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

TL;DR

This study investigates the transition scenarios, microstructure, and dynamics in a two-dimensional vibrofluidized granular bed, revealing novel multi-roll transition and detailed microstructural changes across different states.

Contribution

It provides new insights into the transition sequence, microstructure, and oscillatory behavior in vibrofluidized granular beds, including the discovery of multi-roll transition and detailed state characterizations.

Findings

Identified the transition sequence from solid bed to gas-like state.

Discovered the multi-roll coarsening and transition to granular gas as novel phenomena.

Showed the microstructure differences between bouncing bed and Leidenfrost state.

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 ($\Gamma=A\omega^2/g <1$), the particles remain attached with the base of the vibrating container -- this is known as the solid bed (SB). With increasing $\Gamma$ (at large enough shaking amplitude $A/d$) and/or with increasing $A/d$ (at large enough $\Gamma$), 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 ($\Gamma_{BB}^{LS}$) 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.