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Abstract: In many biological systems, microorganisms swim through complex polymericfluids, and usually deform the medium at a rate faster than the inverse fluidrelaxation time. We address the basic properties of such life at high Deborahnumber analytically by considering the small-amplitude swimming of a body in anarbitrary complex fluid. Using asymptotic analysis and differential geometry,we show that for a given swimming gait, the time-averaged leading-orderswimming kinematics of the body can be expressed as an integral equation on thesolution to a series of simpler Newtonian problems. We then use our results todemonstrate that Purcell-s scallop theorem, which states that time-reversiblebody motion cannot be used for locomotion in a Newtonian fluid, breaks down inpolymeric fluid environments.

Autor: Eric Lauga


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