Life at high Deborah number

TL;DR

This paper analytically investigates microorganism swimming in complex polymeric fluids at high Deborah numbers, revealing that classical constraints like Purcell's scallop theorem no longer apply in such environments.

Contribution

It introduces an analytical framework for understanding swimming in complex fluids at high Deborah numbers, showing the breakdown of Purcell's scallop theorem.

Findings

Swimming kinematics can be expressed via integral equations based on Newtonian solutions.

Purcell's scallop theorem does not hold in polymeric fluids at high Deborah numbers.

Analytical approach applicable to arbitrary complex fluids.

Abstract

In many biological systems, microorganisms swim through complex polymeric fluids, and usually deform the medium at a rate faster than the inverse fluid relaxation time. We address the basic properties of such life at high Deborah number analytically by considering the small-amplitude swimming of a body in an arbitrary complex fluid. Using asymptotic analysis and differential geometry, we show that for a given swimming gait, the time-averaged leading-order swimming kinematics of the body can be expressed as an integral equation on the solution to a series of simpler Newtonian problems. We then use our results to demonstrate that Purcell's scallop theorem, which states that time-reversible body motion cannot be used for locomotion in a Newtonian fluid, breaks down in polymeric fluid environments.