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

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

2006-04-23

arxiv.org/abs/nlin/0604054v2

Physica D219 (2006) 22-34

Nonlinear Sciences

Exactly Solvable and Integrable Systems

27 pages, 9 figures; typo corrected

Scientific paper

10.1016/j.physd.2006.05.010

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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