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Buoyancy-driven motion of a deformable drop toward a planar wall at low Reynolds number

Published online by Cambridge University Press:  26 April 2006

E. P. Ascoli ,
D. S. Dandy  and
L. G. Leal
E. P. Ascoli
Affiliation:
Department of Chemical Engineering, California Institute of Technology, Pasadena, CA 91125, USA Present address: Rockwell International, Rocketdyne Division M/S WC75, 6633 Canoga Avenue, Canoga Park, CA 91303, USA.
D. S. Dandy
Affiliation:
Department of Chemical Engineering, California Institute of Technology, Pasadena, CA 91125, USA Present address: Div. 8363, Sandia National Laboratories, PO Box 969, Livermore, CA 94550, USA.
L. G. Leal
Affiliation:
Department of Chemical Engineering, California Institute of Technology, Pasadena, CA 91125, USA Present address: Department of Chemical and Nuclear Engineering, University of California, Santa Barbara, CA 93106, USA.
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Abstract

The slow viscous motion of a deformable drop moving normal to a planar wall is studied numerically. In particular, a boundary integral technique employing the Green's function appropriate to a no-slip planar wall is used. Beginning with spherical drop shapes far from the wall, highly deformed and ‘dimpled’ drop configurations are obtained as the planar wall is approached. The initial stages of dimpling and their evolution provide information and insight into the basic assumptions of film-drainage theory.

Type
Research Article
Information
Journal of Fluid Mechanics , Volume 213 , April 1990 , pp. 287 - 311
Copyright
© 1990 Cambridge University Press

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References

Ascoli, E. P. 1988 Low-Reynolds number effects of walls on solid particles, bubbles and drops. Ph.D thesis, California Institute of Technology.
Ascoli, E. P., Dandy, D. S. & Leal, L. G. 1989 Low-Reynolds number hydrodynamic interaction of a solid particle with a planar wall. Intl J. Numer. Meth. Fluids 9, 651–688.Google Scholar
Bart, E. 1968 The slow unsteady settling of a fluid sphere toward a flat fluid interface. Chem. Engng Sci. 23, 193–210.Google Scholar
Blake, J. R. 1971 A note on the image system for a Stokeslet in a no-slip boundary. Proc. Camb. Phil. Soc. 70, 303–310.Google Scholar
Brenner, H. 1961 The slow motion of a sphere through a viscous fluid towards a plane surface. Chem. Engng Sci. 16, 242–251.Google Scholar
Chi, B. K. 1986 The motion of immiscible drops and the stability of annular flow. PhD thesis, California Institute of Technology.
Chi, B. K. & Leal, L. G. 1989 A theoretical study of the motion of a viscous drop toward a fluid interface at low Reynolds number. J. Fluid Mech. 201, 123–146.Google Scholar
Dimitrov, D. S. & Ivanov, I. B. 1978 Hydrodynamics of thin liquid films. On the rate of thinning of microscopic films with deformable interfaces. J. Colloid Interface Sci. 64, 97–106.Google Scholar
Frankel, S. P. & Mysels, K. J. 1962 On the ‘dimpling’ during the approach of two interfaces. J. Phys. Chem. 66, 190–191.Google Scholar
Geller, A. S., Lee, S. H. & Leal, L. G. 1986 The creeping motion of a spherical particle normal to a deformable interface. J. Fluid Mech. 169, 27–69.Google Scholar
Haberman, W. L. & Sayre, R. M. 1958 Motion of rigid and fluid spheres in stationary and moving liquids inside cylindrical tubes. David Taylor Model Basin Rep. No. 1143, Washington, DC, pp. 1–66Google Scholar
Hadamard, J. S. 1911 Mouvement permanent lent d'une sphere liquide et visqueuse dans un liquide visqueux. C. R. Acad. Sci. Paris 152, 1735–1738.Google Scholar
Happel, J. & Brenner, H. 1965 Low Reynolds Number Hydrodynamics. Prentice-Hall.
Hartland, S. 1967 The approach of a liquid drop to a flat plate. Chem. Engng Sci. 22, 1675–1687.Google Scholar
Hartland, S. 1969 The profile of the draining film beneath a liquid drop approaching a plane interface. Chem. Engng Prog. Symp. Ser. no. 91, 65, 82–89.Google Scholar
Hartland, S. & Robinson, J. D. 1977 A model for an axisymmetric dimpled draining film. J. Colloid Interface Sci. 60, 72–81.Google Scholar
Jones, A. F. & Wilson, S. D. R. 1978 The film drainage problem in drop coalescence. J. Fluid Mech. 87, 263–288.Google Scholar
Kantorovich, L. V. & Krylov, V. I. 1963 Approximate Methods of Higher Analysis. Interscience.
Lee, S. H. & Leal, L. G. 1982 The motion of a 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, 81–106.Google Scholar
Lin, C. Y. & Slattery, J. C. 1982 Thinning of a liquid film as a small drop or bubble approaches a solid plane. AIChE J. 28, 147–156.Google Scholar
Odqvist, F. K. G. 1930 Uber die Randwertaufgaben der Hydrodynamik Zaher Flussigkeiten. Math. Z. 32, 329–375.Google Scholar
Oseen, C. W. 1927 Hydrodynamik. Akademische Verlagsgesellschaft.
Platikanov, D. 1964 Experimental investigation on the ‘dimpling’ of thin liquid films. J. Phys. Chem. 68, 3619–3624.Google Scholar
Pozrikidis, C. 1987 Creeping flow in two-dimensional channels. J. Fluid Mech. 180, 495–514.Google Scholar
Rallison, J. M. & Acrivos, A. 1978 A numerical study of the deformation and burst of a viscous drop in an extensional flow. J. Fluid Mech. 89, 191–200.Google Scholar
Rybczynski, W. 1911 Uber die Fortschreitende Bewegung einer Flussigen Kugel in einem Zahen Medium. Bull. Acad. Sci. Cracovie (Ser. A), 40–46.Google Scholar
Tran-Cong, T. & Phan-Thien, N. 1989 Stokes problems of multiparticle systems: a numerical method for arbitrary flows. Phys. Fluids A 1, 453–461.Google Scholar
Youngren, G. K. & Acrivos, A. 1975 Stokes flow past a particle of arbitrary shape: a numerical method of solution. J. Fluid Mech. 69, 377–403 (and Corrigendum, 75 (1976) 813).Google Scholar
Youngren, G. K. & Acrivos, A. 1976 On the shape of a gas bubble in a viscous extensional flow. J. Fluid Mech. 76, 433–442.Google Scholar
Zick, A. A. & Homsy, G. M. 1982 Stokes flow through a periodic array of spheres. J. Fluid Mech. 115, 13–26.Google Scholar