Fluid Mechanical Investigations of Ciliary Propulsion

Citation

Keller, Stuart Ronald (1975) Fluid Mechanical Investigations of Ciliary Propulsion. Dissertation (Ph.D.), California Institute of Technology. doi:10.7907/QD11-B584. https://resolver.caltech.edu/CaltechTHESIS:04182012-081505490

Abstract

Fluid mechanical investigations of ciliary propulsion are carried out from two points of view. In Part I, using a planar geometry, a model is developed for the fluid flow created by an array of metachronally coordinated cilia. The central concept of this model is to replace the discrete forces of the cilia ensemble by an equivalent continuum distribution of an unsteady body force within the cilia layer. This approach facilitates the calculation for the case of finite amplitude movement of cilia and takes into account the oscillatory component of the flow. Expressions for the flow velocity, pressure, and the energy expended by a cilium are obtained for small oscillatory Reynolds numbers. Calculations are carried out with the data obtained for the two ciliates Opalina ranarurn and Paramecium multimicronucleatum. The results are compared with those of previous theoretical models and some experimental observations.

In Part II a model is developed for representing the mechanism of propulsion of a finite ciliated micro-organism having a prolate spheroidal shape. The basic concept of the model is to replace the micro-organism by a prolate spheroidal control surface at which certain boundary conditions on the fluid velocity are prescribed. These boundary conditions, which admit specific tangential and normal components of the flow velocity relative to the control surface, are proposed as a reasonable representation of the overall features of the flow field generated by the motion of the cilia system. Expressions are obtained for the velocity of propulsion, the rate of energy dissipation in the fluid exterior to the cilia layer, and the stream function of the motion. The effect of the shape of the organism upon its locomotion is explored. Experimental streak photographs of the flow around both freely swimming and inert sedimenting Paramecia are presented and compared with the theoretical prediction of the streamlines.

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