Kinetic theory for the density plateau in the granular flow down an inclined planeV. Kumaran
Department of Chemical Engineering, Indian Institute of Science Bangalore 560 012, India
received 2 September 2005; accepted in final form 29 November 2005
published online 16 December 2005
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, en 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 . Numerical estimates of both the parameter 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.
45.50.-j - Dynamics and kinematics of a particle and a system of particles.
45.70.Mg - Granular flow: mixing, segregation and stratification.
51.10.+y - Kinetic and transport theory of gases.
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