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Boundary conditions at a rigid wall for rough granular gases

Published online by Cambridge University Press:  18 April 2011

PRABHU R. NOTT
PRABHU R. NOTT*
Affiliation:
Department of Chemical Engineering, Indian Institute of Science, Bangalore 560012, India
*
†Email address for correspondence: prnott@chemeng.iisc.ernet.in
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Abstract

We derive boundary conditions at a rigid wall for a granular material comprising rough, inelastic particles. Our analysis is confined to the rapid flow, or granular gas, regime in which grains interact by impulsive collisions. We use the Chapman–Enskog expansion in the kinetic theory of dense gases, extended for inelastic and rough particles, to determine the relevant fluxes to the wall. As in previous studies, we assume that the particles are spheres, and that the wall is corrugated by hemispheres rigidly attached to it. Collisions between the particles and the wall hemispheres are characterized by coefficients of restitution and roughness. We derive boundary conditions for the two limiting cases of nearly smooth and nearly perfectly rough spheres, as a hydrodynamic description of granular gases comprising rough spheres is appropriate only in these limits. The results are illustrated by applying the equations of motion and boundary conditions to the problem of plane Couette flow.

JFM classification

Granular media: Granular media Rarefied Gas Flow: Kinetic theory
Type
Papers
Information
Journal of Fluid Mechanics , Volume 678 , 10 July 2011 , pp. 179 - 202
Copyright
Copyright © Cambridge University Press 2011

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