Bubble break-off in Hele-Shaw flows-singularities and integrable structures

Seung Yeop Lee; Eldad Bettelheim; Paul Wiegmann

doi:10.1016/j.physd.2006.05.010

Bubble break-off in Hele-Shaw flows-singularities and integrable structures

Seung Yeop Lee^*, Eldad Bettelheim, Paul Wiegmann

^*Corresponding author for this work

Research output: Contribution to journal › Article › peer-review

24 Scopus citations

Abstract

Bubbles of inviscid fluid surrounded by a viscous fluid in a Hele-Shaw cell can merge and break off. During the process of break-off, a thinning neck pinches off to a universal self-similar singularity. We describe this process and reveal its integrable structure: it is a solution of the dispersionless limit of the AKNS hierarchy. The singular break-off patterns are universal, not sensitive to details of the process and can be seen experimentally. We briefly discuss the dispersive regularization of the Hele-Shaw problem and the emergence of the Painlevé II equation at the break-off.

Original language	English
Pages (from-to)	22-34
Number of pages	13
Journal	Physica D: Nonlinear Phenomena
Volume	219
Issue number	1
DOIs	https://doi.org/10.1016/j.physd.2006.05.010
State	Published - 1 Jul 2006
Externally published	Yes

Bibliographical note

Funding Information:
We thank L. Kadanoff for discussion and interest in this work. The work was supported by the NSF MRSEC Program under DMR-0213745, NSF DMR-0220198. E.B. acknowledges H. Swinney for discussions.

Keywords

AKNS
Break-off
Hele-Shaw
Viscous fingering

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10.1016/j.physd.2006.05.010

Cite this

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title = "Bubble break-off in Hele-Shaw flows-singularities and integrable structures",

abstract = "Bubbles of inviscid fluid surrounded by a viscous fluid in a Hele-Shaw cell can merge and break off. During the process of break-off, a thinning neck pinches off to a universal self-similar singularity. We describe this process and reveal its integrable structure: it is a solution of the dispersionless limit of the AKNS hierarchy. The singular break-off patterns are universal, not sensitive to details of the process and can be seen experimentally. We briefly discuss the dispersive regularization of the Hele-Shaw problem and the emergence of the Painlev{\'e} II equation at the break-off.",

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AU - Bettelheim, Eldad

AU - Wiegmann, Paul

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AB - Bubbles of inviscid fluid surrounded by a viscous fluid in a Hele-Shaw cell can merge and break off. During the process of break-off, a thinning neck pinches off to a universal self-similar singularity. We describe this process and reveal its integrable structure: it is a solution of the dispersionless limit of the AKNS hierarchy. The singular break-off patterns are universal, not sensitive to details of the process and can be seen experimentally. We briefly discuss the dispersive regularization of the Hele-Shaw problem and the emergence of the Painlevé II equation at the break-off.

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Bubble break-off in Hele-Shaw flows-singularities and integrable structures

Abstract

Bibliographical note

Keywords

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