Inertial self-propulsion of spherical microswimmers by rotation-translation coupling

TL;DR

This paper investigates how spherical microswimmers can achieve propulsion through rotation-translation coupling, especially when inertia and asymmetric strokes enable overcoming the scallop theorem, with implications for Volvox colonies.

Contribution

It derives velocities for non-axially symmetric strokes including inertia effects, revealing how inertia-driven coupling enables propulsion with time-reversible strokes.

Findings

Inertia contributes to mean speed via rotation-translation coupling.

Asymmetric strokes can break the scallop theorem due to inertia effects.

Optimal flapping frequency and size match realistic Volvox parameters.

Abstract

We study swimming of small spherical particles who regulate fluid flow on their surface by applying tangential squirming strokes. We derive translational and rotational velocities for any given stroke which is not restricted by axial symmetry as assumed usually. The formulation includes inertia of both the fluid and the swimmer, motivated by inertia's relevance for large Volvox colonies. We show that inertial contribution to mean speed comes from dynamic coupling between translation and rotation, which occurs only for strokes that break axial symmetry. Remarkably, this effect enables overcoming the scallop theorem on impossibility of propulsion by time-reversible stroke. We study examples of tangential strokes of axisymmetric travelling wave, and of asymmetric time-reversible flapping. In the latter case, we find that inertia-driven mean speed is optimized for flapping frequency and swimmer's size which fall well within the range of realistic physical values for Volvox colonies. We conjecture that similarly to Paramecium, large Volvox could use time-reversible strokes for inertia-driven swimming coupled with their rotations.