A model for mass shedding in thin-film particle-laden flows*

This study presents a model for mass shedding in gravity-driven particle-laden flow down an inclined plane. We consider a mix of  negatively buoyant particles with a viscous fluid, flowing down an incline. When the concentration of particles and angle of inclination are high, the particles accumulate at the fluid front. Eventually, when enough particles have accumulated, the particles approach their maximum packing fraction and reach a jammed state. In this case, we have experimentally observed that small chunks of mass break off from the main flow and slide down the incline at greater speed. We show how this corresponds to the formation of a singular shock in the continuum theory for particle laden flow.  Moreover, we present a model of mass shedding from the shock layer that extends previous work on modeling of mass accumulation at the fluid front. In particular we develop a model involving the frequency of mass shedding and the amount of mass shed. We explore patterns that emerge when many masses are shed in this way. In particular we present a power law relationship between distance from the fluid front and mass accumulation.