Kinetic theory for the density plateau in the granular flow down an inclined plane

Department of Chemical Engineering, Indian Institute of Science Bangalore 560 012, India

Received: 2 September 2005
Accepted: 29 November 2005

Abstract

The striking lack of observable variation of the volume fraction with height in the center of a granular flow down an inclined plane is analysed using constitutive relations obtained from kinetic theory. It is shown that the rate of conduction in the granular energy balance equation is smaller than the rate of production of energy due to mean shear and the rate of dissipation due to inelastic collisions, where the small parameter , d is the particle diameter, e_n is the normal coefficient of restitution and H is the thickness of the flowing layer. This implies that the volume fraction is a constant in the leading approximation in an asymptotic analysis in small δ. Numerical estimates of both the parameter δ and its pre-factor are obtained to show that the lack of observable variation of the volume fraction with height can be explained by constitutive relations obtained from kinetic theory.