Synchronization of rotating helices by hydrodynamic interactions

TL;DR

This study investigates whether hydrodynamic interactions alone can cause synchronization of rotating helices, similar to bacterial flagella, by modeling two rigid helices driven by constant torques and fixed in traps.

Contribution

It demonstrates that hydrodynamic interactions can synchronize rotating helices in a low Reynolds number regime, depending on trap stiffness, providing insight into bacterial flagella bundling.

Findings

Hydrodynamic interactions lead to synchronization at finite trap stiffness.

Synchronization speed decreases as trap stiffness increases.

No synchronization occurs when trap stiffness approaches infinity.

Abstract

Some types of bacteria use rotating helical flagella to swim. The motion of such organisms takes place in the regime of low Reynolds numbers where viscous effects dominate and where the dynamics is governed by hydrodynamic interactions. Typically, rotating flagella form bundles, which means that their rotation is synchronized. The aim of this study is to investigate whether hydrodynamic interactions can be at the origin of such a bundling and synchronization. We consider two stiff helices that are modelled by rigidly connected beads, neglecting any elastic deformations. They are driven by constant and equal torques, and they are fixed in space by anchoring their terminal beads in harmonic traps. We observe that, for finite trap strength, hydrodynamic interactions do indeed synchronize the helix rotations. The speed of phase synchronization decreases with increasing trap stiffness. In the limit of infinite trap stiffness, the speed is zero and the helices do not synchronize.