Active particles in linear viscoelastic fluids and the scallop theorem

TL;DR

This paper derives a formula for active particle dynamics in viscoelastic fluids and shows that certain fluid models allow for net motion under reciprocal actuation, breaking the scallop theorem.

Contribution

It introduces a modified reciprocal theorem for inertialess active particles in linear viscoelastic fluids and identifies conditions where the scallop theorem is violated.

Findings

Active particles in Maxwell-like fluids behave like in Newtonian fluids.

Jeffreys-like fluids with retardation can enable net motion under reciprocal actuation.

The scallop theorem can be broken in specific viscoelastic fluid models.

Abstract

We derive a general formula for the inertialess dynamics of active particles in linear viscoelastic fluids by means of a modified reciprocal theorem. We then demonstrate that force-free active particles in Maxwell-like linear viscoelastic fluids with no retardation have exactly the same dynamics as in Newtonian fluids. In contrast, active particles in Jeffreys-like fluids with retardation can display markedly different dynamics, including net motion under reciprocal actuation thereby breaking the scallop theorem.