Abstract:
Measurements of diffusivity provide important insights intothe nature of the dynamical processes involved in the slow shear of dense granular materials. We report experiments that determine the diffusivities for a two-dimensional Couette shear system. In these measurements, we track the positions and orientations of particles (disks) undergoing steady shear. The shear is generated by a rotating inner wheel, which creates a roughly exponential mean azimuthal velocity. The variances associated with particle displacements are initially linear with time, which allows us to extract diffusivities. For later times, the variances exhibit nonlinearity, which we understand in terms of Taylor dispersion associated with the nonlinear velocity profile and boundary effects. The diffusivities are proportional to the local shear rate. We also determine the underlying force structures using the fact that the particles are photoelastic. A preferred direction for the force chains leads to a rotation of the principal directions of the diffusion tensor away from radial and azimuthal. These structures also come into play if the shearing direction is reversed. Lastly, we apply an idea suggested by Falk and Langer to characterize the non-affine motion of particles in terms of D 2, the minimum variance from an affine flow field. D 2 and the diffusivities are identical within scale factors (and experimental errors). © 2005 Taylor & Francis Group.
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