Spontaneous formation of density waves in granular matter under swirling excitation

TL;DR

This paper investigates how granular materials spontaneously form density waves under horizontal swirling excitation, revealing a threshold-driven clustering process influenced by local density-dependent grain velocity.

Contribution

It introduces a phenomenological model explaining the density wave formation and validates it with discrete element method simulations, highlighting the role of local density-dependent grain velocity.

Findings

Density waves form beyond a certain oscillation amplitude.

The dense regions travel faster than the driving frequency.

The transition amplitude depends non-monotonically on global density.

Abstract

We study here the spontaneous clustering of a submonolayer of grains under horizontal circular shaking. The clustering of grains occurs when increasing the oscillation amplitude beyond a threshold. The dense area travels in a circular fashion at the driving frequency, even exceeds the speed of driving. It turns out that the observed clustering is due to the formation of density wave. The analysis of a phenomenological model shows that the instability of the uniform density profile arises by increasing the oscillation amplitude and captures the non-monotonic dependence of the transition amplitude of the clustering on the global density of the system. Here, the key ingredient is that the velocity of individual grains increases with the local density. The interplay of dissipative particle-particle interaction and the frictional driving of the substrate results into this dependence, which is tested with discrete element method simulations.