Life at high Deborah number
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.
Keywords
Cite
@article{arxiv.0904.4494,
title = {Life at high Deborah number},
author = {Eric Lauga},
journal= {arXiv preprint arXiv:0904.4494},
year = {2009}
}