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 journalArticlepeer-review

24 Scopus citations


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 languageAmerican English
Pages (from-to)22-34
Number of pages13
JournalPhysica D: Nonlinear Phenomena
Issue number1
StatePublished - 1 Jul 2006
Externally publishedYes

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.


  • AKNS
  • Break-off
  • Hele-Shaw
  • Viscous fingering


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