Droplet breakup in a model of the Hele-Shaw cell

Peter Constantin, Todd F. Dupont, Raymond E. Goldstein, Leo P. Kadanoff, Michael J. Shelley, Su Min Zhou

Research output: Contribution to journalArticle

144 Scopus citations

Abstract

The Hele-Shaw cell involves two immiscible fluids separated by an interface. Possible topology changes in the interface are investigated. In particular, we ask whether a thin neck between two masses of the fluid can develop, get thinner, and finally break. To study this, we employ the lubrication approximation, which implies for a symmetrical neck that the neck thickness h obeys ht+(hhxxx)x=0. The question is whether, starting with smooth positive initial data for h, one can achieve h=0, and hence a possible broken neck within a finite time. One possibility is that, instead of breaking, the neck gets continually thinner and finally goes to zero thickness only at infinite time. Here, we investigate one set of initial data and argue that in this case the system does indeed realize this infinite-time breakage scenario.

Original languageEnglish (US)
Pages (from-to)4169-4181
Number of pages13
JournalPhysical Review E
Volume47
Issue number6
DOIs
StatePublished - 1993

ASJC Scopus subject areas

  • Statistical and Nonlinear Physics
  • Statistics and Probability
  • Condensed Matter Physics

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    Constantin, P., Dupont, T. F., Goldstein, R. E., Kadanoff, L. P., Shelley, M. J., & Zhou, S. M. (1993). Droplet breakup in a model of the Hele-Shaw cell. Physical Review E, 47(6), 4169-4181. https://doi.org/10.1103/PhysRevE.47.4169