From Darcy to Gaussian to fully mobilised grain flow in a confined channel

Fluid-driven grain flow through a confined channel filled with non-buoyant grains is herein observed to exist in three regimes according to total imposed flow rate. (1) At low imposed flow rates, no grain flow occurs as the fluid stress is insufficient to mobilise the grains and Darcy flow is observed. (2) At a sufficient imposed flow rate, grains begin to flow at the top of the channel with self-similar Gaussian velocity profiles that become faster and encroach deeper into the channel with increased flow rate. (3) At high flow rates, significant grain flow occurs at the base of the channel, distorting the Gaussian profile, resulting in a gradual transition towards a more symmetric, full-channel flow. Each regime, and the transitions between them, is discussed in relation to experimental grain velocity measurements.