Kinematics of a two-dimensional granular Couette experiment at the transition to shearing

We describe experiments on a two-dimensional granular Couette system consis ting of photoelastic disks undergoing slow shearing. The disks rest on a sm ooth surface and are confined between an inner wheel and an outer ring. Onl y shearing from the inner wheel is considered here. We obtain velocity, par ticle rotation rate (spin), and density distributions for the system by tra cking positions and orientations of individual particles. At a characterist ic packing fraction, gamma(c)similar or equal to 0.77, the wheel just engag es the particles. In a narrow range of gamma, 0.77 less than or equal to y less than or equal to 0.80 the system changes from just able to shear to de nsely packed. The transition at gamma(c) has a number of hallmarks of a cri tical transition, including critical slowing down, and an order parameter. For instance, the mean stress grows from 0 as gamma increases above gamma(c ), and hence plays the role of an order parameter. Also, the mean particle velocity vanishes at the transition point, implying slowing down at y(c). A bove gamma(c), the mean azimuthal velocity decreases roughly exponentially with distance from the inner shearing wheel, and the local packing fraction shows roughly comparable exponential decay from a highly dilated region ne xt to the wheel to a denser but frozen packing further away. Approximate bu t not perfect shear rate invariance occurs; variations from perfect rate in variance appear to be related to small long-time rearrangements of the disk s. The characteristic width of the induced "shear band" near the wheel vari es most rapidly with distance from the wheel for gamma=gamma(c), and is rel atively insensitive to the packing fraction for the larger gamma's studied here. The mean particle spin oscillates near the wheel, and falls rapidly t o zero away from the shearing surface. The distributions for the tangential velocity and particle spins are wide and show a complex shape, particularl y for the disk layer nearest to the shearing surface. The two-variable dist ribution function for tangential velocity and spin reveals a separation of the kinematics into a slipping state and a nonslipping state consisting of a combination of rolling and translation. [S1063-651X(99)06001-8].