Flow rule of dense granular flows down a rough incline

TL;DR

This study investigates the flow behavior of dense granular materials on inclined planes, comparing different materials and shapes, and proposes improved scaling laws to better describe the flow velocity and thickness relationships.

Contribution

The paper introduces an improved scaling law for granular flow velocity on inclined planes, accounting for material properties and flow divergence angles, enhancing previous models.

Findings

Pouliquen flow rule provides reasonable data collapse for sand and glass beads.

An improved scaling law with a tangent squared term yields better collapse of flow data.

Copper particles with different shapes do not conform well to the proposed flow rules.

Abstract

We present experimental findings on the flow rule for granular flows on a rough inclined plane using various materials including sand and glass beads of various sizes and four types of copper particles with different shapes. We characterize the materials by measuring $h_s$ (the thickness at which the flow subsides) as a function of the plane inclination $\theta$ on various surfaces. Measuring the surface velocity $u$ of the flow as a function of flow thickness $h$, we find that for sand and glass beads the Pouliquen flow rule $u/\sqrt{gh} \sim \beta h/h_s$ provides reasonable but not perfect collapse of the $u(h)$ curves measured for various $\theta$ and mean particle diameter $d$. Improved collapse is obtained for sand and glass beads by using a recently proposed scaling of the form $u/\sqrt{gh} =\beta \cdot h \tan^2\theta /h_s\ \tan^2\theta_1$ where $\theta_1$ is the angle at which the $h_s(\theta)$ curves diverge. Measuring the slope $\beta$ for ten different sizes of sand and glass beads, we find a systematic, strong increase of $\beta$ with the divergence angle $\theta_1$ of $h_s$. The copper materials with different shapes are not well described by either flow rule with $u \sim h^{3/2}$.