Rheology of dense granular flows in two dimensions: Comparison of fully two-dimensional flows to unidirectional shear flow

TL;DR

This study uses simulations to compare the rheology of two-dimensional granular flows with unidirectional shear flows, confirming the validity of the $mbda$-$I$ scaling and revealing that granular fluidity depends mainly on solid fraction.

Contribution

It demonstrates that the $mbda$-$I$ scaling applies to both flow types and introduces a unified scaling of granular fluidity based on solid fraction.

Findings

$mbda$-$I$ scaling holds for both flow types.

Granular fluidity depends primarily on solid fraction.

Data collapse achieved with Zhang and Kamrin's scaling.

Abstract

This work utilizes soft-particle discrete element simulations to examine the rheology of steady two-dimensional granular flows with reference to a unidirectional shear flow, which has been extensively employed for validating the local visco-plastic model of Jop et al. [Nature 441, 727--730 (2006)]. The $\mu$-$I$ scaling proposed by Jop et al. is found to be valid in both two-dimensional and unidirectional flows, as observed in previous studies, however, each flow type results in a different curve. Here $\mu$, ratio of the shear stress magnitude to the pressure, is the friction coefficient and $I$ is the dimensionless inertial number, which is proportional to the ratio of the magnitude of the rate of strain tensor, $\dot{\gamma}$, to the square root of the pressure. The friction coefficient is found not to scale in a simple way with the flow classification parameter $\psi$, which characterizes the local flow type. All the data collapse to a single curve using the scaling proposed by Zhang and Kamrin [Phys. Rev. Lett. 118, 058001 (2017)], in which the scaled granular fluidity ($f=1/(\mu T)$, where $T \propto u/\dot{\gamma}$ and $u$ is the fluctuation velocity) is found to depend only on the solid fraction $\phi$. The data for variation of $\phi$ with inertial number $I$ collapse to a single curve for all the flows.