Minimal Model for Hydrodynamic Synchronization

TL;DR

This paper demonstrates through experiments and modeling that hydrodynamic interactions can synchronize rotating paddles in viscous fluids, with synchronization dependent on paddle symmetry and shaft flexibility.

Contribution

It introduces a minimal hydrodynamic model showing synchronization arises from fluid interactions and shaft flexibility, supported by experiments and theoretical analysis.

Findings

Synchronization occurs only with flexible shafts.

Phase difference depends on paddle symmetry.

Scaling laws for synchronization time are derived.

Abstract

Motivated by the observed coordination of nearby beating cilia, we use a scale model experiment to show that hydrodynamic interactions can cause synchronization between rotating paddles driven at constant torque in a very viscous fluid. Synchronization is only observed when the shafts supporting the paddles have some flexibility. The phase difference in the synchronized state depends on the symmetry of the paddles. We use the method of regularized stokeslets to model the paddles and find excellent agreement with the experimental observations. We also use a simple analytic theory based on far-field approximations to derive scaling laws for the synchronization time as a function of paddle separation.