Theory for Shock Dynamics in Particle-Laden Thin Films

We present a theory to explain the emergence of a particle-rich ridge observed experimentally in a thin film particle-laden flow on an incline. We derive a lubrication theory for this system which is qualitatively compared to preliminary experimental data. The ridge formation arises from the creation of two shocks due to the differential transport rates of fluid and particles. This parallels recent findings of double shocks in thermal-gravity-driven flow [ A. L. Bertozzi et al. Phys. Rev. Lett. 81 5169 (1998); J. Sur et al. Phys. Rev. Lett. 90 126105 (2003); A. Münch Phys. Rev. Lett. 91 016105 (2003)]. However, here the emergence of the shocks arises from a new mechanism involving the settling rates of the species.