Vortices enhance diffusion in dense granular flows

Abstract

This Letter introduces unexpected diffusion properties in dense granular flows, and shows that they result from the development of partially jammed clusters of grains, or granular vortices. Transverse diffusion coefficients $D$ and average vortex sizes $\ell$ are systematically measured in simulated plane shear flows at differing internal numbers $I$ revealing (i) a strong deviation from the expected scaling $D\propto d^2 \dot γ$ involving the grain size $d$ and shear rate $\dot γ$ and (ii) an increase in average vortex size $\ell$ at low $I$, following $\ell\propto dI^{-\frac{1}{2}}$ but limited by the system size. A general scaling $D\propto \ell d \dot γ$ is introduced that captures all the measurements and highlights the key role of vortex size. This leads to establishing a scaling for the diffusivity in dense granular flow as $D\propto d^2 \sqrt{\dot γ/ t_i}$ involving the geometric average of shear time $1/\dotγ$ and inertial time $t_i$ as the relevant time scale. Analysis of grain trajectories further evidence that this diffusion process arises from a vortex-driven random walk.