Shear-induced diffusion in non-local granular flows

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 flows with gravity and Poiseuille flows, in which non-local effects induce some creep flow in zones where stresses are below the yield criterion. Results show that shear-induced diffusion is qualitatively different in zones above and below the yield criterion. In sub-yield layers, diffusivity is no longer governed by instantaneous velocity fluctuations, and we evidence a direct scaling between diffusivity and local shear rate. This is interpreted by analysing the grain trajectories, which exhibit some caging in zones below the yield. Finally, we 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.