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Nonlinear oscillations of liquid shells in zero gravity

Published online by Cambridge University Press:  26 April 2006

N. A. Pelekasis ,
J. A. Tsamopoulos  and
G. D. Manolis
N. A. Pelekasis
Affiliation:
Department of Chemical Engineering
J. A. Tsamopoulos
Affiliation:
Department of Chemical Engineering
G. D. Manolis
Affiliation:
Department of Civil Engineering, State University of New York at Buffalo, Buffalo, NY 14260, USA
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Abstract

It has been shown experimentally (Lee et al. 1982) that water drops with injected air bubbles inside them may be forced dynamically to assume the spherosymmetric shape. Linear analysis is unable to predict a centring mechanism, but provides two distinct modes of oscillation. Weakly nonlinear theory (Tsamopoulos & Brown 1987) indicates that centring of the bubble inside the drop occurs when the two interfaces move out of phase. A hybrid boundary element-finite element schemes is used here to study the complete effect of nonlinearity on the dynamics of the motion. The gas inside the liquid shell may be considered either incompressible or compressible by using a polytropic relation. In both cases, the present calculations show that besides the fast oscillation of the shell due to an initial disturbance, a slow oscillatory motion of the centres of the bubble and the drop is induced around the concentric configuration. This occurs in both modes of oscillation and is a direct result of Bernoulli's law. Furthermore, when this slow oscillation is damped by viscous forces, it is anticipated that it will lead to a spherosymmetric shape.

Type
Research Article
Information
Journal of Fluid Mechanics , Volume 230 , September 1991 , pp. 541 - 582
Copyright
© 1991 Cambridge University Press

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