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 large, and the dynamics of the multi-particle interactions have to be considered. Due to the inherent energy dissipation in a particle collision and the consistent rearrangement of particles, there are relaxation times associated with them. In a binary collision, this energy dissipation is represented by coefficient of restitution. In a dense granular system, multi-particle interactions occur frequently. The energy dissipation and system relaxation have to be studied by the consideration of the dynamics in the duration of particle interaction and cannot be represented by a single coefficient of restitution. In this case, the relaxation times must be introduced explicitly. By modification of the network theory for rubber material, a constitutive model for dense granular material is developed based on the dynamics of multi-particle interaction. The finite particle interaction time and system relaxation times are considered.