  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 within the flow - at the free surface, diffusivity is
thus 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.
