Kinetic theory of granular shear flow: Constitutive relations for the hard-disk model

A kinetic theory for the constitutive Theological relations of rapid granular shear flow of hard circular disks, characterized by a coefficient of restitutione and a surface roughness coefficient, is formulated. From a set of general constitutive equations for single-particle dynamical variables, the approximate expressions for the limit of small and large dimensionless dissipative parameterR_t are obtained. HereR_t is defined as the ratio /, where is the fluctuation of translational velocity from the mean flow velocity, is the diameter of a disk, and is the shear rate. At smallR_t the theoretical predictions can be compared with exact computer simulation results of granular dynamics that are also reported. The agreement between theory and simulation is better than expected; the present theory is accurate up to high packing density in this region ofR_t.