Ciliary propulsion, chaotic filtration and a `blinking' stokeslet
type: Item
instance of: scholarly article
title: Ciliary propulsion, chaotic filtration and a `blinking' stokeslet
zbMATH Open document ID: 0891.76099
DOI: 10.1007/BF00118828
author: John R. Blake
author: S. R. Otto
published in: Journal of Engineering Mathematics
publication date: 1998-08-02T00:00:00Z
review text: 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.
Mathematics Subject Classification ID: 76Z10
Mathematics Subject Classification ID: 76D07
zbMATH DE Number: 1050923
zbMATH Keywords: Oseen's solution for sphere
zbMATH Keywords: fundamental singularity
zbMATH Keywords: locomotion
zbMATH Keywords: Lorentz's mirror image technique
zbMATH Keywords: Fourier transform
zbMATH Keywords: multipole derivatives
zbMATH Keywords: streamfunction representation
zbMATH Keywords: toroidal eddy structure
zbMATH Keywords: Poincaré sections
zbMATH Keywords: particle dispersion
MaRDI profile type: Publication
cites work: Q5656515
cites work: Fundamental singularities of viscous flow. I: The image systems in the vicinity of a stationary no-slip boundary
cites work: The stress system in a suspension of force-free particles
cites work: Action of a force near the planar surface between semi-infinite immiscible liquids at very low Reynolds numbers: Addendum
cites work: Existence of viscous eddies near boundaries
cites work: The generation of feeding currents by flagellar motions
cites work: Stirring by chaotic advection
cites work: Chaotic advection in a Stokes flow
cites work: An easily implementable fourth-order method for the time integration of wave problems
full work available at URL: https://doi.org/10.1007/bf00118828
OpenAlex ID: W4243292187
description: scientific article; zbMATH DE number 1050923