The Mathematical Institute, University of Oxford, Eprints Archive

The three sphere swimmer in a nonlinear viscoelastic medium

Curtis, M P and Gaffney, E A (2013) The three sphere swimmer in a nonlinear viscoelastic medium. Physical Review E, 87 (4). 043006.

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Abstract

A simple model for a swimmer consisting of three colinearly linked spheres attached by rods and oscillating out of phase to break reciprocal motion is analyzed. With a prescribed forcing of the rods acting on the three spheres, the swimming dynamics are determined analytically in both a Newtonian Stokes fluid and a zero Reynolds number, nonlinear, Oldroyd-B viscoelastic fluid with Deborah numbers of order one (or less), highlighting the effects of viscoelasticity on the net displacement of swimmer. For instance, the model predicts that the three-sphere swimmer with a sinusoidal, but nonreciprocal, forcing cycle within an Oldroyd-B representation of a polymeric Boger fluid moves a greater distance with enhanced efficiency in comparison with its motility in a Newtonian fluid of the same viscosity. Furthermore, the nonlinear contributions to the viscoelastic constitutive relation, while dynamically nontrivial, are predicted a posteriori to have no effect on swimmer motility at leading order, given a prescribed forcing between spheres.

Item Type:Article
Subjects:A - C > Biology and other natural sciences
Research Groups:Centre for Mathematical Biology
ID Code:1792
Deposited By: Sara Jolliffe
Deposited On:16 Feb 2014 09:26
Last Modified:29 May 2015 19:29

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