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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.

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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References

REFERENCES

Bird, R. B., Armstrong, R. C. & Hassager, O. 1987 Dynamics of Polymeric Liquids, 2nd edn., vol. 1. Wiley-Interscience.Google Scholar
Brennen, C. & Winet, H. 1977 Fluid mechanics of propulsion by cilia and flagella. Annu. Rev. Fluid Mech. 9, 339–398.Google Scholar
Chaudhury, T. K. 1979 On swimming in a visco-elastic liquid. J. Fluid Mech. 95, 189–197.CrossRefGoogle Scholar
Dunn, P. F. & Picologlou, B. F. 1976 Viscoelastic properties of cumulus oophorus. Biorheology 13, 379–384.Google Scholar
Elfring, G. J. & Lauga, E. 2009 Hydrodynamic phase locking of swimming microorganisms. Phys. Rev. Lett. 103, 088101.CrossRefGoogle ScholarPubMed
Fauci, L. J. 1990 Interaction of oscillating filaments: a computational study. J. Comput. Phys. 86, 294–313.CrossRefGoogle Scholar
Fauci, L. J. & Dillon, R. 2006 Biofluidmechanics of reproduction. Annu. Rev. Fluid Mech. 38, 371–394.CrossRefGoogle Scholar
Fauci, L. J. & McDonald, A. 1995 Sperm motility in the presence of boundaries. Bull. Math. Biol. 57, 679–699.CrossRefGoogle ScholarPubMed
Fu, H. C., Powers, T. R. & Wolgemuth, C. W. 2007 Theory of swimming filaments in viscoelastic media. Phys. Rev. Lett. 99, 258101.Google Scholar
Fulford, G. R., Katz, D. F. & Powell, R. L. 1998 Swimming of spermatozoa in a linear viscoelastic fluid. Biorheology 35, 295–309.CrossRefGoogle Scholar
Kim, S. & Karrila, S. J. 1991 Microhydrodynamics: Principles and Selected Applications. Butterworth-Heineman.Google Scholar
Lauga, E. 2007 Propulsion in a viscoelastic fluid. Phys. Fluids 19, 083104.Google Scholar
Lauga, E. 2009 Life at high Deborah number. Europhys. Lett. 86, 64001.Google Scholar
Lauga, E. & Powers, T. R. 2009 The hydrodynamics of swimming microorganisms. Rep. Prog. Phys. 72, 096601.CrossRefGoogle Scholar
Lighthill, J. 1976 Flagellar hydrodynamics: the John von Neumann lecture, 1975. SIAM Rev. 18, 161–230.Google Scholar
Oldroyd, J. G. 1950 On the formulation of rheological equations of state. Proc. R. Soc. Lond. A 200, 523–541.Google Scholar
Purcell, E. M. 1977 Life at low Reynolds number. Am. J. Phys. 45, 11.CrossRefGoogle Scholar
Sturges, L. D. 1981 Motion induced by a waving plate. J. Non-Newtonian Fluid Mech. 8, 357–364.CrossRefGoogle Scholar
Suarez, S. S. & Pacey, A. A. 2006 Sperm transport in the female reproductive tract. Human Reprod. Update 12, 23–37.CrossRefGoogle ScholarPubMed
Tam, P. Y., Katz, D. F. & Berger, S. A. 1980 Nonlinear viscoelastic properties of cervical mucus. Biorheology 17, 465–478.Google Scholar
Taylor, G. 1951 Analysis of the swimming of microscopic organisms. Proc. R. Soc. Lond. A 209, 447–461.Google Scholar
Woolley, D. M., Crockett, R. F., Groom, W. D. I. & Revell, S. G. 2009 A study of synchronization between the flagella of bull spermatozoa, with related observations. J. Exp. Biol. 212, 2215–2223.CrossRefGoogle ScholarPubMed
Yang, Y., Elgeti, J. & Gompper, G. 2008 Cooperation of sperm in two dimensions: synchronization, attraction and aggregation through hydrodynamic interactions. Phys. Rev. E 78, 061903.Google Scholar