Integration through transients approach to the $\mu(\mathcal{I})$ rheology

TL;DR

This paper extends the integration through transients formalism to calculate pressure in granular flows within the Bagnold regime, providing theoretical support for the empirical ul() rheology laws and confirming the irrelevance of interparticle friction in this context.

Contribution

It generalizes the formalism to include pressure determination and supports the empirical ul() laws theoretically in the Bagnold regime.

Findings

The formalism is extended to pressure calculation.

Empirical ul() laws are supported theoretically.

Interparticle friction is shown to be irrelevant in the ul() regime.

Abstract

This work generalises the granular integration through transients formalism introduced by Kranz et al. [Phys. Rev. Lett. 121, 148002 (2018)] to the determination of the pressure. We focus on the Bagnold regime, and provide theoretical support to the empirical $\mu(\mathcal{I})$ rheology laws, that have been successfully applied in many granular flow problems. In particular, we confirm that the interparticle friction is irrelevant in the regime where the $\mu(\mathcal{I})$ laws apply.