Collision statistics of driven granular materials

TL;DR

This study experimentally investigates the collision dynamics, energy transfer, and statistical properties of driven granular particles on an inclined plane, revealing non-Gaussian velocity distributions and clustering behaviors.

Contribution

It provides detailed measurements of collision statistics, energy inelasticity, and spatial-temporal correlations in driven granular materials, highlighting the role of rotational degrees and deviations from elastic sphere models.

Findings

Broad distribution of restitution coefficients.

Energy inelasticity can exceed one, indicating rotational energy transfer.

Velocity distributions are strongly non-Gaussian and show clustering.

Abstract

We present an experimental investigation of the statistical properties of spherical granular particles on an inclined plane that are excited by an oscillating side-wall. The data is obtained by high-speed imaging and particle tracking techniques. We identify all particles in the system and link their positions to form trajectories over long times. Thus, we identify particle collisions to measure the effective coefficient of restitution and find a broad distribution of values for the same impact angles. We find that the energy inelasticity can take on values greater than one, which implies that the rotational degrees play an important role in energy transfer. We also measure the distance and the time between collision events in order to directly determine the distribution of path lengths and the free times. These distributions are shown to deviate from expected theoretical forms for elastic spheres, demonstrating the inherent clustering in this system. We describe the data with a two-parameter fitting function and use it to calculated the mean free path and collision time. We find that the ratio of these values is consistent with the average velocity. The velocity distribution are observed to be strongly non-Gaussian and do not demonstrate any apparent universal behavior. We report the scaling of the second moment, which corresponds to the granular temperature, and higher order moments as a function of distance from the driving wall. Additionally, we measure long time correlation functions in both space and in the velocities to probe diffusion in a dissipative gas.