Abstract
A vortex sheet formalism is used to search for equilibrium shapes in the centrifugally driven interfacial elastic fingering problem. We study the development of interfacial instabilities when a viscous fluid surrounded by another of smaller density flows in the confined environment of a rotating Hele-Shaw cell. The peculiarity of the situation is associated to the fact that, due to a chemical reaction, the two-fluid boundary becomes an elastic layer. The interplay between centrifugal and elastic forces leads to the formation of a rich variety of stationary shapes. Visually striking equilibrium morphologies are obtained from the numerical solution of a nonlinear differential equation for the interface curvature (the shape equation), determined by a zero vorticity condition. Classification of the various families of shapes is made via two dimensionless parameters: an effective bending rigidity (ratio of elastic to centrifugal effects) and a geometrical radius of gyration.
| Original language | English |
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| Article number | 063009 |
| Journal | Physical Review E |
| Volume | 90 |
| Issue number | 6 |
| DOIs | |
| Publication status | Published - 10 Dec 2014 |