Cluster Formation in a Granular Medium Fluidized by Vibrations in Low Gravity

Abstract

We report an experimental study of a "gas" of inelastically colliding particles, excited by vibrations in low gravity. In the case of a dilute granular medium, we observe a spatially homogeneous gaslike regime, the pressure of which scales like the 3͞2 power of the vibration velocity. When the density of the medium is increased, the spatially homogeneous fluidized state is no longer stable but displays the formation of a motionless dense cluster surrounded by low particle density regions. 81.70.Ha, 83.10.Pp, 83.70.Fn Vibrated granular media display striking fluidlike properties: convection and heaping [1,2], period doubling instabilities [3], and parametric extended [4] or localized [5] surface waves. When the vibration is strong enough, the granular medium undergoes a transition to a fluidized state. It looks like a gas of particles that can be described using kinetic theory [6]. The "granular temperature," i.e., the mean kinetic energy per particle, is determined by the balance between the power input due to the external vibration and dissipation by inelastic collisions. Fluidization by vibrations has been studied experimentally [7,8] and numerically [8,9], but no agreement has been found so far for the dependence of the granular temperature on the amplitude and the frequency of external vibrations [10][11][12].One of the most interesting properties of such "granular gases" is the tendency to form clusters. Although this has probably been known since the early observation of planetary rings [13], there exist only a few recent laboratory experiments. One experiment, with a horizontally shaken two-dimensional layer of particles, displayed a cluster formation, but the coherent friction force acting on all the particles was far from being negligible [14]. We performed a similar three-dimensional experiment in the laboratory and observed clustering, but we could not rule out the possibility of a resonance mechanism between the time of flight under gravity and the excitation frequency [15]. Various cluster types in granular flows have also been observed numerically [16]. The mechanisms of cluster formation are an active subject of research that still deserves more study because of its relevance to technical, astrophysical [17], or geophysical [18] applications of granular media. At a more fundamental level, it is of a primary interest to understand the new qualitative behaviors due to inelasticity of collisions, i.e., nonconservation of energy, in kinetic theory.In this Letter, we report a study of the kinetic regimes of a granular medium, fluidized by vibrating its container in a low gravity environment. The motivation for low gravity is to achieve an experimental situation in which inelastic collisions are the only interaction mechanism. The aim of the experiment is to observe new phenomena which result from the inelasticity of the collisions and are thus absent in a usual gas. In the dilute case, we show that the pressure of a granular gas scales like the 3͞2 power of the vibration velocity. When the density o...

Simulations of dense granular gases without gravity with impact-velocity-dependent restitution coefficient

“…One difference between our simulations and the microgravity experiments on granular gases is that it is common to shake the whole container filled with particles in the experiments [4]. One experiment has been recently performed by agitating dilute particles with a piston in low gravity [5].…”

“…These experiments, however, often result in situations quite unlike those 1 eric.falcon@univ-paris-diderot.fr considered theoretically. Some experiments have then been carried out in microgravity [4,5] to limit the number of parameters in the problem in order to make easier the comparison with kinetic theory of dissipative granular gases. However, the interaction between experiments and theory has remained sporadic.…”

Power injected in dissipative systems and the fluctuation theorem

“…Fluidization of a vibrated granular medium has been widely studied in the past years, both experimentally [14][15][16] and numerically [17]. Since a fraction 1 − r 2 of the particle kinetic energy is dissipated during the collisions (r is the restitution coefficient, 0 < r < 1), a stationary fluidized state necessitates a mean external flow of energy, P , into the system.…”

Experimental Study of a Granular Gas Fluidized by Vibrations

“…We did observe clustering, but we could not rule out a lock-in mechanism involving the time scale connected with gravity and the period of vibration [14]. We thus repeated this experiment in a low-gravity environment, where inelastic collisions were the only interaction mechanism, and observed a motionless dense cluster that confirms that the inelasticity of collisions alone can generate clustering [15]. This paper is devoted to the study of the low-density situation, where clustering does not occur.…”