Growth of surface undulations at the Rosensweig instability

We investigate the growth of a pattern of liquid crests emerging in a layer of magnetic liquid when subjected to a magnetic field oriented normally to the fluid surface. After a steplike increase of the magnetic field, the temporal evolution of the pattern amplitude is measured by means of a Hall-sensor array. The extracted growth rate is compared with predictions from linear stability analysis by taking into account the proper nonlinear magnetization curve M(H). The remaining discrepancy can be resolved by numerical calculations via the finite-element method. By starting with a finite surface perturbation, it can reproduce the temporal evolution of the pattern amplitude and the growth rate. The investigations are performed for two magnetic liquids, one with low and one with high viscosity.Comment: 12 pages, 12 figure

The growth of localized states on the surface of magnetic fluids

AbstractBy means of a local magnetic perturbation we generate localized states on the surface of a ferrofluid in the bistable regime of the Rosensweig instability. Establishing a magnetic ramp at the edge of the vessel enables us to record the growth of the localized spikes with a high speed camera. From the pictures we extract their growth rate. Under variation of the local induction we find a square-root scaling of the growth rate, which can be understood by a saddle-node bifurcation, induced by the local variation of the magnetic induction

Hexagons become second if symmetry is broken

Pattern formation on the free surface of a magnetic fluid subjected to a magnetic field is investigated experimentally. By tilting the magnetic field the symmetry can be broken in a controllable manner. When increasing the amplitude of the tilted field, the flat surface gives way to liquid ridges. A further increase results in a hysteretic transition to a pattern of stretched hexagons. The instabilities are detected by means of a linear array of magnetic hall sensors and compared with theoretical predictions.Comment: accepted for publication by Physical Review E/Rapid Communicatio