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A spherical squirming swimmer in unsteady Stokes flow

Published online by Cambridge University Press:  16 April 2013

Kenta Ishimoto
Kenta Ishimoto*
Affiliation:
Research Institute for Mathematical Sciences, Kyoto University, Kyoto 606-8502, Japan
*
†Email address for correspondence: ishimoto@kurims.kyoto-u.ac.jp
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Abstract

The motion of a spherical squirmer in unsteady Stokes flow is investigated for a deeper understanding of unsteady inertial effects on swimming micro-organisms and differences of swimming strokes between a wave pattern and a flapping motion. An asymptotic analysis with respect to the small amplitude and the small inertia is performed, and the average swimming velocity after a long period of time under an assumption of a time-periodic stroke is obtained. This analysis shows that the scallop theorem still holds in a long-time asymptotic sense for tangential deformation, but that the time variation of the shape generates a net velocity even for a reciprocal swimmer. It is also found that the inertial effects on the swimming velocity are significant for a flapping swimmer, as contrasted with little influence on that of a swimmer with a wave pattern. The inertial effect is also illustrated with a simple squirmer, so that a reciprocal motion can be almost an optimal stroke under a constraint on energy consumption.

JFM classification

Biological Fluid Dynamics: Biological Fluid Dynamics Biological Fluid Dynamics: Micro-organism dynamics Biological Fluid Dynamics: Propulsion
Type
Papers
Information
Journal of Fluid Mechanics , Volume 723 , 25 May 2013 , pp. 163 - 189
Copyright
©2013 Cambridge University Press 

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