Dense granular flows: two-particle argument accounts for friction-like constitutive law with threshold

TL;DR

This paper derives a scalar constitutive law for dense granular flows using a two-particle approach, capturing a flow threshold and differing between inertial and viscous regimes, aligning with experimental data.

Contribution

It introduces a novel two-particle argument to derive a flow threshold in the constitutive law for dense granular flows, highlighting regime differences.

Findings

The law predicts a finite flow threshold at flow onset.

Compatibility with existing data requires empirical saturation at high velocities.

The law differs between inertial and viscous regimes, indicating no universal law.

Abstract

A scalar constitutive law is obtained for dense granular flows, both in the inertial regime where the grain inertia dominates, and in the viscous regime. Considering a pair of grains rather than a single grain, the classical arguments yield a constitutive law that exhibits a flow threshold expressed as a finite effective friction at flow onset. The value of the threshold is not predicted. The resulting law seems to be compatible with existing data, provided the saturation at high velocity (collisional regime) is added empirically. The law is not exactly the same in both regimes, which seems to indicate that there is no "universal" law.