Mathematical model for unsteady ciliary propulsion

A mathematical model is proposed for the time-dependent ciliary propulsion of a finite micro-organism. The overall effect of cilia is replaced by velocities prescribed as functions of time and polar angle θ on a spherical control surface. Expressions for the fluid mechanical forces experienced by the organism, the velocity of free propulsion, are obtained. Situations where the initial conditions generate at large time either a steady flow or an oscillatory flow (superposed about steady state) are deduced as particular cases. The streamline patterns for particular cases are also given. © 1988.