Particle diffusion in slow granular bulk flows

We probe the diffusive motion of particles in slowly sheared three-dimensional granular suspensions. For sufficiently large strains, the particle dynamics exhibits diffusive Gaussian statistics, with the diffusivity proportional to the local strain rate - consistent with a local, quasi-static picture. Surprisingly, the diffusivity is also inversely proportional to the depth of the particles below the granular surface - at their free surface, the diffusivity thus appears to diverge and is ill defined. We find that the crossover to Gaussian displacement statistics is governed by the same depth dependence, evidencing a non-trivial strain scale in three-dimensional granular flows.