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.
Bibliographical noteFunding 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.
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