Universal velocity distributions in an experimental granular fluid

TL;DR

This study experimentally investigates the velocity distribution in a uniformly heated granular fluid, revealing universal behavior and deviations from Maxwell-Boltzmann, consistent with recent theoretical predictions.

Contribution

First experimental measurement of Sonine polynomial deviations in the velocity distribution of a driven granular fluid, confirming theoretical models.

Findings

Velocity distribution is universal across various filling fractions.

Tail of the distribution scales as exp(constant × c^{-3/2}).

Central region deviates from Maxwell-Boltzmann by a Sonine polynomial.

Abstract

We present experimental results on the velocity statistics of a uniformly heated granular fluid, in a quasi-2D configuration. We find the base state, as measured by the single particle velocity distribution $f(c)$, to be universal over a wide range of filling fractions and only weakly dependent on all other system parameters. There is a consistent overpopulation in the distribution's tails, which scale as $f\propto\exp(\mathrm{const.}\times c^{-3/2})$. More importantly, the high probability central region of $f(c)$, at low velocities, deviates from a Maxwell-Boltzmann by a second order Sonine polynomial with a single adjustable parameter, in agreement with recent theoretical analysis of inelastic hard spheres driven by a stochastic thermostat. To our knowledge, this is the first time that Sonine deviations have been measured in an experimental system.