Journal of Fluid Mechanics

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

J. T.  Jenkins a1 and S. B.  Savage a2
a1 Department of Theoretical and Applied Mechanics, Cornell University, Ithaca, New York
a2 Department of Civil Engineering and Applied Mechanics, McGill University, Montreal, Quebec

Article author query
jenkins jt   [Google Scholar] 
savage sb   [Google Scholar] 


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.

(Published Online April 20 2006)
(Received May 25 1982)