Kinetic model for sheared granular flows in the high Knudsen number limit

Abstract

The sheared granular flow of rough inelastic granular disks is analyzed in the high Knudsen number limit, where the frequency of particle-wall collisions is large compared with particle-particle collisions, using a kinetic theory approach. An asymptotic expansion is used in the small parameter ε=(nσL), which is the ratio of the frequencies of particle-particle and particle-wall collisions, where n is the number of disks per unit area, σ is the disk diameter, and L is the channel width. The collisions are specified using a normal coefficient of restitution e_n and a tangential coefficient of restitution e_t. The analysis identifies two regions in the e_t-e_n parameter space, one where the final steady state is a static one in which the translational velocities of all particles decrease to zero, and the second where the final steady state is a dynamic one in which the mean square velocities scale as a power of ε in the limit ε→0. Both of these predictions are shown to be in quantitative agreement with computer simulations.