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 which propagate 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 novelty of this model is twofold. First, we 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 remains very simple and turns out to be effective despite the complex nature of interactions involved in these phenomena. Secondly, the sedimentation dynamics of the grains is observed to not be strongly affected by the flow, remaining comparable to that measured in static suspensions. The mathematical 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 is properly adjusted from a threshold Reynolds number, i.e. when the flow becomes sufficiently agitated to disturb and delay the deposition processes.