The steady inhomogeneous rapid granular shear flow of nearly elastic spheres

The steady inhomogeneous rapid granular shear flows of identical, smooth, n early elastic spheres were considered, which interact with a flat wall to w hich identical, evenly spaced half-spheres have been attached. The boundary -value problem for the steady inhomogeneous shear flows, which are maintain ed by the relative motion of parallel bumpy boundaries, was solved by emplo ying the constitutive relations of Jenkins and Richman (Arch. Rational Mech . Anal. 87 (1985) 355) and the boundary conditions of Richman (Acta. Mech. 75 (1988) 227) in the balance equations for mean fields of mass density of flow, velocity, and the granular temperature. How the resulting profiles of velocity, solid fraction, and granular temperature were affected by change s in the geometrical configuration of the boundary and the coefficient of r estitution was demonstrated. Additionally, predicting how the slip velocity would vary with the geometrical configuration of the boundary, the coeffic ient of restitution, the flow depth and the average solid fraction within t he flow was under taken. Special emphasis was placed on the manner in which the shear and normal stresses vary with boundary characteristics and the c oefficient of restitution, primarily because the stresses are the quantitie s most easily measured by the experimentalist. Variations in slip velocity were observed to be partially responsible for the corresponding variations in the stresses. (C) 2000 Elsevier Science B.V. All rights reserved.