Identifying states in shallow vibrated beds

Discrete and continuum descriptions of shaken granular matter

“…That is, we focus on a vertically vibrated Hele-Shaw cell with the walls parallel to gravity, inside which the grains are located. The first reported classification of the different states present in this geometry was realised by Thomas et al [60], in what would now be considered the low energy injection limit. Research then focused on the wave-like dynamics of the granular bed, and its variations with the frequency and the amplitude of oscillation [61,63].…”

“…When subject to vertical vibrations, grains inside the vertical quasi-2D container develop several distinct stable states. For low energy injections and a high enough number of particles, the granular bed bounces in sync with the vibrating box, and its behaviour is analogous to that of a single particle bouncing on a moving plate [60,61]. This occurs after the maximal acceleration of the bottom plate has exceeded the acceleration of gravity by a considerable amount, providing enough energy for the bed of grains to detach from the moving plate.…”

“…The wavelength of such states roughly decreases as the energy is increased, and seems to depend heavily on dissipation, both due to the filling height and the restitution coefficient [64,65,66]. If, on the other hand, the number of particle layers is low, a gaseous state is found where particle motion is essentially uncorrelated [60].…”

“…The granular bed slightly expands during this period, until it collides again with the moving bottom plate, compresses, and moves together with the box, completing the cycle at the next detachment point. That is, the dynamics of the whole bed is analogous to that of a solid with coefficient of restitution zero [60]. The sudden loss of energy due to the impact with the bottom wall has been referred to as granular damping [120].…”

“…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). This term refers to the periodicity observed in the motion of a granulate in a density-inverted state, i.e.…”