Ciliary propulsion, chaotic filtration and a `blinking' stokeslet
The authors discuss the fundamental singularity of Stokes flow in context of applications to locomotion and feeding currents in microorganism. It is reported that the image system for a stokeslet in a rigid plane boundary can be derived by using the Lorentz's mirror image technique or by an appropriate limit of Oseen's solution for a sphere near a plane boundary. The authors present an alternative derivation by using Fourier transform methods which leads to an immediate physical interpretation of the image system in terms of a stokeslet and its multipole derivatives. The schematic illustration of a stokeslet and its image system in a plane boundary are exploited to explain the fluid dynamical principles of ciliary propulsion. For a point force oriented normal to the plane boundary, the resulting axisymmetric motion leads to a Stokes streamfunction representation which illustrates the toroidal eddy structure of the flow field. The authors obtain a similar eddy structure for two-dimensional system replacing toroidal structure by two eddies. A closed streamlined model is developed to model chaotic filtration which uses the concept of a blinking stokeslet (a stokeslet variation in its vertical position according to a prescribed regime). The resulting behaviour is illustrated via Poincaré sections, particle dispersion, and length of particle path tracings. Finally, the authors remark that sessile microorganisms can exploit a similar process, namely they can filter as large volume of fluid as possible in search of food and nutrients.
scientific article; zbMATH DE number 1050923