No many-scallop theorem: Collective locomotion of reciprocal swimmers

TL;DR

This paper demonstrates that unlike the classical scallop theorem for single swimmers, multiple reciprocal swimmers can achieve collective propulsion and interactions, revealing new principles for low Reynolds number locomotion.

Contribution

It introduces the concept that the many-scallop theorem does not hold, showing collective swimming and interactions among reciprocal particles using a minimal model and symmetry arguments.

Findings

Two reciprocal particles can swim collectively.

Polar particles experience effective long-range interactions.

Collective locomotion can be realized experimentally with soft particles.

Abstract

To achieve propulsion at low Reynolds number, a swimmer must deform in a way that is not invariant under time-reversal symmetry; this result is known as the scallop theorem. We show here that there is no many-scallop theorem. We demonstrate that two active particles undergoing reciprocal deformations can swim collectively; moreover, polar particles also experience effective long-range interactions. These results are derived for a minimal dimers model, and generalized to more complex geometries on the basis of symmetry and scaling arguments. We explain how such cooperative locomotion can be realized experimentally by shaking a collection of soft particles with a homogeneous external field.