Nonlinear Saffman-Taylor instability.
We show, both theoretically and experimentally, that the interface between two viscous fluids in a Hele-Shaw cell can be nonlinearly unstable before the Saffman-Taylor linear instability point is reached. We identify the family of exact elastica solutions [Nye et al., Eur. J. Phys. 5, 73 (1984)]] as the unstable branch of the corresponding subcritical bifurcation which ends up at a topological singularity defined by interface pinchoff. We devise an experimental procedure to prepare arbitrary initial conditions in a Hele-Shaw cell. This is used to test the proposed bifurcation scenario and quantitatively asses its practical relevance.
Departament ECM, Universitat de Barcelona, Avinguda Diagonal 647, E-08028, Barcelona, Spain. enric@ecm.ub.es
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Alvarez-Lacalle
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Ortín
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Casademunt