Shear-Rate-Independent Diffusion in Granular Flows

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 γd¯2, where d¯ is the local mean particle diameter and γ is the local shear rate. When γ is large, D is proportional to γd¯2, as in previous studies. However, for γd¯2 below a critical value, D is independent of γd¯2. The acceleration due to gravity g and particle stiffness (or, equivalently, the binary collision time tc) 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 (d¯/g) and particle stiffness (tcd¯g), respectively.