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

We describe experiments on a two-dimensional granular Couette system consisting of photoelastic disks undergoing slow shearing. The disks rest on a smooth surface and are confined between an inner wheel and an outer ring. Only shearing from the inner wheel is considered here. We obtain velocity, particle rotation rate (spin), and density distributions for the system by tracking positions and orientations of individual particles. At a characteristic packing fraction, ${\gamma }_c\simeq 0.77,$ the wheel just engages the particles. In a narrow range of $\gamma ,$ $0.77<~\gamma <~0.80$ the system changes from just able to shear to densely packed. The transition at ${\gamma }_c$ has a number of hallmarks of a critical 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 ${\gamma }_c.$ Above ${\gamma }_c,$ 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 next to the wheel to a denser but frozen packing further away. Approximate but not perfect shear rate invariance occurs; variations from perfect rate invariance appear to be related to small long-time rearrangements of the disks. The characteristic width of the induced “shear band” near the wheel varies most rapidly with distance from the wheel for $\gamma \simeq {\gamma }_c,$ and is relatively insensitive to the packing fraction for the larger $\gamma$’s studied here. The mean particle spin oscillates near the wheel, and falls rapidly to zero away from the shearing surface. The distributions for the tangential velocity and particle spins are wide and show a complex shape, particularly for the disk layer nearest to the shearing surface. The two-variable distribution 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.