Rotation of slender swimmers in isotropic-drag media

TL;DR

This paper reveals that slender swimmers can achieve net rotation in isotropic drag media, contrasting with the necessity of drag anisotropy for translation, through theoretical analysis and illustrative examples.

Contribution

It demonstrates that net rotation is possible in isotropic drag media, challenging the traditional view that anisotropic drag is essential for all swimming motions.

Findings

Net rotation can occur under isotropic drag conditions.

Hydrodynamic forces play different roles in translation and rotation.

Examples include a three-rod swimmer and a bacterium with helical flagella.

Abstract

The drag anisotropy of slender filaments is a critical physical property allowing swimming in low-Reynolds number flows, and without it linear translation is impossible. Here we show that, in contrast, net rotation can occur under isotropic drag. We first demonstrate this result formally by considering the consequences of the force- and torque-free conditions on swimming bodies and we then illustrate it with two examples (a simple swimmers made of three rods and a model bacterium with two helical flagellar filaments). Our results highlight the different role of hydrodynamic forces in generating translational vs.~rotational propulsion.