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Force distribution along a slender body straddling an interface

Published online by Cambridge University Press:  17 February 2009

G. R. Fulford  and
J. R. Blake
G. R. Fulford
Affiliation:
Department of Mathematics, LaTrobe University, Bundoora, Vic., Australia.
J. R. Blake
Affiliation:
Department of Mathematics, The University of Wollongong, Wollongong, N.S.W. 2500, Australia.
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Abstract

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Line distributions of Stokes flow singularities are used to model the flow around a slender body which is straddling a flat interface between two viscous fluids. Motion of the slender body parallel to the interface and normal to the interface is considered where the axis of symmetry of the slender body is always perpendicular to the undisturbed interface. Asymptotic approximations to the force distributions on the slender body are evaluated and the relative contributions of that part of the slender body in one fluid to the force distribution in the other fluid and of the interface interaction to the force distribution are examined. It is observed that a shielding region exists about the interface which is due to the interaction with that part of the slender body in the other fluid. Finally, for parallel motion, the first order interface deformation is calculated.

Type
Research Article
Information
The ANZIAM Journal , Volume 27 , Issue 3 , January 1986 , pp. 295 - 315
Copyright
Copyright © Australian Mathematical Society 1986

References

[1]Aderogba, K., “On stokeslets in a two-fluid space”, J. Engrng Math. 10 (1976), 143–151.Google Scholar
[2]Aderogba, K. and Blake, J. R., “Action of a force near the planar surface between two semi-infinite immiscible liquids at very low Reynolds numbers”, Bull. Austral. Math. Soc. 19 (1978), 109–318.Google Scholar
[3]Batchelor, G. K., “Slender body theory for particles of arbitrary cross-section in Stokes flow”, J. Fluid Mech. 44 (1970), 419–440.Google Scholar
[4]Berdan, C. and Leal, L. G., “Motion of a sphere in the presence of a deformable interface. 1. Perturbation of the interface from the flat: The effects of drag and torque”, J. Colloid & Interface Sci. 87 (1982), 62–80.CrossRefGoogle Scholar
[5]Blake, J. R., “On the movement of mucus in the lung”, J. Biomech. 8 (1975), 179–190.Google Scholar
[6]Blake, J. R., “Mechanics of Muco-ciliary transport”, IMA J. Appl. Math. 32 (1984), 69–87.Google Scholar
[7]Davis, S. H., “Contact-line problems in fluid mechanics”, J. App. Mech. 50 (1983), 997–982.Google Scholar
[8]Fulford, G. R. and Blake, J. R., “On the motion of a slender body near an interface between two immiscible liquids at very low Reynolds numbers”, J. Fluid Mech. 127 (1983), 203–217.Google Scholar
[9]Leal, L. G. and Lee, S. H., “Particle motion near a deformable interface”, Adv. Colloid & Int. Sci. 17 (1982), 61–81.Google Scholar
[10]Lee, S. H., Chadwick, R. S. and Leal, L. G., “Motion of a sphere in the presence of a plane interface. Part 1. An approximate solution by generalisation of the method of Lorentz”, J. Fluid Mech. 93 (1979), 705–726.Google Scholar
[11]Lee, S. H. and Leal, L. G., “Motion of a sphere in the presence of a plane interface. Part 2. An exact solution in bipolar co-ordinates”, J. Fluid Mech. 98 (1980), 193–224.Google Scholar
[12]Lee, S. H. and Leal, L. G., “The motion of sphere in the presence of a deformable interface. II. A numerical study of the translation of a sphere normal to an interface”, J. Colloid & Interface Sci. 87 (1982), 81–106.CrossRefGoogle Scholar
[13]de Mestre, N. J. and Russel, W. B., “Low-Reynolds-number translation of a slender cylinder near a plane wall”, J. Engrng Math. 9 (1975), 81–91.CrossRefGoogle Scholar
[14]Ranger, K. B., “The circular disc straddling the interface of a two-phase flow”, Int. J. Multiphase Flow 4 (1978), 263–277.Google Scholar
[15]Russel, W. B. and Acrivos, A., “On the effective moduli of composite materials: slender rigid inclusions at dilute concentrations”, Z. A. M. P. 23 (1972), 434–464.Google Scholar
[16]Russel, W. B., Hinch, E. J., Leal, L. G. and Tieffenbruck, G., “Rods falling near a vertical wall”, J. Fluid Mech. 83 (1977), 273–287.Google Scholar
[17]Schneider, J. C., O'Neill, M. E. and Brenner, H., “On the slow viscous rotation of a body straddling the interface between two immiscible semi-infinite fluids”, Mathematika 20 (1973), 175–196.Google Scholar
[18]Sleigh, M. A., “Movement and coordination of tracheal cilia and the relation of these to mucus transport”, Cell Motility Supp. 1 (1982), 19–24.Google Scholar
[19]Tuck, E. O., “Some methods for flows past blunt slender bodies”. J. Fluid Mech. 18 (1964), 619–635.Google Scholar
[20]Yang, S. M. and Leal, L. G., “Slender-body theory in Stokes flow near a plane fluid-fluid interface”, J. Fluid Mech. 136 (1983), 393–421.Google Scholar