Stability of the shape of a viscous drop under buoyancy-driven translation in a Hele-Shaw cell

Nivedita R. Gupta, Ali Nadim, Hossein Haj-Hariri, Ali Borhan

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6 Scopus citations

Abstract

It has been shown (N. R. Gupta, A. Nadim, H. Haj-Hariri, and A. Borhan, J. Colloid Interface Sci. 218, 338 1999) 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. (C) 2000 Academic Press.

Original languageEnglish (US)
Pages (from-to)107-116
Number of pages10
JournalJournal of Colloid And Interface Science
Volume222
Issue number1
DOIs
StatePublished - Feb 1 2000

All Science Journal Classification (ASJC) codes

  • Electronic, Optical and Magnetic Materials
  • Biomaterials
  • Surfaces, Coatings and Films
  • Colloid and Surface Chemistry

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