Volume 86, Number 6, June 2009
|Number of page(s)
|Electromagnetism, Optics, Acoustics, Heat Transfer, Classical Mechanics, and Fluid Dynamics
|01 July 2009
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: email@example.com
Accepted: 29 May 2009
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.
PACS: 47.63.Gd – Swimming microorganisms / 47.63.mf – Low-Reynolds-number motions / 47.57.-s – Complex fluids and colloidal systems
© EPLA, 2009
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