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Slender axisymmetric Stokesian swimmers

Published online by Cambridge University Press:  01 April 2014

S. Toppaladoddi  and
N. J. Balmforth
S. Toppaladoddi*
Affiliation:
Mathematical Institute, University of Oxford, Andrew Wiles Building, Woodstock Road, Oxford OX2 6GG, UK Department of Geology & Geophysics, Yale University, P.O. Box 208109, New Haven, CT 06520-8109, USA
N. J. Balmforth
Affiliation:
Department of Mathematics, University of British Columbia, 1984 Mathematics Road, Vancouver, BC, V6T 1Z2, Canada
*
†Email address for correspondence: srikanth.toppaladoddi@yale.edu
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Abstract

Slender-body theory is used to study axisymmetric swimmers propelled by motions of their surfaces. To leading order, the locomotion speed is given by an integral involving the fluid velocity at the surface of the slender body. Locomotion speeds are calculated for fixed-shape swimmers with prescribed fluid surface velocities and for impermeable swimmers driven by propagating surface waves. Next, the internal mechanics is considered, modelling the swimmer as a viscous fluid bounded by an elastic shell. Prescribed forces are exerted on the shell to drive both the internal and external fluid flow and the surface waves. The internal fluid mechanics is determined using lubrication theory. Locomotion speeds are calculated for transverse and longitudinal waves of surface deformation, and the efficiency of the motions is determined. Transverse surface waves are both weaker and less efficient at driving locomotion than longitudinal waves. The results indicate how estimates of swimming speed based on nearly spherical swimmers with low-amplitude surface waves can be adapted for slender swimmers with nonlinear surface deformations.

JFM classification

Low-Reynolds-number flows: Low-Reynolds-number flows Biological Fluid Dynamics: Propulsion Low-Reynolds-number flows: Slender-body theory
Type
Papers
Information
Journal of Fluid Mechanics , Volume 746 , 10 May 2014 , pp. 273 - 299
Copyright
© 2014 Cambridge University Press 

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