Confined ferrofluid droplet in crossed magnetic fields
Department of Physics and Astronomy, Dickinson College, 17013, Carlisle, PA, USA
2 Departamento de Fısica-LFTC, UFPE, 50670-901, Recife, PE, Brazil
Accepted: 28 June 2007
Published online: 22 August 2007
When a ferrofluid drop is trapped in a horizontal Hele-Shaw cell and subjected to a vertical magnetic field, a fingering instability results in the droplet evolving into a complex branched structure. This fingering instability depends on the magnetic field ramp rate but also depends critically on the initial state of the droplet. Small perturbations in the initial droplet can have a large influence on the resulting final pattern. By simultaneously applying a stabilizing (horizontal) azimuthal magnetic field, we gain more control over the mode selection mechanism. We perform a linear stability analysis that shows that any single mode can be selected by appropriately adjusting the strengths of the applied fields. This offers a unique and accurate mode selection mechanism for this confined magnetic fluid system. We present the results of numerical simulations that demonstrate that this mode selection mechanism is quite robust and “overpowers” any initial perturbations on the droplet. This provides a predictable way to obtain patterns with any desired number of fingers.
PACS: 47.65.Cb Magnetic fluids and ferrofluids – / 47.15.gp Hele-Shaw flows –
© EDP Sciences, Società Italiana di Fisica and Springer-Verlag, 2007