title: Stationary patterns in centrifugally driven interfacial elastic fingering.
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.
authors.affiliation: Departamento de Física, Universidade Federal de Pernambuco, Recife, Pernambuco 50670-901, Brazil.
authors.forename: Gabriel D
authors.initials: GD
authors.lastname: Carvalho
authors.affiliation: Wolfson Centre for Mathematical Biology, Mathematical Institute, University of Oxford, Oxford OX2 6GG, United Kingdom.
authors.forename: Hermes
authors.initials: H
authors.lastname: Gadêlha
authors.affiliation: Departamento de Física, Universidade Federal de Pernambuco, Recife, Pernambuco 50670-901, Brazil.
authors.forename: José A
authors.initials: JA
authors.lastname: Miranda
mesh_terms: D002498:Centrifugation; D004548:Elasticity; D008962:Models, Theoretical; D012399:Rotation; D014783:Viscosity