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On the buoyancy-driven motion of a drop towards a rigid surface or a deformable interface

Published online by Cambridge University Press:  26 April 2006

Stergios G. Yiantsios  and
Robert H. Davis
Stergios G. Yiantsios
Affiliation:
Department of Chemical Engineering and Center for Low Gravity Fluid Mechanics and Transport Phenomena, University of Colorado, Boulder, CO 80309-0424, USA
Robert H. Davis
Affiliation:
Department of Chemical Engineering and Center for Low Gravity Fluid Mechanics and Transport Phenomena, University of Colorado, Boulder, CO 80309-0424, USA
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Abstract

The deformation of a viscous drop, driven by buoyancy towards a solid surface or a deformable interface, is analysed in the asymptotic limit of small Bond number, for which the deformation becomes important only when the drop is close to the solid surface or interface. Lubrication theory is used to describe the flow in the thin gap between the drop and the solid surface or interface, and boundary-integral theory is used in the fluid phases on either side of the gap. The evolution of the drop shape is traced from a relatively undeformed state until a dimple is formed and a long-time quasi-steady-state pattern is established. A wide range of drop to suspending phase viscosity ratios is examined. It is shown that a dimple is always formed, independently of the viscosity ratio, and that the long-time thinning rates take simple forms as inverse fractional powers of time.

Type
Research Article
Information
Journal of Fluid Mechanics , Volume 217 , August 1990 , pp. 547 - 573
Copyright
© 1990 Cambridge University Press

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