Droplet breakup in a model of the Hele-Shaw cell

Peter Constantin, Todd F. Dupont, Raymond E. Goldstein, Leo P. Kadanoff, Michael J. Shelley, and Su-Min Zhou
Phys. Rev. E 47, 4169 – Published 1 June 1993
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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.

  • Received 24 November 1992

DOI:https://doi.org/10.1103/PhysRevE.47.4169

©1993 American Physical Society

Authors & Affiliations

Peter Constantin and Todd F. Dupont

  • Computational and Applied Mathematics Program, Ryerson Laboratory, The University of Chicago, Chicago, Illinois 60637

Raymond E. Goldstein

  • Department of Physics, Princeton University, Princeton, New Jersey 08544

Leo P. Kadanoff and Michael J. Shelley

  • Computational and Applied Mathematics Program, Ryerson Laboratory, The University of Chicago, Chicago, Illinois 60637

Su-Min Zhou

  • Department of Physics, The University of Chicago, 5640 South Ellis Avenue, Chicago, Illinois 60637

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Vol. 47, Iss. 6 — June 1993

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