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

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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.
27 pages, 9 figures; typo corrected

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Exactly Solvable and Integrable Systems, Soft Condensed Matter, High Energy Physics - Theory, Pattern Formation and Solitons

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http://salesiana.dossiersoluciones.com/handle/123456789/120590

Consulte el texto completo en el siguiente enlace:

https://arxiv.org/abs/nlin/0604054
 http://arxiv.org/abs/nlin/0604054
 Physica D219 (2006) 22-34
 doi:10.1016/j.physd.2006.05.010

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arXiv