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Viscous oscillations of a supported drop in an immiscible fluid

Published online by Cambridge University Press:  21 April 2006

M. Strani  and
F. Sabetta
M. Strani
Affiliation:
Dipartimento di Meccanica e Aeronautica, Universita’ di Roma ‘La Sapienza’, Rome, Italy
F. Sabetta
Affiliation:
Dipartimento di Meccanica e Aeronautica, Universita’ di Roma ‘La Sapienza’, Rome, Italy
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Abstract

The small-amplitude free vibrations of a spherical drop immersed in an outer immiscible fluid and in partial contact with a solid support are considered when both fluids are assumed to be viscous and incompressible, while gravity effects are neglected. Using the normal-mode decomposition and the Green-function method, the solution of the linearized Navier-Stokes equations is reduced to the solution of an eigenvalue problem. The model includes as particular cases the viscous model for a free drop proposed by Prosperetti (1980) and the inviscid model for a supported drop previously proposed by the authors.

The influence of the viscosity and of the support size are analysed both for the bubble and for the drop. At large values of the viscosity, the free drop shows significant differences with respect to the unsupported drop and a singular behaviour of the eigenvalue problem as the support size tends to zero.

The comparison with the available experimental data shows a quite satisfactory agreement for both the vibration frequency and the damping constant, provided that the support angle is not too large.

Type
Research Article
Information
Journal of Fluid Mechanics , Volume 189 , April 1988 , pp. 397 - 421
Copyright
© 1988 Cambridge University Press

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References

Bisch, C., Lasek, A. & Rodot, H. A. 1982 Comportement hydrodynamique de volumes liquides spheriques semi-libres en apesanteur simulee. J. Méc. Theor. Appl. 1, 165–183.Google Scholar
Collins, W. D. 1961 On some dual series equations and their application to electrostatic problems for spheroidal caps. Proc. Camb. Phil. Soc. 57, 367–383.Google Scholar
Lamb, H. 1932 Hydrodynamics. Cambridge University Press.
Marston, P. 1980 Shape oscillation and static deformation of drops and bubbles driven by modulated radiation stresses - Theory. J. Acoust. Soc. Am. 67, 15–26.Google Scholar
Miller, C. A. & Scriven, L. E. 1968 The oscillation of fluid droplets immersed in another fluid. J. Fluid Mech. 32, 417–435.Google Scholar
Morse, P. M. & Feshbach, H. 1953 Methods of Theoretical Physics. McGraw-Hill.
Prosperetti, A. 1980 Normal mode analysis for the oscillations of a viscous liquid drop in an immiscible liquid. J. Méc. 19, 149–182.Google Scholar
Rodot, H. A. & Bisch, C. 1984 Oscillations de volumes liquides semi-libres en microgravite - Experience ES326 dans Spacelab 1. 5th European Symp. on Material Sciences under Microgravity, Paper ESA SP-222, pp. 23–29.
Strani, M. & Sabetta, F. 1984 Free vibrations of a drop in partial contact with a solid support. J. Fluid Mech. 141, 233–247.Google Scholar
Trinh, E. & Wang, T. G. 1982 Proc. 2nd Intl Colloq. on Drops and Bubbles. Publ. 82–87. JPL, Pasadena (USA).
Trinh, E., Zwern, A. & Wang, T. G. 1982 An experimental study of small-amplitude drop oscillations in immiscible liquid system. J. Fluid Mech. 115, 453–474.Google Scholar
Tsamopolous, J. A. & Brown, R. A. 1983 Nonlinear oscillations of inviscid drops and bubbles. J. Fluid Mech. 127, 519–527.Google Scholar