Effect of particle size on energy dissipation in viscoelastic granular collisions.

We analyze the scaling properties of the Hertz-Kuwabara-Kono (HKK) model, which is commonly used in numerical simulations to describe the collision of macroscopic noncohesive viscoelastic spherical particles. Parameters describing the elastic and viscous properties of the material, its density, and the size of the colliding particles affect the restitution coefficient ɛ and collision time τ only via appropriate rescaling but do not change the shape of ɛ(v) and τ(v) curves, where v is the impact velocity. We have measured the restitution coefficient experimentally for relatively large (1 cm) particles of microcrystalline cellulose to deduce material parameters and then to predict collision properties for smaller microcrystalline cellulose (MCC) particles by assuming the scaling properties of the HKK model. In particular, we demonstrate that the HKK model predicts the restitution coefficient of microscopic particles of about 100 μm to be considerably smaller than that of the macroscopic particles. In fact, the energy dissipation is so large that only completely inelastic collisions occur for weakly attractive particles. We propose a straightforward self-consistent extension to the Johnson-Kendall-Roberts (JKR) model to include dissipative forces and discuss the implications of our findings for the behavior of experimental powder systems.