Slender body theory near an interface at very low Reynolds' number

This dissertation contributes to an improved understanding of the mechanics of a particle, moving in the vicinity of an interface between two viscous fluids, by considering several fundamental problems involving slender bodies. In these problems it is assumed that the Reynolds' number is very small. Several useful applications of this study are discussed, including a theoretical model of muco-ciliary transport in the lung, where the force acting on a cilium near an interface is of primary importance. One problem considered is that of a slender body translating near a flat interface, where the centreline of the slender body is oriented either parallel or perpendicular to the interface. The force distributions and the total drag force acting on the body are evaluated. For motion normal to the interface, the drag increases as the body gets closer to the interface, whereas for parallel motion, the drag increases or decreases depending on the ratio of viscosities of the fluids. The external couple, required to prevent the body from rotating when it moves parallel to the interface, is calculated. It is observed that two different mechanisms are responsible for the interface induced rotation of a particle, corresponding to parallel and perpendicular orientations of the slender body. A first order approximation of the interface deformation is also evaluated.