Getting drowned in a swirl: deformable bead-spring model microswimmers in external flow fields

TL;DR

This study models deformable microswimmers in a swirl flow, revealing that two-bead swimmers circle while three- and four-bead swimmers tend to drown, deforming their orbits and exhibiting complex rotational behaviors.

Contribution

It introduces a simple theoretical model for deformable microswimmers in flow fields, analyzing their behavior and orbit deformation in a circular swirl.

Findings

Two-bead swimmers circle with slight drift outward.

Triangular and square swimmers tend to drown in the swirl.

Swimmers exhibit deformed 'egg-shaped' orbits and flow-induced rotations.

Abstract

Deformability is a central feature of many types of microswimmers, e.g. for artificially generated self-propelled droplets. Here, we analyze deformable bead-spring microswimmers in an externally imposed solvent flow field as simple theoretical model systems. We focus on their behavior in a circular swirl flow in two spatial dimensions. Linear (straight) two-bead swimmers are found to circle around the swirl with a slight drift to the outside with increasing activity. In contrast to that, we observe for triangular three-bead or square-like four-bead swimmers a tendency of being drawn into the swirl and finally getting drowned, although a radial inward component is absent in the flow field. During one cycle around the swirl, the self-propulsion direction of an active triangular or square-like swimmer remains almost constant, while their orbits become deformed exhibiting an ``egg-like'' shape. Over time, the swirl flow induces slight net rotations of these swimmer types, which leads to net rotations of the egg-shaped orbits. Interestingly, in certain cases, the orbital rotation changes sense when the swimmer approaches the flow singularity. Our predictions can be verified in real-space experiments on artificial microswimmers.