caa a22 4500 477077374 CHVBK 20180405111441.0 cr unu---uuuuu 170330e19960301xx s 000 0 eng 10.1007/BF00118828 doi (NATIONALLICENCE)springer-10.1007/BF00118828 Ciliary propulsion, chaotic filtration and a ‘blinking' stokeslet [Elektronische Daten] [J. Blake, S. Otto] The paper discusses the fundamental singularity of Stokes flow (the stokeslet) in the context of applications to locomotion and feeding currents in micro-organisms. The image system for a Stokeslet in a rigid plane boundary may be derived from Lorentz's mirror image technique [1] or by an appropriate limit of Oseen's solution for a sphere near a plane boundary [2]. An alternative derivation using Fourier transform methods [3] 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 stream function representation which illustrates the toroidal eddy structure of the flow field. A similar eddy structure is also obtained for the two-dimensional system, although in this case, the toroidal structure is replaced by two eddies. This closed streamline model is developed to model chaotic filtration through the concept of a ‘blinking stokeslet', a stokeslet alternating its vertical position according to a specific protocol. The resulting behaviour is illustrated via Poincaré sections, particle dispersion and length of particle path tracings. Sessile micro-organisms may exploit a similar process so they can filter as large a volume of liquid as possible in search of food and nutrients. Kluwer Academic Publishers, 1996 Blake J. School of Mathematics and Statistics, The University of Birmingham, Edgbaston, B15 2TT, Birmingham, United Kingdom aut Otto S. School of Mathematics and Statistics, The University of Birmingham, Edgbaston, B15 2TT, Birmingham, United Kingdom aut Journal of Engineering Mathematics Kluwer Academic Publishers; http://www.wkap.nl 30/1-2(1996-03-01), 151-168 0022-0833 30:1-2<151 1996 30 10665 https://doi.org/10.1007/BF00118828 text/html Onlinezugriff via DOI 1 research-article jats NATIONALLICENCE 856 40 https://doi.org/10.1007/BF00118828 text/html Onlinezugriff via DOI NATIONALLICENCE 700 1- Blake J. School of Mathematics and Statistics, The University of Birmingham, Edgbaston, B15 2TT, Birmingham, United Kingdom aut NATIONALLICENCE 700 1- Otto S. School of Mathematics and Statistics, The University of Birmingham, Edgbaston, B15 2TT, Birmingham, United Kingdom aut NATIONALLICENCE 773 0- Journal of Engineering Mathematics Kluwer Academic Publishers; http://www.wkap.nl 30/1-2(1996-03-01), 151-168 0022-0833 30:1-2<151 1996 30 10665 Metadata rights reserved Springer special CC-BY-NC licence nationallicence BK010053 XK010053 XK010000 NATIONALLICENCE NATIONALLICENCE NL-springer