Internal length and time scales in a simple shear granular flow

Abstract

Kinetic theory has been successfully applied to mathematically model the constitutive relations for flowing granular materials. However, the basis for kinetic theory is the assumption of binary collisions between particles. Both physical and numerical experiments of granular flows have questioned the validity of this assumption. It is known that when solid concentration or shear-rate increase, collision contact time becomes long relative to free-flight duration. Multiple collisions begin to prevail. Interactions between groups of particles may dominate the dynamics of the flow. This paper addresses both the size and lifetime of multiple collision groups in a granular flow. Computer simulations of a simple shear two-dimensional assembly of visco-elastic particles with or without friction are performed. It is found that as the shear-rate or solid concentration increase the shearing particles begin to form distinct groups within each group particles collide simultaneously. The group size grows with further increase of shear-rate or solid concentration to the extent that force chains spanning the whole shearing assembly may form. Concomitantly the collision duration also increases far beyond that of a binary collision. The evolution of the group size and the collision duration are associated with the change of the constitutive behavior of the granular materials. The existence of additional length and time scales demands new formulation for granular flows.