A porous prolate-spheroidal model for ciliated micro-organisms
A fluid-mechanical model is developed for representing the mechanism of propulsion of a finite ciliated micro-organism having a prolate-spheroidal shape. The basic concept is the representation of the micro-organism by a prolate-spheroidal control surface upon which certain boundary conditions on the tangential and normal fluid velocities are prescribed. 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 good agreement with the theoretical prediction of the streamlines is found.(Published Online April 11 2006)
(Received April 5 1976)
p1 Present address: Department of Civil Engineering and Engineering Mechanics, Columbia University, New York 10027.