Granular Brownian motion with dry friction

TL;DR

This study investigates the effects of Coulomb dry friction on granular Brownian motion through experiments with a rotating probe in a granular gas, comparing results with theoretical models across different collision regimes.

Contribution

It provides experimental validation of a linear Boltzmann equation with Coulomb friction, bridging high and low collision frequency limits with theoretical predictions.

Findings

Good agreement between theory and experiment at high and low collision frequencies.

Deviations at very small velocities due to real bearings not perfectly modeling Coulomb friction.

Experimental velocity distributions match theoretical models in the respective limits.

Abstract

The interplay between Coulomb friction and random excitations is studied experimentally by means of a rotating probe in contact with a stationary granular gas. The granular material is independently fluidized by a vertical shaker, acting as a 'heat bath' for the Brownian-like motion of the probe. Two ball bearings supporting the probe exert nonlinear Coulomb friction upon it. The experimental velocity distribution of the probe, autocorrelation function, and power spectra are compared with the predictions of a linear Boltzmann equation with friction, which is known to simplify in two opposite limits: at high collision frequency, it is mapped to a Fokker-Planck equation with nonlinear friction, whereas at low collision frequency, it is described by a sequence of independent random kicks followed by friction-induced relaxations. Comparison between theory and experiment in these two limits shows good agreement. Deviations are observed at very small velocities, where the real bearings are not well modeled by Coulomb friction.