Self-similar velocity profiles and mass transport of grains carried by fluid through a confined channel

Abstract

Confined fluid-driven granular flows are present in a plethora of natural and industrial settings, yet even the most fundamental of these is not completely understood. While widely studied grain flows such as bed load and density-matched Poiseuille flows have been observed to exhibit exponential and Bingham style velocity profiles, respectively, this work finds that a fluid-driven bed of non-buoyant grains filling a narrow horizontal channel—confined both from the sides and above—exhibits self-similar Gaussian velocity profiles. As the imposed flow rate is increased and the grain velocity increases, the Gaussian flow profiles penetrate deeper into the packing of the channel. Filling fractions were observed to be also self-similar and qualitatively consistent with granular theory relating to the viscous number I, which at a given position on the self-similar Gaussian curve is found to be generally constant regardless of the imposed flow rate or velocity magnitude. An empirical description of the flow is proposed, and local velocity and filling fraction measurements were used to obtain the local grain flux and accurately recover a total grain flow rate.