A spherical envelope approach to ciliary propulsion

TLDR

Ciliary propulsion can be approximated by an envelope model when cilia are densely packed, as in a symplectic metachronal wave that travels in the same direction as the effective beat. This paper models ciliary propulsion dynamics using an envelope concept covering the ends of numerous cilia on a microscopic organism. A spherical envelope model is employed, correcting Lighthill’s 1952 squirming motion analysis for a nearly spherical organism. The model yields velocity and efficiency estimates that are compared to both inert and ciliated organisms.

Abstract

In this paper, an attempt has been made to model the dynamics of ciliary propulsion through the concept of an ‘envelope’ covering the ends of the numerous cilia of the microscopic organism. This approximation may be made in the case when the cilia are close together, as can occur in the case of the symplectic metachronal wave (i.e. the wave travels in the same direction as the effective beat). For simplicity, a spherical model has been chosen, and the analysis which follows is a correction to Lighthill's (1952) paper on squirming motions of a nearly spherical organism. The velocity and efficiency compared to the work done in pushing an inert organism are obtained, and compared to that of a ciliated organism.