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The hydrodynamics of an oscillating porous sphere

Phys. Fluids 16, 62 (2004); doi:10.1063/1.1630051

Published 3 December 2003

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Jason R. Looker and Steven L. Carnie
Department of Mathematics and Statistics, The University of Melbourne, Parkville, 3010 Victoria, Australia
We determine the hydrodynamics of a rigid, weakly permeable sphere undergoing translational oscillations in an incompressible Newtonian fluid. We check using homogenization and scaling arguments that the flow inside the sphere may be modeled by Darcy's law and that the Beavers–Joseph–Saffman (BJS) boundary condition still applies for oscillatory flows, provided the frequency of oscillation is not too high. The BJS boundary condition introduces a slip velocity and to leading order in epsilon= sqrt(k)/a, where k is the particle permeability and a is the radius, the particle may be regarded as impermeable with a slip length independent of frequency. Under these circumstances we solve for the flow field, pressure distribution and drag explicitly and show their behavior for 0<=epsilon<=0.05 and frequencies relevant to electroacoustics (1–10 MHz). From the drag we find the leading order corrections due to particle permeability of the pseudo-steady drag, Basset force and added mass. ©2004 American Institute of Physics.
History: Received 19 June 2003; accepted 6 October 2003; published 3 December 2003
Permalink: http://link.aip.org/link/?PHFLE6/16/62/1
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EDITORIALLY RELATED

  1. Comment on "The hydrodynamics of an oscillating porous sphere" [Phys. Fluids 16, 62 (2004)]
    Efstathios E. Michaelides et al.
    Phys. Fluids 16, 4758 (2004)
  2. Response to "Comment on `The hydrodynamics of an oscillating porous sphere' " [Phys. Fluids 16, 4758 (2004)]
    Jason R. Looker et al.
    Phys. Fluids 16, 4760 (2004)

KEYWORDS and PACS

Keywords
PACS
  • 47.55.Mh
    Flows through porous media
  • 47.35.+i
    Hydrodynamic waves
  • 47.20.-k
    Hydrodynamic stability
  • 47.80.+v
    Instrumentation for fluid dynamics
  • 47.11.+j
    Computational methods in fluid dynamics
  • YEAR: 2004

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PUBLICATION DATA

ISSN:
1070-6631 (print)   1089-7666 (online)
Publisher:
AIP is a member of CrossRef AIP

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