Journal of Fluid Mechanics

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

Stergios G.  Yiantsios a1 and Robert H.  Davis a1
a1 Department of Chemical Engineering and Center for Low Gravity Fluid Mechanics and Transport Phenomena, University of Colorado, Boulder, CO 80309-0424, USA

Article author query
yiantsios sg   [Google Scholar] 
davis rh   [Google Scholar] 


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.

(Published Online April 26 2006)
(Received August 14 1989)