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The action of waving cylindrical rings in a viscous fluid

Published online by Cambridge University Press:  07 March 2011

HOA NGUYEN ,
RICARDO ORTIZ ,
RICARDO CORTEZ  and
LISA FAUCI
HOA NGUYEN
Affiliation:
Department of Mathematics and Center for Computational Science, Tulane University, New Orleans, LA 70118, USA
RICARDO ORTIZ
Affiliation:
Department of Mathematics and Center for Computational Science, Tulane University, New Orleans, LA 70118, USA
RICARDO CORTEZ
Affiliation:
Department of Mathematics and Center for Computational Science, Tulane University, New Orleans, LA 70118, USA
LISA FAUCI*
Affiliation:
Department of Mathematics and Center for Computational Science, Tulane University, New Orleans, LA 70118, USA
*
†Email address for correspondence: ljf@math.tulane.edu
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Abstract

Dinoflagellates (Pfisteria piscicida) are unicellular micro-organisms that swim due to the action of two eucaryotic flagella: a trailing, longitudinal flagellum that propagates planar waves and a transverse flagellum that propagates helical waves. Motivated by the wish to understand the role of the transverse flagellum in dinoflagellate motility, we study the fundamental fluid dynamics of a waving cylindrical tube wrapped into a closed helix. Given an imposed travelling wave on the structure, we determine that the helical ring propels itself in the direction normal to the plane of the circular axis of the helix. The magnitude of this translational velocity is proportional to the square of the helix amplitude. Additionally, the helical ring exhibits rotational motion tangential to its axis. These calculated swimming velocities are consistent when using the method of regularized Stokeslets with prescribed wave kinematics, regularized Stokeslets with dynamic forcing and Lighthill's slender-body theory, except in cases where the slenderness parameter is not small. The translational velocity results are nearly indistinguishable using the three approaches, leading to the conjecture that the main contribution to this velocity at a cross-section is the far-field flow generated by the portion on the opposite side of the ring. The largest contribution to the rotational velocity at a cross-section comes from the cross-section itself and others nearby, thus the geometric details of the slender body have a larger effect on the results.

JFM classification

Biological Fluid Dynamics: Micro-organism dynamics Low-Reynolds-number flows: Slender-body theory Biological Fluid Dynamics: Swimming/flying
Type
Papers
Information
Journal of Fluid Mechanics , Volume 671 , 25 March 2011 , pp. 574 - 586
Copyright
Copyright © Cambridge University Press 2011

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References

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Nguyen et al. supplementary movie

This movie illustrate that the waving ring undergoes flexible motion, and not the rigid body motion of a helix rotating about its axis. In addition, we depict a material patch on the ring surface, along with the distribution of forces.

Download Nguyen et al. supplementary movie(Video)
Video 6.3 MB

Nguyen et al. supplementary movie

This movie illustrate that the waving ring undergoes flexible motion, and not the rigid body motion of a helix rotating about its axis. In addition, we depict a material patch on the ring surface, along with the distribution of forces.

Download Nguyen et al. supplementary movie(Video)
Video 1.7 MB