Hard-sphere limit of soft-sphere model for granular materials: Stiffness   dependence of steady granular flow
  Dynamical behavior of steady granular flow is investigated numerically in the inelastic hard sphere limit of the soft sphere model. We find distinctively different limiting behaviors for the two flow regimes, i.e., the collisional flow and the frictional flow. In the collisional flow, the hard sphere limit is straightforward; the number of collisions per particle per unit time converges to a finite value and the total contact time fraction with other particles goes to zero. For the frictional flow, however, we demonstrate that the collision rate diverges as the power of the particle stiffness so that the time fraction of the multiple contacts remains finite even in the hard sphere limit although the contact time fraction for the binary collisions tends to zero. 
Namiko Mitarai and Hiizu Nakanishi