Life at high Deborah number

Department of Mechanical and Aerospace Engineering, University of California San Diego 9500 Gilman Dr., La Jolla, CA 92093-0411, USA

Corresponding author: elauga@ucsd.edu

Received: 20 April 2009
Accepted: 29 May 2009

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.