Hostname: page-component-7dd5485656-c8zdz Total loading time: 0 Render date: 2025-10-30T11:53:48.087Z Has data issue: false hasContentIssue false
  • English
  • Français

Stokes flow due to a Stokeslet in a pipe

Published online by Cambridge University Press:  12 April 2006

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

Abstract

Velocity and pressure fields for Stokes flow due to a force singularity (Stokeslet) of arbitrary orientation and at arbitrary location inside an infinite circular pipe are obtained. Two alternative expressions for the solution, one in terms of a Fourier-Bessel type expansion, and the other as a doubly infinite series, are given. The latter is especially suitable for computational purposes as it is shown to be an exponentially decaying series. From the series it is found that all velocity components decay exponentially to zero up- or downstream away from the Stokeslet. This is also true for pressure fields of Stokeslets perpendicular to the axis of the pipe. A Stokeslet parallel to the axis of the pipe raises the pressure difference between − ∞ to + ∞ by a finite non-zero amount. Some numerical results for a Stokeslet parallel to the axis are given. Comparison of the results with flow in a two-dimensional channel is also discussed.

Information

Type
Research Article
Information
Journal of Fluid Mechanics , Volume 86 , Issue 4 , 28 June 1978 , pp. 727 - 744
Copyright
© 1978 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.)

Article purchase

Temporarily unavailable

References

Abramowitz, M. A. & Stegun, I. A. 1965 Handbook of Mathematical Functions. Dover.
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
Happel, J. & Brenner, H. 1973 Low Reynolds Number Hydrodynamics, with Special Applications to Particulate Matter, 2nd rev. ed. Leiden: Noordhoff.
Lardner, T. J. & Shack, W. J. 1972 Cilia transport. Bull. Math. Biophys. 34, 325–335.Google Scholar
Liron, N. 1978 Fluid transport by cilia between parallel plates. J. Fluid Mech. 86, 705–726.Google Scholar
Liron, N. & Mochon, S. 1976a The discrete-cilia approach to propulsion of ciliated microorganisms. J. Fluid Mech. 75, 593–607.Google Scholar
Liron, N. & Mochon, S. 1976b Stokes flow for a Stokeslet between two parallel flat plates. J. Engng Math. 10, 287–303.Google Scholar
Lorentz, H. A. 1896 Zittingsverlag. Akad. v. Wet. 5, 168–182.