ABSTRACT
The experiments were carried out in a quasi-2D Couette apparatus that is sketched in Fig. 1.The particles, disks made of a photoelastic material, rested on a smooth Plexiglas sheet, and were contained between an inner wheel, which rotated, and a static outer ring. There were roughly 40,000 of these disks, with a bidisperse distribution. The two disk diameters were
dS = 0.42 cm and d + L = 0.50 cm, with roughly 3/4 of the disks having the smaller diameter. All disks were 0.32 cm thick. Disks within the dynamic region formed by the shear band were also marked with a thin bar along the diameter so that it was possible to track the center of mass and orientation of these particles. The assembly was sandwiched between crossed circular polarizers, and we obtained digital images via a camera mounted above the apparatus. Hence, it was possible to also obtain information on the forces at the particle scale. Specifically, we determine the mean force on a particle by computing the squared gradient of the photoelastic image intensity, integrated over each particle (Howell & Behringer 1999). It is possible to related this measure to the mean force by a separate calibration. (In principle, it is possible to determine the forces at contacts by solving a nonlinear inverse problem for a map between contact forces, the stress fields within each particle, and the resulting photoelastic image. See Majmudar and Behringer, elsewhere in this proceedings.)
3 EXPERIMENTAL RESULTS
Much of what we present concerns the mean square displacement of particles in the dynamic region of the shear band. For simple Brownian diffusion in an isotropic system, moments such as 〈x2〉 or 〈y2〉 grow linearly in time. However, velocity gradients or a rigid boundary significantly affect the evolution of these moments. For instance, in an infinite 2D system for which there is a mean velocity oriented along the x-axis, and for which there is a uniform shear gradient in the y-direction, Taylor dispersion, i.e. the presence of the velocity gradient, causes the moment 〈x2〉 to increase cubically in the time for large t, although the increase is initially linear.
