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 $D\propto d^2 \dot \gamma$ involving the grain size $d$ and shear rate $\dot \gamma$ 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 \gamma $ 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 $D\propto d^2 \sqrt{\dot \gamma/ t_i}$ involving the geometric average of shear time $1/\dot\gamma$ 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.