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Bubble break-off in Hele-Shaw flows : Singularities and integrable structures

Seung-Yeop Lee·Eldad Bettelheim·Paul Wiegmann
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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.

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Seung-Yeop Lee, Eldad Bettelheim, Paul Wiegmann. 2006-04-25. Bubble break-off in Hele-Shaw flows : Singularities and integrable structures. https://doi.org/10.1016/j.physd.2006.05.010

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