Synchronization of wave-propelled capillary spinners

TL;DR

This study investigates how wave-propelled chiral spinners on a vibrating liquid bath synchronize their rotation through hydrodynamic interactions, revealing complex behaviors influenced by their spacing and intrinsic differences.

Contribution

It introduces a hydrodynamic wave model explaining synchronization phenomena among multiple wave-propelled spinners, highlighting the role of wave coupling and initial conditions.

Findings

Spinners can synchronize their rotation with phase differences depending on spacing.

Synchronization can cease when coupling strength exceeds a threshold.

Non-identical spinners can also synchronize if their differences are small.

Abstract

When a millimetric body is placed atop a vibrating liquid bath, the relative motion between the object and interface generates outward propagating waves with an associated momentum flux. Prior work has shown that isolated chiral objects, referred to as spinners, can thus rotate steadily in response to their self-generated wavefield. Here, we consider the case of two co-chiral spinners held at a fixed spacing from one another but otherwise free to interact hydrodynamically through their shared fluid substrate. Two identical spinners are able to synchronize their rotation, with their equilibrium phase difference sensitive to their spacing and initial conditions, and even cease to rotate when the coupling becomes sufficiently strong. Non-identical spinners can also find synchrony provided their intrinsic differences are not too disparate. A hydrodynamic wave model of the spinner interaction is proposed, recovering all salient features of the experiment. In all cases, the spatially periodic nature of the capillary wave coupling is directly reflected in the emergent equilibrium behaviors.