  In this letter, we discuss how flow inhomogeneity affects the self-diffusion
behavior in granular flows. Whereas self-diffusion scalings have been well
characterized in the past for homogeneous shearing, the effect of shear
localization and nonlocality of the flow has not been studied. We therefore
present measurements of self-diffusion coefficients in discrete numerical
simulations of steady, inhomogeneous, and collisional shearing flows of nearly
identical, frictional, and inelastic spheres. We focus on a wide range of dense
solid volume fractions, that correspond to geophysical and industrial shearing
flows that are dominated by collisional interactions. We compare the measured
values first, with a scaling based on shear rate and, then, on a scaling based
on the granular temperature. We find that the latter does much better than the
former in collapsing the data. The results lay the foundations of diffusion
models for inhomogeneous shearing flows, which should be useful in treating
problems of mixing and segregation.
