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Synchronization of flexible sheets

Published online by Cambridge University Press:  22 March 2011

GWYNN J. ELFRING  and
ERIC LAUGA
GWYNN J. ELFRING
Affiliation:
Department of Mechanical and Aerospace Engineering, University of California San Diego, 9500 Gilman Drive, La Jolla, CA 92093-0411, USA
ERIC LAUGA*
Affiliation:
Department of Mechanical and Aerospace Engineering, University of California San Diego, 9500 Gilman Drive, La Jolla, CA 92093-0411, USA
*
†Email address for correspondence: elauga@ucsd.edu
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Abstract

When swimming in close proximity, some microorganisms such as spermatozoa synchronize their flagella. Previous work on swimming sheets showed that such synchronization requires a geometrical asymmetry in the flagellar waveforms. Here we inquire about a physical mechanism responsible for such symmetry breaking in nature. Using a two-dimensional model, we demonstrate that flexible sheets with symmetric internal forcing deform when interacting with each other via a thin fluid layer in such a way as to systematically break the overall waveform symmetry, thereby always evolving to an in-phase conformation where energy dissipation is minimized. This dynamics is shown to be mathematically equivalent to that obtained for prescribed waveforms in viscoelastic fluids, emphasizing the crucial role of elasticity in symmetry breaking and synchronization.

JFM classification

Biological Fluid Dynamics: Biological Fluid Dynamics Low-Reynolds-number flows: Low-Reynolds-number flows Biological Fluid Dynamics: Micro-organism dynamics
Type
Papers
Information
Journal of Fluid Mechanics , Volume 674 , 10 May 2011 , pp. 163 - 173
Copyright
Copyright © Cambridge University Press 2011

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