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On the propulsion of micro-organisms near solid boundaries

Published online by Cambridge University Press:  29 March 2006

David F. Katz
David F. Katz
Affiliation:
Department of Applied Mathematics and Theoretical Physics, University of Cambridge
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Abstract

In this paper an infinite waving sheet is used to model a micro-organism swimming either parallel to a single plane wall, or along a channel formed by two such walls. The sheet surface, which undergoes small amplitude waves, can represent either a single flagellum or the envelope of the tips of numerous cilia. Two different solutions of the equations of motion are presented, depending upon whether or not the wave amplitude is small compared with the separation distances between the sheet and walls. It is found that the velocity of propulsion is bounded by the velocity of wave propagation by the sheet. Both the propulsive velocity and rate of working by the sheet increase as the separation distances decrease. However, it is demonstrated that suitable alterations in wave speed or wave shape can fix the rate of working while still causing increases in propulsive velocity. Reductions in propagated wave speed, i.e. beat frequency, are particularly effective in this regard.

Type
Research Article
Information
Journal of Fluid Mechanics , Volume 64 , Issue 1 , 3 June 1974 , pp. 33 - 49
Copyright
© 1974 Cambridge University Press

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