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Two-dimensional flagellar synchronization in viscoelastic fluids

Published online by Cambridge University Press:  08 March 2010

GWYNN J. ELFRING ,
ON SHUN PAK  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
ON SHUN PAK
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

Experimental studies have demonstrated that spermatozoa synchronize their flagella when swimming in close proximity. In a Newtonian fluid, it was shown theoretically that such synchronization arises passively due to hydrodynamic forces between the two swimmers if their waveforms exhibit a front–back geometrical asymmetry. Motivated by the fact that most biological fluids possess a polymeric microstructure, here we address synchronization in a viscoelastic fluid analytically. Using a two-dimensional infinite sheet model, we show that the presence of polymeric stresses removes the geometrical asymmetry constraint and therefore even symmetric swimmers synchronize. Such synchronization occurs on asymptotically faster time scales than in a Newtonian fluid, and the swimmers are seen to be driven into a stable in-phase conformation minimizing the energy dissipated in the surrounding fluid.

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Type
Papers
Information
Journal of Fluid Mechanics , Volume 646 , 10 March 2010 , pp. 505 - 515
Copyright
Copyright © Cambridge University Press 2010

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