The dynamics of thin vibrated granular layers

Abstract

We describe a series of experiments and computer simulations on vibrated granular media in a geometry chosen to eliminate gravitationally induced settling. The system consists of a collection of identical spherical particles on a horizontal plate vibrating vertically, with or without a confining lid. Previously reported results are reviewed, including the observation of homogeneous, disordered liquid-like states, an instability to a 'collapse' of motionless spheres on a perfect hexagonal lattice, and a fluctuating, hexagonally ordered state. In the presence of a confining lid we see a variety of solid phases at high densities and relatively high vibration amplitudes, several of which are reported for the first time in this article. The phase behavior of the system is closely related to that observed in confined hard-sphere colloidal suspensions in equilibrium, but with modifications due to the effects of the forcing and dissipation. We also review measurements of velocity distributions, which range from Maxwellian to strongly non-Maxwellian depending on the experimental parameter values. We describe measurements of spatial velocity correlations that show a clear dependence on the mechanism of energy injection. We also report new measurements of the velocity autocorrelation function in the granular layer and show that increased inelasticity leads to enhanced particle selfdiffusion.

Effect of inelasticity on the phase transitions of a thin vibrated granular layer

“…Ordered phases observed in non-cohesive granular media demonstrate both profound similarities to and differences from those observed in elastic systems, where the results of equilibrium statistical mechanics apply [1,2,3,4,5]. Controlled experiments on simple model systems are necessary to develop and test extensions of statistical mechanics to nonequilibrium systems [6].…”

“…Controlled experiments on simple model systems are necessary to develop and test extensions of statistical mechanics to nonequilibrium systems [6]. In previous research [3,7,8,9], we have reported the existence of ordered phases in vibrated dense thin layers of identical metal spheres. For monolayers at high densities, hexagonal ordering is observed [7], and recent results from our group [9] and, in a somewhat different setup, Reis et al [1], show that the crystallization of the ordered phase can be directly mapped onto the analogous 2D equilibrium system.…”

Discrete and continuum descriptions of shaken granular matter

“…Spontaneous phase-separation in vertically vibrated monolayers inspired a whole range of experiments, theory and simulations [30,31,38,39,40,41,42,43]. Emerging patterns and localized structures yielded interesting relations with general dynamics based on the amplitude of the observed patterns [44,29,45,46].…”

“…Vibrated beds of granular materials present a wide range of different behaviours: phase separation [38,40], Faraday-like pattern formation instabilities [111,64], heap formation and convection [112,113], segregation [114,59], clustering [91] and periodic cluster expansions [56], among many others. These systems generally present a remarkable collection of distinct nonequilibrium inhomogeneous stable states for relatively small changes in the energy injection parameters.…”

“…They can exist in numerous states, many of which are analogous to those of a molecular material. Examples include convection [121], phase separation [38,40], Faraday-like patterns [61], and the granular Leidenfrost state [15], wherein a dense region of grains is supported from below by a dilute, energetic gaseous region, in direct analogy to the eponymous state observed in classical fluids [74]. Although the vertically vibrated narrow box geometry has been extensively studied [60,79,71,122], recent simulational and theoretical work [123] has suggested the presence of a previously unobserved phenomenon: low-frequency oscillations (LFOs).…”