velocity difference in- gas induced by the pressure perturbation drives the particle interface to grow via dragcoupling effects. Inspired by the interfacial instability mechanism, we estimate the growth of the particle interface in the linear stage. The model incorporates the multiphase Atwood number and the Stokes number, and well captures the linear growth rate of the particle-phase interface amplitude at moderate Atwood and Stokes numbers.