Journal of Fluid Mechanics

Kinetic theories for granular flow: inelastic particles in Couette flow and slightly inelastic particles in a general flowfield

C. K. K.  Lun a1, S. B.  Savage a1, D. J.  Jeffrey a1 and N.  Chepurniy a1
a1 Faculty of Engineering, McGill University, 817 Sherbrooke St West, Montreal, Canada

Article author query
lun ck   [Google Scholar] 
savage sb   [Google Scholar] 
jeffrey dj   [Google Scholar] 
chepurniy n   [Google Scholar] 


The flow of an idealized granular material consisting of uniform smooth, but nelastic, spherical particles is studied using statistical methods analogous to those used in the kinetic theory of gases. Two theories are developed: one for the Couette flow of particles having arbitrary coefficients of restitution (inelastic particles) and a second for the general flow of particles with coefficients of restitution near 1 (slightly inelastic particles). The study of inelastic particles in Couette flow follows the method of Savage & Jeffrey (1981) and uses an ad hoc distribution function to describe the collisions between particles. The results of this first analysis are compared with other theories of granular flow, with the Chapman-Enskog dense-gas theory, and with experiments. The theory agrees moderately well with experimental data and it is found that the asymptotic analysis of Jenkins & Savage (1983), which was developed for slightly inelastic particles, surprisingly gives results similar to the first theory even for highly inelastic particles. Therefore the ‘nearly elastic’ approximation is pursued as a second theory using an approach that is closer to the established methods of Chapman-Enskog gas theory. The new approach which determines the collisional distribution functions by a rational approximation scheme, is applicable to general flowfields, not just simple shear. It incorporates kinetic as well as collisional contributions to the constitutive equations for stress and energy flux and is thus appropriate for dilute as well as dense concentrations of solids. When the collisional contributions are dominant, it predicts stresses similar to the first analysis for the simple shear case.

(Published Online April 20 2006)
(Received June 22 1983)