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The creeping motion of a spherical particle normal to a deformable interface

Published online by Cambridge University Press:  21 April 2006

A. S. Geller
Affiliation:
Department of Chemical Engineering, California Institute of Technology, Pasadena, CA 91125
S. H. Lee
Affiliation:
Department of Chemical Engineering, California Institute of Technology, Pasadena, CA 91125 Present address: Chevron Oil Field Research Co., La Habra, CA 90631.
L. G. Leal
Affiliation:
Department of Chemical Engineering, California Institute of Technology, Pasadena, CA 91125

Abstract

Numerical results are presented for the approach of a rigid sphere normal to a deformable fluid-fluid interface in the velocity range for which inertial effects may be neglected. Both the case of a sphere moving with constant velocity, and that of a sphere moving under the action of a constant non-hydrodynamic body force are considered for several values of the viscosity ratio, density difference and interfacial tension between the two fluids. Two distinct modes of interface deformation are demonstrated: a film drainage mode in which fluid drains away in front of the sphere leaving an ever-thinning film, and a tailing mode where the sphere passes several radii beyond the plane of the initially undeformed interface, while remaining encapsulated by the original surrounding fluid which is connected with its main body by a thin thread-like tail behind the sphere. We consider the influence of the viscosity ratio, density difference, interfacial tension and starting position of the sphere in deter-mining which of these two modes of deformation will occur.

Type
Research Article
Copyright
© 1986 Cambridge University Press

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References

Berdan, C. 1982 Ph.D. dissertation. California Institute of Technology.
Berdan, C. & Leal, L. G. 1982 Motion of a sphere in the presence of a deformable interface. Part 3: Numerical study of the translation of a sphere parallel to an interface. J. Colloid Interface Sci. 87, 62.Google Scholar
Chin, H. B. & Han, C. D. 1979 Studies on droplet deformation and breakup. I. Droplet deformation in extensional flow. J. Rheol. 23, 557.Google Scholar
Geller, A. S. 1986 A study of the creeping motion of a sphere normal to a deformable fluid interface: deformation and breakthrough. Ph.D. dissertation. California Institute of Technology.
Grace, H. P. 1971 Eng. Foundation 3rd Res. Conf. on Mixing. Andover, NH.
Hartland, S. 1968 The approach of a rigid sphere to a deformable liquid/liquid interface. J. Colloid Interface Sci. 26, 383.Google Scholar
Hartland, S. 1969 The profile of a draining film between a rigid sphere and a deformable fluid-liquid interface. Chem. Engng Sci. 24, 987.Google Scholar
Jeffreys, G. V. & Davies, G. A. 1971 In Recent Advances in Liquid/Liquid Extraction (ed. C. Hanson), p. 495, Pergamon Press.
Johnson, R. E. & Sadhal, S. S. 1985 Fluid mechanics of compound multiphase drops and bubbles. Ann. Rev. Fluids 17, 289.Google Scholar
Jones, A. F. & Wilson, S. D. R. 1978 The film drainage problem in droplet coalescence. J. Fluid Mech. 87, 263.Google Scholar
Kirkpatric, R. D. & Lockett, M. J. 1974 The influence of approach velocity on bubble coalescence. Chem. Engng Sci. 29, 2363.Google Scholar
Lang, S. B. & Wilke, C. R. 1971 A hydrodynamic mechanism for the coalescence of liquid drops. I. Theory of coalescence at a planar interface. I. and E. C. Fundamentals 10, 329.Google Scholar
Ladyzhenskaya, O. A. 1963 The Mathematical Theory of Viscous Incompressible Flow. Gordon and Breach.
Leal L. G. & Lee S. H. 1981 Proceedings of IUTAM-IUTPAC Symposium on Interactions of Particles in Colloid Dispersions, March 16–21. Canberra.
Lee, S. H., Chadwick, R. S. & Leal, L. G. 1979 Motion of a sphere in the presence of a plane interface. Part 1: An approximate solution by generalization of the method of Lorentz. J. Fluid Mech. 93, 705.Google Scholar
Lee, S. H. & Leal, L. G. 1980 Motion of a sphere in the presence of a plane interface. Part 2: An exact solution in bipolar coordinates. J. Fluid Mech. 98, 193.Google Scholar
Lee, S. H. & Leal, L. G. 1982 Motion of a sphere in the presence of a deformable interface. Part 2: Numerical study of the translation of a sphere normal to an interface. J. Colloid and Interface Sci. 87, 81.Google Scholar
Maru, H. C., Wasan, D. T. & Kintner, R. C. 1971 Behavior of a rigid sphere at a liquid-liquid interface. Chem. Engng Sci. 26, 1615.Google Scholar
Mikami, T., Cox, R. G. & Mason, S. G. 1975 Breakup of extending liquid threads. Intl J. Multiphase Flow 2, 113.Google Scholar
Narayaran, S., Gossens, L. H. J. & Kossen, N. W. F. 1974 Coalescence of two bubbles rising in line at low Reynolds number. Chem. Engng Sci. 29, 2071.Google Scholar
Olbricht, W. L. & Leal, L. G. 1983 The creeping motion of immiscible drops through a converging/diverging tube. J. Fluid Mech. 134, 329.Google Scholar
Princen, H. M. 1963 Shape of a fluid drop at a liquid-liquid interface. J. Colloid Sci. 18, 178.Google Scholar
Rayleigh, Lord 1892 On the instability of a cylinder of viscous liquid under capillary force. Phil. Mag. 34, 145.Google Scholar
Shah, S. T., Wasan, D. T. & Kintner, R. C. 1972 Passage of a liquid drop through a liquid-liquid interface. Chem. Engng Sci. 27, 881.Google Scholar
Smith, P. G. & Van de Ven, T. G. M. 1984 The effect of gravity on the drainage of a thin liquid film between a solid sphere and a liquid/fluid interface. J. Colloid Interface Sci. 100, 456.Google Scholar
Tomotika, S. 1936 Breaking up of a drop of viscous liquid immersed in another viscous fluid which is extending at a uniform rate. Proc. R. Soc. Lond. A 153, 302.Google Scholar
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