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

TL;DR

This paper presents a simple yet effective three-layer model for particle-laden flows driven by sedimentation, accurately capturing flow behavior and deposit morphology in experiments with fine glass beads.

Contribution

The paper introduces a novel three-layer shallow water-type model that characterizes sedimentation-driven flows and deposit formation, validated against experimental data.

Findings

Model accurately predicts flow velocity and deposit shape.

Sedimentation dynamics are largely unaffected by flow agitation.

Model remains effective across different flow regimes when settling rate is adjusted.

Abstract

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.