Stochastic Nature of Particle Collisions and its Impact on Granular Material Properties

The dynamics of rapid granular flows is governed by dissipative interactions of particles with each other and with the system walls. To adequately describe these interactions, roughness and particle shape must be taken into account. The coefficient of restitution for arbitrary particles thus depends not only on material properties and impact velocity but also on the angular orientation at the instant of the collision. By measurements of the coefficient of restitution from the sound signal emitted by a sphere bouncing repeatedly off the ground, it was found that small deviations from the perfect shape of the sphere lead to large measurement errors. Using stochastic methods, the effective coefficient of restitution for the collision of a rough sphere with a plane was described as a fluctuating quantity, characterized by a rather uncommon probability density function. It was shown that modelling the coefficient of restitution as a stochastic variable significantly affects the dynamics of particles under rapid granular flows. The decay of temperature of rapid granular flows in the homogeneous cooling state deviates from Haff’s law for gases of particles interacting via a constant coefficient of restitution also from the scaling law for gases of viscoelastic particles.