Brennen, Christopher
(1975)
*Hydromechanics of Propulsion for Ciliated Micro-Organisms.*
In:
Swimming and Flying in Nature.
Plenum Press
, New York, pp. 235-253.
ISBN 0306370883.
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## Abstract

To the present time much of the hydrodynamic analysis of the locomotion of ciliated micro-organisms has concentrated on the localized interaction between the cilia and the fluid medium. In doing so most investigators have found it necessary to simplify the larger scale flow and to consider "infinite sheet models" in which the fluid flow solutions are purely harmonic and the wave properties invariant in the rectilinear coordinate parallel to the sheet. The resulting mean motion is purely unidirectional and thus the hydrodynamic solution greatly simplified. Since these "infinite sheet models" conveniently termed the "envelope" and "sub-layer" models are discussed in detail by Blake and Sleigh (1974a, b) elsewhere in this volume further amplification is unnecessary. It is convenient, however, for our purposes to think of these as fluid/cilia interaction models describing the local interaction between the cilia and the fluid. The relative merits of the two types of model and criteria which describe their respective region of validity are discussed by Brennen (1974) and by Blake and Sleigh (1974b). In the present paper we will discuss some of the characteristics of the flow around "finite" ciliated micro-organisms, pointing out along the way those effects not experienced in the infinite sheet models but which are important in evaluating, say, the propulsive velocity of a ciliated micro-organism. The only previous solution for a "finite" body to appear in the literature seems to be that of Lighthill (1952), later modified by Blake (1971a) in which traveling surface waves on a sphere (to use the "envelope" model) are approximated by combining two spherical harmonic functions whose orders differ by one. But this solution is very restrictive in terms of the permitted variation of waveform and wave amplitude over the body and its extension to nonspheriodal bodies would involve prohibitive algebraic complexity.

Item Type: | Book Section |
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Additional Information: | Proceedings of the first half of the Symposium on Swimming and Flying in Nature, held at the California Institute of Technology, Pasadena, Calif., July 8-12, 1974. This work was sponsored by the National Science Foundation under grant GK-31l6lX and by the Office of Naval Research under contract N00014-67-A-0094-0012. The author deeply appreciates the advice and encouragement of Professor T. Y. Wu and many helpful discussions with Dr. John Blake, Dr. Allen Chwang and Dr. Howard Winet. |

Record Number: | CaltechAUTHORS:BREsfn75 |

Persistent URL: | http://resolver.caltech.edu/CaltechAUTHORS:BREsfn75 |

Usage Policy: | No commercial reproduction, distribution, display or performance rights in this work are provided. |

ID Code: | 186 |

Collection: | CaltechAUTHORS |

Deposited By: | Christopher Brennen |

Deposited On: | 07 Jan 2005 |

Last Modified: | 26 Dec 2012 08:39 |

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