Velocity statistics in excited granular media

Abstract

We present an experimental study of velocity statistics for a partial layer of inelastic colliding beads driven by a vertically oscillating boundary. Over a wide range of parameters (accelerations 3-8 times the gravitational acceleration), the probability distribution P (v) deviates measurably from a Gaussian for the two horizontal velocity components. It can be described by P (v) ∼ exp(−|v/v c | 1.5 ), in agreement with a recent theory. The characteristic velocity v c is proportional to the peak velocity of the boundary. The granular temperature, defined as the mean square particle velocity, varies with particle density and exhibits a maximum at intermediate densities. On the other hand, for free cooling in the absence of excitation, we find an exponential velocity distribution. Finally, we examine the sharing of energy between particles of different mass. The more massive particles are found to have greater kinetic energy. PACS: 83.70.Fn, 05.20.Dd, 83.10.Pp Typeset using REVT E X 1 We determine the statistical properties of particles in a vibrated granular medium experimentally. While many similarities between ordinary gases and excited granular media have been found, a fundamental difference is that collisions between particles in granular matter are inelastic. As a consequence, the velocity distribution deviates measurably from a Gaussian, but can be described by P (v) ∼ exp(−|v/v c | 1.5 ) for a large range of parameters where external excitation is sufficiently frequent, in agreement with a recent theory.

Velocity fluctuations in a slowly sheared bubble raft

“…This agreement raises the question of how robust this exponent is, and what features of the system determine its value. Even further, this exponent is in general agreement with similar measurements in granular flow [13,14,15,16], providing further support for a potential generalized description of these systems in terms of a jamming transition [26,27] A clear disagreement between the bubble model and the experiments is the behavior of the second moment at high rates of strain. For the experiments, the second moment of the velocity distribution appears to decrease above a rate of strain of approximately 0.02 s −1 .…”

Temperature probes in binary granular gases

“…The loss of energy due to collisions can be compensated in various ways. In experiments the energy is typically supplied at the boundaries, leading the system to a heterogeneous stationary state [3,4,5,18]. In order to avoid the complication of strong temperature heterogeneities, we will use a homogeneous driving in the form of a "thermostat": in this mechanism (which recently has attracted the attention of many theorists [19,20,21,22,23,24,25]), the particles are submitted, between collisions, to a random force in the form of an uncorrelated white noise (e.g.…”

Collision statistics in sheared inelastic hard spheres

“…The velocity of elastic hard spheres is governed by the Maxwell distribution, which is isotropic and Gaussian. The velocity distribution of flowing inelastic hard spheres is, in general anisotropic [34], and can show significant deviations from the Gaussian distribution, especially when there is clustering.…”