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A two-dimensional model of low-Reynolds number swimming beneath a free surface

Published online by Cambridge University Press:  29 June 2011

DARREN CROWDY ,
SUNGYON LEE ,
OPHIR SAMSON ,
ERIC LAUGA  and
A. E. HOSOI
DARREN CROWDY*
Affiliation:
Department of Mathematics, Imperial College, London SW7 2AZ, UK
SUNGYON LEE
Affiliation:
Hatsopoulos Microfluids Laboratory, Department of Mechanical Engineering, Massachusetts Institute of Technology, 77 Massachusetts Avenue, Cambridge, MA 02139, USA
OPHIR SAMSON
Affiliation:
Department of Mathematics, Imperial College, London SW7 2AZ, UK
ERIC LAUGA
Affiliation:
Department of Mechanical and Aerospace Engineering, University of California San Diego, 9500 Gilman Drive, La Jolla CA 92093-0411, USA
A. E. HOSOI
Affiliation:
Hatsopoulos Microfluids Laboratory, Department of Mechanical Engineering, Massachusetts Institute of Technology, 77 Massachusetts Avenue, Cambridge, MA 02139, USA
*
†Email address for correspondence: d.crowdy@imperial.ac.uk
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Abstract

Biological organisms swimming at low-Reynolds number are often influenced by the presence of rigid boundaries and soft interfaces. In this paper, we present an analysis of locomotion near a free surface with surface tension. Using a simplified two-dimensional singularity model and combining a complex variable approach with conformal mapping techniques, we demonstrate that the deformation of a free surface can be harnessed to produce steady locomotion parallel to the interface. The crucial physical ingredient lies in the nonlinear hydrodynamic coupling between the disturbance flow created by the swimmer and the free boundary problem at the fluid surface.

JFM classification

Interfacial Flows (free surface): Interfacial Flows (free surface) Nonlinear Dynamical Systems: Low-dimensional models
Type
Papers
Information
Journal of Fluid Mechanics , Volume 681 , 25 August 2011 , pp. 24 - 47
Copyright
Copyright © Cambridge University Press 2011

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