Modeling the nonlocal behavior of granular flows down inclines

TL;DR

This paper applies a nonlocal granular fluidity model to inclined granular flows, successfully capturing nonlocal phenomena, predicting critical stopping heights, and aligning with experimental and simulation data, thus validating the model's effectiveness.

Contribution

The study demonstrates the nonlocal granular fluidity model's ability to predict flow behavior and critical stopping heights in inclined granular flows, extending its validation beyond steady flows.

Findings

Model accurately predicts critical stopping height for glass beads.

Flow profiles match discrete particle simulation results.

Froude number collapse explained through model insights.

Abstract

Flows of granular media down a rough inclined plane demonstrate a number of nonlocal phenomena. We apply the recently proposed nonlocal granular fluidity model to this geometry and find that the model captures many of these effects. Utilizing the model's dynamical form, we obtain a formula for the critical stopping height of a layer of grains on an inclined surface. Using an existing parameter calibration for glass beads, the theoretical result compares quantitatively to existing experimental data for glass beads. This provides a stringent test of the model, whose previous validations focused on driven steady-flow problems. For layers thicker than the stopping height, the theoretical flow profiles display a thickness-dependent shape whose features are in agreement with previous discrete particle simulations. We also address the issue of the Froude number of the flows, which has been shown experimentally to collapse as a function of the ratio of layer thickness to stopping height. While the collapse is not obvious, two explanations emerge leading to a revisiting of the history of inertial rheology, which the nonlocal model references for its homogeneous flow response.