Abstract
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 coefficientβ, 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 σγ/〈ν〉, where ν is the fluctuation of translational velocity from the mean flow velocity, σ is the diameter of a disk, and γ 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 .
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Kim, S.R., Woodcock, L.V. Kinetic theory of granular shear flow: Constitutive relations for the hard-disk model. J Stat Phys 71, 143–162 (1993). https://doi.org/10.1007/BF01048092
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DOI: https://doi.org/10.1007/BF01048092