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Action of a force near the planar surface between two semi-infinite immiscible liquids at very low Reynolds numbers

Published online by Cambridge University Press:  17 April 2009

K. Aderogba  and
J.R. Blake
K. Aderogba
Affiliation:
Engineering Analysis Unit, University of Lagos, Lagos, Nigeria;
J.R. Blake
Affiliation:
CSIRO, Division of Mathematics and Statistics, Canberra, ACT.
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Abstract

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Explicit expressions for the Green's functions due to a point force in one of two half space fluids are presented for the case when inertial effects of the fluid are negligible (Stokes flow) and the interface between the two fluids is considered to be flat due to the action of surface tension. The analytic expressions are discussed in terms of singularity diagrams. For the case of a force parallel to the interface a first approximation to the interface displacement is made.

Type
Research Article
Information
Bulletin of the Australian Mathematical Society , Volume 18 , Issue 3 , June 1978 , pp. 345 - 356
Copyright
Copyright © Australian Mathematical Society 1978

References

[1]Aderogba, K., “On stokeslets in a two-fluid space”, J. Engrg. Math. 10 (1976), 143–151.CrossRefGoogle Scholar
[2]Blake, J.R., “A note on the image system for a stokeslet in a no-slip boundary”, Proc. Cambridge Philos. Soc. 70 (1971), 303–310.CrossRefGoogle Scholar
[3]Blake, John, “On the movement of mucus in the lung”, J. Biomech. 8 (1975), 179–190.CrossRefGoogle ScholarPubMed
[4]Blake, J.R. and Chwang, A.T., “Fundamental singularities of viscous flow. Part I: The image systems in the vicinity of a stationary no-slip boundary”, J. Engrg. Math. 8 (1974), 23–29.CrossRefGoogle Scholar
[5]Happel, John, Brenner, Howard, Low Reynolds number hydrodynamics with special applications to particulate media (Prentice-Hall, Englewood Cliffs, New Jersey, 1965).Google Scholar
[6]Katz, D.F., Blake, J.R. and Paveri-Fontana, S.L., “On the movement of slender bodies near plane boundaries at low Reynolds number”, J. Fluid Mech. 72 (1975), 529–540.CrossRefGoogle Scholar
[7]Landau, L.D. and Lifshitz, E.M., Fluid mechanics (Pergamon Press, Oxford, 1959).Google Scholar
[8]SirLighthill, James, Mathematical biofluiddynamics (Society for Industrial and Applied Mathematics, Philadelphia, Pennsylvania, 1975).CrossRefGoogle Scholar
[9]de Mestre, N.J., “Low-Reynolds-number fall of slender cylinders near boundaries”, J. Fluid Mech. 58 (1973), 641–656.CrossRefGoogle Scholar
[10]de Mestre, N.J., Russell, W.B., “Low-Reynolds-number translation of a slender cylinder near a plane wall”, J. Engrg. Math. 9 (1975), 81–91.CrossRefGoogle Scholar