## Title data

Richter, Reinhard ; Lange, Adrian:

**Surface Instabilities of Ferrofluids.**

*In:* Odenbach, Stefan
(ed.):
Colloidal magnetic fluids : basics, development and applications of ferrofluids. -
Berlin
: Springer
,
2009
. - pp. 157-247
. - (Lecture notes in physics
; 763
)

ISBN 978-3-540-85386-2

DOI: https://doi.org/10.1007/978-3-540-85387-9_3

## Abstract in another language

We report on recent progress in understanding the formation of surface protuberances on a planar layer of ferrofluid in a magnetic field oriented normally to the surface. This normal field or Rosensweig 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 are 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.

## Further data

Item Type: | Article in a book |
---|---|

Refereed: | No |

Institutions of the University: | Faculties Faculties > Faculty of Mathematics, Physics und Computer Science Faculties > Faculty of Mathematics, Physics und Computer Science > Department of Physics Faculties > Faculty of Mathematics, Physics und Computer Science > Department of Physics > Former Professors Faculties > Faculty of Mathematics, Physics und Computer Science > Department of Physics > Chair Experimental Physics V Faculties > Faculty of Mathematics, Physics und Computer Science > Department of Physics > Former Professors > Chair Experimental Physics V - Univ.-Prof. Dr. Ingo Rehberg Profile Fields Profile Fields > Advanced Fields Profile Fields > Advanced Fields > Nonlinear Dynamics |

Result of work at the UBT: | Yes |

DDC Subjects: | 500 Science > 530 Physics |

Date Deposited: | 26 Sep 2018 11:35 |

Last Modified: | 08 Jul 2021 11:00 |

URI: | https://eref.uni-bayreuth.de/id/eprint/45888 |