# Fluid Mechanics of Ciliary Propulsion

## Abstract

Cilia have many functions in the animal kingdom, some of these being cleansing, feeding, excretion, locomotion and reproduction. They occur in all phyla of the animal kingdom with the possible exception of the class *Nematoda*. This lecture will discuss the development of fluid mechanical models and theories that help with our understanding and interpretation of locomotion of protozoa, mucous transport in the lung, filter feeding in bivalve molluscs and gamete transport.

The theoretical development for the fluid mechanics requires obtaining the fundamental singularities and image systems pertinent to the system under study, the physical interpretation of them and their constructive use to model the flow fields generated by fields of cilia.

These theories allow estimates of the flow fields in the cilia sublayer and for a greater understanding of propulsive mechanisms in both micro-organisms and mucous transport in the lower respiratory tract. The sophisticated models in turn allow us to develop better approximations for simplified models that provide an improved understanding of more complicated flows involving filter feeding in bivalve molluscs and with ovum transport in the oviduct.

Finally, studies of possible filter feeding strategies in the sessile organism, *Vorticella*, which alters the length of its stalk periodically, has led to the development of some interesting non-linear mathematics in a simplified ‘blinking stokeslet’ model of this filter feeding phenomenon. We shall demonstrate that this can lead to chaotic dynamics, which has been shown to enhance mixing and hence improve the efficiency of feeding currents. The continuous system is reduced to an area-preserving map, which allows for greater analytical progress to be made in this inertia-free system. Poincaré sections and Lyapunov exponents are used alongside other chaotic measures to determine the nature and extent of the chaos. Effects of molecular diffusion are mimicked via the incorporation of white noise in the map and enhanced feeding levels are predicted.

The author of this paper acknowledges, with gratitude, the enormous influence that Sir James Lighthill has had on his life and academic career. This paper is dedicated to his memory and is based on research work conducted by the author of this review over the last 30 years with the material in this article being taken from papers over this period.

## Keywords

Muscular Activity Volume Flow Rate Mucous Layer Recovery Stroke Poincare Section## Preview

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