The effect of inter-particle contact time in granular flows - a network theory

摘要

In a kinetic theory, it is usually assumed that the time duration of particle collision is vanishingly small and only binary collisions are considered. The validity of these assumptions depends on the ratio of collision time to mean free flight time. If this ratio is small, the kinetic theory description is appropriate. In a dense system, however, this ratio is usually not negligible, and the dynamics of the multi-particle interactions must be considered. For instance, during a collision, the contacting pair usually has a relative tangential velocity that causes a rotation in the direction of the collisional force. This implies a dependence of the granular stress on the vorticity of the mean flow field. Furthermore the inherent energy dissipation in a particle collision and the continuous rearrangement of particles also have relaxation times associated with them. In a binary collision, energy dissipation is represented by coefficient of restitution. In a dense granular system, multi-particle interactions occur frequently. The energy dissipation and system relaxation must be studied by considering the dynamics occurring during particle interactions. This cannot be represented by a single coefficient of restitution, and thus relaxation times must be introduced explicitly. By modification of network theory for rubber-like material, a constitutive model for dense granular material is developed based on the dynamics of multi-particle interaction. Finite particle interaction timernand system relaxation times are considered.rnIn numerical simulations performed for this paper, we study flows of granular particles coated with resin. To account for both the elasticity of the particles and the viscosity of the resin between particles, the force between a pair of contacting particles is modeled by a serial connection of a spring and a dashpot. In the limit of small relaxation time relative to the time scale of macroscopic strain rate, the effective viscosity of a granular system is calculated from discrete element simulations. At low particle concentrations, the effective viscosity is found to be proportional to shear rate, while at a high particle concentration the viscosity is independent of the shear rate. The physical reason for this transition is explained. Formation of shear bands occurs at large shear rates in dense systems.