Shear-induced diffusion in non-local granular flows

TL;DR

This paper studies how particle diffusion behaves in dense granular flows with non-local effects, revealing different mechanisms above and below the yield stress and providing a scaling law for diffusivity based on local shear rate and stress.

Contribution

It introduces a new scaling law for diffusivity in non-local granular flows, linking it to local shear rate and stress, and analyzes grain trajectories to understand caging dynamics below the yield.

Findings

Diffusivity scales with local shear rate below the yield.

Non-local effects induce creep flow in sub-yield zones.

Explicit scaling law for diffusivity as a function of stress and position.

Abstract

We investigate the properties of self-diffusion in heterogeneous dense granular flows involving a gradient of stress and inertial number. The study is based on simulated plane shear with gravity and Poiseuille flows, in which non-local effects induce some creep flow in zones where stresses are below the yield. Results show that shear-induced diffusion is qualitatively different in zones above and below the yield. Below the yield, diffusivity is no longer governed by velocity fluctuations, and we evidenced a direct scaling between diffusivity and local shear rate. This is interpreted by analysing the grain trajectories, which exhibit a caging dynamics developing in zones below the yield. We finally introduce an explicit scaling for the profile of local inertial number in these zones, which leads to a straightforward expression of the diffusivity as a function of the stress and position in non-local flows.