### 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 language | English (US) |
---|---|

Pages (from-to) | 4169-4181 |

Number of pages | 13 |

Journal | Physical Review E |

Volume | 47 |

Issue number | 6 |

DOIs | |

State | Published - 1993 |

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### ASJC Scopus subject areas

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

### Cite this

*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; Zhou, Su Min.

Research output: Contribution to journal › Article

*Physical Review E*, vol. 47, no. 6, pp. 4169-4181. https://doi.org/10.1103/PhysRevE.47.4169

}

TY - JOUR

T1 - Droplet breakup in a model of the Hele-Shaw cell

AU - Constantin, Peter

AU - Dupont, Todd F.

AU - Goldstein, Raymond E.

AU - Kadanoff, Leo P.

AU - Shelley, Michael

AU - Zhou, Su Min

PY - 1993

Y1 - 1993

N2 - 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.

AB - 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.

UR - http://www.scopus.com/inward/record.url?scp=12444298596&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=12444298596&partnerID=8YFLogxK

U2 - 10.1103/PhysRevE.47.4169

DO - 10.1103/PhysRevE.47.4169

M3 - Article

AN - SCOPUS:12444298596

VL - 47

SP - 4169

EP - 4181

JO - Physical Review E - Statistical Physics, Plasmas, Fluids, and Related Interdisciplinary Topics

JF - Physical Review E - Statistical Physics, Plasmas, Fluids, and Related Interdisciplinary Topics

SN - 1063-651X

IS - 6

ER -