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Plane simple shear of smooth inelastic circular disks: the anisotropy of the second moment in the dilute and dense limits

Published online by Cambridge University Press:  21 April 2006

J. T. Jenkins  and
M. W. Richman
J. T. Jenkins
Affiliation:
Department of Theoretical and Applied Mechanics, Cornell University, Ithaca, NY 14853, USA
M. W. Richman
Affiliation:
Department of Mechanical Engineering, Worcester Polytechnic Institute, Worcester, MA 01609, USA
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Abstract

We consider a plane, steady, homogeneous flow of circular disks. The disks are identical, smooth, and inelastic. We adopt the assumption of molecular chaos and introduce an anisotropic Maxwellian velocity distribution function based on the full second moment of the velocity fluctuations. In the limits of dilute and dense flows, we determine approximate analytic solutions of the balance law for the second moment that result in stresses whose qualitative behaviour and magnitudes are in good agreement with numerical simulations.

Type
Research Article
Information
Journal of Fluid Mechanics , Volume 192 , July 1988 , pp. 313 - 328
Copyright
© 1988 Cambridge University Press

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