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Infinite models for ciliary propulsion

Published online by Cambridge University Press:  29 March 2006

J. R. Blake
J. R. Blake
Affiliation:
Department of Applied Mathematics and Theoretical Physics, University of Cambridge
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Abstract

This paper discusses two infinite length models (planar and cylindrical) for ciliary propulsion of microscopic organisms. Through the concept of an extensible envelope (instantaneous surface covering the numerous cilia) over the organism, we consider a small amplitude analysis for the velocity of propulsion. A comparison of the velocities of propulsion for the infinite models reveals that they are just over twice that obtained for the finite spherical model (Blake 1971). This indicates that planeness is more important than finiteness, as the solution for typical micro-organisms (e.g. disk-shaped) should occur somewhere between these two models. The maximum velocity of propulsion obtained is one quarter of the wave velocity; that inferred for Opalina, the organism modelled, is nearly one fifth of the wave velocity. Associated shapes of the surface and paths of movement of the tips of the cilia are illustrated.

Type
Research Article
Information
Journal of Fluid Mechanics , Volume 49 , Issue 2 , 29 September 1971 , pp. 209 - 222
Copyright
© 1971 Cambridge University Press

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References

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