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A theory for the rapid flow of identical, smooth, nearly elastic, spherical particles

Published online by Cambridge University Press:  20 April 2006

J. T. Jenkins  and
S. B. Savage
J. T. Jenkins
Affiliation:
Department of Theoretical and Applied Mechanics, Cornell University, Ithaca, New York
S. B. Savage
Affiliation:
Department of Civil Engineering and Applied Mechanics, McGill University, Montreal, Quebec
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Abstract

We focus attention on an idealized granular material comprised of identical, smooth, imperfectly elastic, spherical particles which is flowing at such a density and is being deformed at such a rate that particles interact only through binary collisions with their neighbours. Using general forms of the probability distribution functions for the velocity of a single particle and for the likelihood of binary collisions, we derive local expressions for the balance of mass, linear momentum and fluctuation kinetic energy, and integral expressions for the stress, energy flux and energy dissipation that appear in them. We next introduce simple, physically plausible, forms for the probability densities which contain as parameters the mean density, the mean velocity and the mean specific kinetic energy of the velocity fluctuations. This allows us to carry out the integrations for the stress, energy flux and energy dissipation and to express these in terms of the mean fields. Finally, we determine the behaviour of these fields as solutions to the balance laws. As an illustration of this we consider the shear flow maintained between two parallel horizontal plates in relative motion.

Type
Research Article
Information
Journal of Fluid Mechanics , Volume 130 , May 1983 , pp. 187 - 202
Copyright
© 1983 Cambridge University Press

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