Droplet breakup in a model of the Hele-Shaw cell

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

Research output: Contribution to journalArticle

137 Citations (Scopus)

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 - Jan 1 1993

Fingerprint

Hele-Shaw
Breakup
Droplet
Cell
cells
Lubrication Approximation
Immiscible Fluids
Breakage
Model
fluids
Topology
Imply
Fluid
Scenarios
lubrication
Zero
topology
approximation

ASJC Scopus subject areas

  • Statistical and Nonlinear Physics
  • Mathematical Physics
  • Condensed Matter Physics
  • Physics and Astronomy(all)

Cite this

Constantin, P., Dupont, T. F., Goldstein, R. E., Kadanoff, L. P., Shelley, M. J., & Zhou, S. (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

Droplet breakup in a model of the Hele-Shaw cell. / Constantin, Peter; Dupont, Todd F.; Goldstein, Raymond E.; Kadanoff, Leo P.; Shelley, Michael J.; Zhou, Sumin.

In: Physical Review E, Vol. 47, No. 6, 01.01.1993, p. 4169-4181.

Research output: Contribution to journalArticle

Constantin, P, Dupont, TF, Goldstein, RE, Kadanoff, LP, Shelley, MJ & Zhou, S 1993, 'Droplet breakup in a model of the Hele-Shaw cell', Physical Review E, vol. 47, no. 6, pp. 4169-4181. https://doi.org/10.1103/PhysRevE.47.4169
Constantin P, Dupont TF, Goldstein RE, Kadanoff LP, Shelley MJ, Zhou S. Droplet breakup in a model of the Hele-Shaw cell. Physical Review E. 1993 Jan 1;47(6):4169-4181. https://doi.org/10.1103/PhysRevE.47.4169
Constantin, Peter ; Dupont, Todd F. ; Goldstein, Raymond E. ; Kadanoff, Leo P. ; Shelley, Michael J. ; Zhou, Sumin. / Droplet breakup in a model of the Hele-Shaw cell. In: Physical Review E. 1993 ; Vol. 47, No. 6. pp. 4169-4181.
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