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Stokes flow due to a Stokeslet in a pipe

  • N. Liron (a1) and R. Shahar (a1)


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.



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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, 303310.
Blake, J. R. 1972 A model for the micro-structure in ciliated organisms. J. Fluid Mech. 55, 123.
Blake, J. R. & Sleigh, M. A. 1974 Mechanics of ciliary locomotion. Biol. Rev. 49, 85125.
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, 325335.
Liron, N. 1978 Fluid transport by cilia between parallel plates. J. Fluid Mech. 86, 705726.
Liron, N. & Mochon, S. 1976a The discrete-cilia approach to propulsion of ciliated microorganisms. J. Fluid Mech. 75, 593607.
Liron, N. & Mochon, S. 1976b Stokes flow for a Stokeslet between two parallel flat plates. J. Engng Math. 10, 287303.
Lorentz, H. A. 1896 Zittingsverlag. Akad. v. Wet. 5, 168182.
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