A three-layer model for the flow of particulate suspensions driven by sedimentation

We introduce a system of shallow water-type equations to model laboratory experiments of particle-laden flows. We explore homogeneous liquid–solid suspensions of fine, non-cohesive, monodisperse glass beads propagating as an equivalent fluid that progressively sediments and forms a growing deposit at the bottom of a smooth channel and simultaneously creates a thin layer of pure liquid at the surface. The flow front displays three phases of transport: a brief gravitational collapse where no sedimentation occurs, a dominant phase of constant velocity where both solid deposition and fluid expulsion develop, and a short decelerating phase. We derive a three-layer depth-averaged model to describe the flows propagation, designing novel source terms in the equations to carefully account for the deposition processes of particles, based on a general experimental law validated on static sedimenting fluid–solid suspensions. The model is very simple and turns out to be effective despite the complex nature of interactions involved in these phenomena, being apple to fully characterize the first-order behavior of these flows (mean velocity, runout distances, and deposits geometry) through the sole sedimentation process of the grains. The model is validated by comparing the experimental kinematics and deposit profiles with the simulations. The results highlight that this simplified model is able to describe the general features of these flows as well as their deposit morphology, provided that the settling rate measured in static suspensions is properly adjusted starting from a threshold Reynolds number, i.e., when the flow becomes sufficiently agitated to disturb and delay the deposition processes.