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.

References in corpus (3)

• Propulsion in a viscoelastic fluid
• Theory of swimming filaments in viscoelastic media
• Flapping motion and force generation in a viscoelastic fluid

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• Reciprocal microswimmers in a viscoelastic fluid
• Load response of shape-changing microswimmers scales with their energy efficiency
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• Dynamics of a simple model microswimmer in an anisotropic fluid: implications for alignment behavior and active transport in a nematic liquid crystal