Collisional Diffusion of Granular Materials: From Creep to Rapid Flow

The diffusion of granular material is driven by random collisions between particles and quantified by the diffusion coefficient, $D$. We computationally study the dependence of $D$ on local shear rate, $\dot{\gamma}$, from the dense flow regime to the creep flow regime in open and closed heap flows. Measurements of $D$ obtained for both geometries, monodisperse and bidisperse systems, various flow rates, and at different streamwise positions collapse onto a single curve when plotted vs.\ $\dot{\gamma}\bar{d}^2,$ where $\bar{d}$ is the local mean particle diameter. In the dense flow regime, where $\dot{\gamma}$ is larger, $D$ is proportional to $\dot{\gamma}\bar{d}^2$, similar to previous studies. However, in the creep flow regime, where $\dot{\gamma}$ is smaller, $D$ is independent of $\dot{\gamma}.$ The solids fraction and velocity fluctuations are also constant in this regime. Further study of the effect of gravity on $D$ shows that it determines the transition between rate-dependent and rate-independent regimes and controls the value of $D$ in the creep regime. These results demonstrate that the shear rate is not the relevant time scale in the creeping flow regime.