Hostname: page-component-848d4c4894-nr4z6 Total loading time: 0 Render date: 2024-06-10T03:04:37.967Z Has data issue: false hasContentIssue false
  • English
  • Français

The discrete-cilia approach to propulsion of ciliated micro-organisms

Published online by Cambridge University Press:  29 March 2006

N. Liron  and
S. Mochon
N. Liron
Affiliation:
Department of Applied Mathematics, The Weizmann Institute of Science, Rehovot, Israel
S. Mochon
Affiliation:
Department of Applied Mathematics, The Weizmann Institute of Science, Rehovot, Israel
Get access Rights & Permissions [Opens in a new window]

Abstract

The discrete-cilia approach, or cilia sublayer model, is considered for propulsion of ciliated micro-organisms. Natural periodicity assumptions enable us to obtain a readily usable expression for the velocity where dependences on the direction of propulsion of the metachronal wave and on the time are not averaged out. Thus instantaneous interaction of the cilia with the fluid is calculable, and time-dependent velocity profiles are obtained. Calculations show that the velocity above the cilia sublayer is time independent and uniform. Closer to the bases fluid velocity fluctuations are large.

Type
Research Article
Information
Journal of Fluid Mechanics , Volume 75 , Issue 3 , 11 June 1976 , pp. 593 - 607
Copyright
© 1976 Cambridge University Press

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

Barton, C. & Raynor, S. 1967 Analytic investigations of cilia induced mucous flow Bull. Math. Biophys. 29, 419–428.Google Scholar
Blake, J. R. 1971 A note on the image system for a Stokeslet in a no-slip boundary Proc. Camb. Phil. Soc. 70, 303–310.Google Scholar
Blake, J. R. 1972 A model for the micro-structure in ciliated organisms J. Fluid Mech. 55, 1–23.Google Scholar
Blake, J. R. & Sleigh, M. A. 1974 Mechanics of ciliary locomotion Biol. Rev. 49, 85–125.Google Scholar
Gray, J. & Hancock, G. J. 1955 The propulsion of sea-urchin spermatozoa J. Exp. Biol. 32, 802–814.Google Scholar
Lighthill, M. J. 1975 Mathematical Biofluiddynamics. Philadelphia: SIAM.
Machemer, H. 1972 Ciliary activity and origin of metachrony in Paramecium: effects of increased viscosity. J. Exp. Biol. 57, 239–810.Google Scholar
Watson, G. N. 1948 A Treatise on the Theory of Bessel Functions, 2nd edn. Cambridge University Press.