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

Abstract

We introduce a system of Saint-Venant-type equations to model laboratory experiments of dam-break particle-laden flows. We explore homogeneous and non-cohesive liquid-solid suspensions of monodispersed glass beads that propagate as single-phase flows, forming a progressively growing deposit of particles at the bottom of a smooth channel and creating 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, thus avoiding the use of any artificial friction to stop the flow. 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 being mainly affected by the flow, but remains 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 sufficient to describe the general features of these flows as well as their deposit morphology, provided that the settling rate is adjusted starting from a critical value of the Reynolds number where the flow agitation begins to significantly delay the mean sedimentation velocity.