From the granular Leidenfrost state to buoyancy-driven convection

TL;DR

This study investigates the transition from a granular Leidenfrost state to buoyancy-driven convection in vibrated grains, revealing critical behavior, transient convective states, and a new oscillator-based interpretation of the transition.

Contribution

It introduces a simulational analysis of precursors to the granular convection transition, proposing a novel amplitude equation and oscillator analogy for the process.

Findings

Critical behavior in structure factor near transition

Transient convective states with increasing correlation time

Amplitude modulations described by a quintic supercritical equation

Abstract

Grains inside a vertically vibrated box undergo a transition from a density inverted and horizontally homogeneous state, referred to as the granular Leidenfrost state, to a buoyancy-driven convective state. We perform a simulational study of the precursors of such a transition, and quantify their dynamics as the bed of grains is progressively fluidized. The transition is preceded by transient convective states, which increase their correlation time as the transition point is approached. Increasingly correlated convective flows lead to density fluctuations, as quantified by the structure factor, that also shows critical behaviour near the transition point. The amplitude of the modulations in the vertical velocity field are seen to be best described by a quintic supercritical amplitude equation with an additive noise term. The validity of such an amplitude equation, and previously observed collective semi-periodic oscillations of the bed of grains, suggests a new interpretation of the transition analogous to a coupled chain of vertically vibrated damped oscillators. Increasing the size of the container shows metastability of convective states, as well as an overall invariant critical behaviour close to the transition.