Pattern transition, microstructure, and dynamics in a two-dimensional vibrofluidized granular bed.

Abstract

Experiments are conducted in a two-dimensional monolayer vibrofluidized bed of glass beads, with a goal to understand the transition scenario and the underlying microstructure and dynamics in different patterned states. At small shaking accelerations (Γ=Aω^{2}/g<1, where A and ω=2πf are the amplitude and angular frequency of shaking and g is the gravitational acceleration), the particles remain attached to the base of the vibrating container; this is known as the solid bed (SB). With increasing Γ (at large enough shaking amplitude A/d) and/or with increasing A/d (at large enough Γ), the sequence of transitions/bifurcations unfolds as follows: SB ("solid bed") to BB ("bouncing bed") to LS ("Leidenfrost state") to "2-roll convection" to "1-roll convection" and finally to a gas-like state. For a given length of the container, the coarsening of multiple convection rolls leading to the genesis of a "single-roll" structure (dubbed the multiroll transition) and its subsequent transition to a granular gas are two findings of this work. We show that the critical shaking intensity (Γ_{BB}^{LS}) for the BB→LS transition has a power-law dependence on the particle loading (F=h_{0}/d, where h_{0} is the number of particle layers at rest and d is the particle diameter) and the shaking amplitude (A/d). The characteristics of BB and LS states are studied by calculating (i) the coarse-grained density and temperature profiles and (ii) the pair correlation function. It is shown that while the contact network of particles in the BB state represents a hexagonal-packed structure, the contact network within the "floating cluster" of the LS resembles a liquid-like state. An unsteadiness of the Leidenfrost state has been uncovered wherein the interface (between the floating cluster and the dilute collisional layer underneath) and the top of the bed are found to oscillate sinusoidally, with the oscillation frequency closely matching the frequency of external shaking. Therefore, the granular Leidenfrost state is a period-1 wave as is the case for the BB state.