We computationally study the behavior of the diffusion coefficient $D$ in granular flows of monodisperse and bidisperse particles spanning regions of relatively high and low shear rate in open and closed laterally confined heaps. Measurements of $D$ at various flow rates, streamwise positions, and depths collapse onto a single curve when plotted as a function of $\dot{\gamma }{\overline{d}}^2$, where $\overline{d}$ is the local mean particle diameter and $\dot{\gamma }$ is the local shear rate. When $\dot{\gamma }$ is large, $D$ is proportional to $\dot{\gamma }{\overline{d}}^2$, as in previous studies. However, for $\dot{\gamma }{\overline{d}}^2$ below a critical value, $D$ is independent of $\dot{\gamma }{\overline{d}}^2$. The acceleration due to gravity $g$ and particle stiffness (or, equivalently, the binary collision time $t_c$) together determine the transition in $D$ between regimes. This suggests that while shear rate and particle size determine diffusion at relatively high shear rates in surface-driven flows, diffusion at low shear rates is an elastic phenomenon with time and length scales dependent on gravity ($\sqrt{\overline{d}/g}$) and particle stiffness ($t_c\sqrt{\overline{d}g}$), respectively.

• Received 21 April 2014

DOI:https://doi.org/10.1103/PhysRevLett.115.088001