Diphasic non-local model for granular surface flows

TL;DR

This paper introduces a diphasic non-local rheological model for granular surface flows that captures complex velocity profiles and scaling behaviors observed in experiments and rotating drum setups.

Contribution

The paper develops a novel non-local constitutive law accounting for multi-scale grain clusters, improving understanding of granular surface flow rheology.

Findings

Successfully predicts exponential velocity decay in static phase

Reproduces linear velocity profiles in flowing layer

Matches observed scalings in rotating drum experiments

Abstract

Considering recent results revealing the existence of multi-scale rigid clusters of grains embedded in granular surface flows, i.e. flows down an erodible bed, we describe here the surface flows rheology through a non-local constitutive law. The predictions of the resulting model are compared quantitatively to experimental results: The model succeeds to account for the counter-intuitive shape of the velocity profile observed in experiments, i.e. a velocity profile decreasing exponentially with depth in the static phase and remaining linear in the flowing layer with a velocity gradient independent of both the flowing layer thickness, the angle between the flow and the horizontal, and the coefficient of restitution of the grains. Moreover, the scalings observed in rotating drums are recovered, at least for small rotating speed.