title: Azimuthal field instability in a confined ferrofluid.
abstract: We report the development of interfacial ferrohydrodynamic instabilities when an initially circular bubble of a nonmagnetic inviscid fluid is surrounded by a viscous ferrofluid in the confined geometry of a Hele-Shaw cell. The fluid-fluid interface becomes unstable due to the action of magnetic forces induced by an azimuthal field produced by a straight current-carrying wire that is normal to the cell plates. In this framework, a pattern formation process takes place through the interplay between magnetic and surface tension forces. By employing a perturbative mode-coupling approach we investigate analytically both linear and intermediate nonlinear regimes of the interface evolution. As a result, useful analytical information can be extracted regarding the destabilizing role of the azimuthal field at the linear level, as well as its influence on the interfacial pattern morphology at the onset of nonlinear effects. Finally, a vortex sheet formalism is used to access fully nonlinear stationary solutions for the two-fluid interface shapes.
authors.affiliation: Departamento de Física, Universidade Federal de Pernambuco, Recife, Pernambuco 50670-901 Brazil.
authors.forename: Eduardo O
authors.initials: EO
authors.lastname: Dias
authors.affiliation: Departamento de Física, Universidade Federal de Pernambuco, Recife, Pernambuco 50670-901 Brazil.
authors.forename: José A
authors.initials: JA
authors.lastname: Miranda