Stability of the Shape of a Viscous Drop under Buoyancy-Driven Translation in a Hele-Shaw Cell

✍ Scribed by Nivedita R. Gupta; Ali Nadim; Hossein Haj-Hariri; Ali Borhan

• Publisher: Elsevier Science
• Year: 2000
• Tongue: English
• Weight: 134 KB
• Volume: 222
• Category: Article
• ISSN: 0021-9797
• DOI: 10.1006/jcis.1999.6601

✦ Synopsis

that a circular drop translating in a Hele-Shaw cell under the action of gravity is linearly stable for nonzero interfacial tension. In this paper, we use the boundary integral method to examine the nonlinear evolution of the shape of initially noncircular drops translating in a Hele-Shaw cell. For prolate initial deformations, it is found that the drop reverts to a circular shape for all finite Bond numbers considered. Initially oblate drops, on the other hand, are found to become unstable and break up if the initial shape perturbation is of sufficiently large magnitude. The critical conditions for the onset of drop breakup are examined in terms of the magnitude of the initial deformation as a function of Bond number. Two branches of marginal stability are identified and the effects of viscosity ratio and asymmetric initial perturbations on the stability diagram are discussed.