Shear-rate-independent collisional diffusion in granular materials

We computationally study the diffusion coefficient, D, in granular flows of monodisperse and bidisperse particles spanning regions of rapid, dense flow, and quasi-static creep flow 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 g ̇d ̅ 2, where d is the local mean particle diameter and g ̇ is the local shear rate. When g ̇ is large, D is proportional to g ̇d ̅ 2, as in earlier studies. However, for g ̇d ̅ 2 below a critical value, D is constant. The acceleration of gravity and particle stiffness together determine the location of the transition in D between the shear-rate-dependent regime in rapid, dense flow and the shear-rate-independent regime in quasi-static creep flow. Our study supports earlier work showing that g –1 is the relevant time scale in rapid, dense flow; however, in quasi-static creep flow, the time scale depends instead on gravity √(d ̅/g) and the particle binary collision time. Funded by the Dow Chemical Company