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

Abstract

Experiments are conducted in a two-dimensional mono-layer 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 ($Γ=Aω^2/g <1$), the particles remain attached with 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 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 {\it multi-roll transition}), and its subsequent transition to a granular-gas are two novel findings of this work. We show that the critical shaking intensity ($Γ_{BB}^{LS}$) for "$BB\to LS$"-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 represents a hexagonal-packed structure, the contact network within the LS resembles a liquid-like state. An unsteadiness of the LS has been uncovered wherein the interface (between the floating-cluster and the dilute gas underneath) and the top of the bed are found to oscillate sinusoidally, with its oscillation frequency closely matching with the frequency of external shaking.