Article ID | Journal | Published Year | Pages | File Type |
---|---|---|---|---|
1898287 | Physica D: Nonlinear Phenomena | 2006 | 13 Pages |
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.
Keywords
Related Topics
Physical Sciences and Engineering
Mathematics
Applied Mathematics
Authors
Seung-Yeop Lee, Eldad Bettelheim, Paul Wiegmann,