Abstract
We report on recent progress in understanding the formation of surface structures on a plain layer of ferrofluid in a vertical magnetic field. This normal field instability can be tackled by a linear and a nonlinear description. In the linear regime of small amplitudes we focus on the wave number of maximal growth, its corresponding growth rate and the oscillatory decay of metastable pattern, accessible via a pulse technique. A quantitative comparison of measurements with predictions of the linear stability analysis is performed, whereby the viscosity and the finite depth of the liquid layer is taken into account.
In the nonlinear regime the fully developed peak pattern can be predicted by a minimization of the free energy and by numerics employing the finite element method. For a comparison with the results of both methods, the three-dimensional surface profile is recorded by a radioscopic measurement technique. In the bistable regime of the flat and patterned state we generate localized states (ferrosolitons) which are recovered in analytical and numerical model descriptions. For higher fields an inverse hysteretic transition from hexagonal to square planforms is measured.
Via a horizontal field component the symmetry can be broken in the experiment, resulting in liquid ridges and distorted hexagons, as predicted by theory. Replacing ferrofluid by ferrogel also an elastic energy contribution has to be taken into account for a proper model description, yielding a linear shift of the threshold and an increased bistability range.
Parametric excitation in combination with magnetic fields is
widening the horizon of pattern formation even further. For the
mono-spike oscillator harmonic and subharmonic response as well as
deterministic chaos is observed and modeled. In a ring of spikes the
formation of domains of different wavelengths, and spatio-temporal
intermittency is quantitatively studied. For an extended layer of
ferrofluid we predict that a stabilizing horizontal field
counteracted by vertical vibrations will result in oblique rolls
with preselected orientation.
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