Life at high Deborah number

• Published in: Europhysics letters Vol. 86; no. 6; pp. 64001 - 64001P6
• Main Author: Lauga, E
• Format: Journal Article
• Language: English
• Published: IOP Publishing 01.06.2009; EDP Sciences
• Subjects: 47.57.-s; 47.63.Gd; 47.63.mf
• ISSN: 0295-5075; 1286-4854
• DOI: 10.1209/0295-5075/86/64001

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.