A conservation law model for a bidisperse particle laden flow on an incline

We present theoretical and experimental studies on constant-volume gravity-driven particle-laden flow in thin films. These slurries comprise of viscous fluid and two species of negatively buoyant, spherical particles with different size but the same density. The particles migrate within the fluid via a combination of shear-induced migration and hindered settling driven by gravity. We extend models from previous work to develop a conservation law model. We validate our numerical simulations with experiments by comparing the particle and fluid fronts and note the following trends. The larger particles move to the front of the mixture, resulting in one of two long-term behaviors: (a) the larger particles concentrate at the leading edge of the front or (b) the larger particles flow ahead of smaller particles and are all overtaken by a clear fluid front. Further, at high particle concentrations in case (a) one can observe a jamming transition in which particle clumps break away from the leading edge and slide down the incline as a solid body on a lubricating layer. This corresponds to a singular shock in the model in which the particle volume fraction concentrates at the maximum packing fraction. The experimental behavior seen corresponds to mass shedding from the singular shock.