Pre-labyrinthine, cross-sectional instabilities of captive ferrofluid drops: computations and experiments

A. G. Papathanasiou - A. G. Boudouvis

Department of Chemical Engineering, National Technical University of Athens, Zografou Campus, Athens 15780, Greece

Abstract
A ferrofluid drop held captive between two horizontal solid plates suffers cross-sectional, symmetry-breaking instabilities when the strength of a magnetic field, applied perpendicularly to the plates, exceeds a critical value. These instabilities are caused by the competition between gravity, capillary and magnetic forces and are observed in experiments as transitions between equilibrium shapes. The circular cross-section turns to dumbbell-shaped, to multi-lobbed and, eventually, to a labyrinthine configuration. The pre-labyrinthine instability of the circular cross-section is investigated theoretically and experimentally. The experiments show a hysteretical circle-to-dumbbell transition. Theoretical predictions of drop equilibrium and stability are drawn from the equations of capillary magnetohydrostatics. Accounting for interesting realities in the governing equations and the boundary conditions, gives rise to a three-dimensional, nonlinear and free boundary problem that is dealt with the Galerkin/finite element method and computer-implemented bifurcation analysis. The results of the computational analysis include the effect of applied field strength and of wetting on drop equilibrium and stability near the onset of the instability and beyond. The results compare well with experimental measurements and they reveal the mechanism of the hysteretical instability. Figs 13, Refs 16.