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Knieling, Holger ; Lange, Adrian ; Matthies, Gunar ; Rehberg, Ingo ; Richter, Reinhard:
Maximal growth rate at the Rosensweig instability : theory, experiment, and numerics.
In: Proceedings in Applied Mathematics and Mechanics.
Bd. 7
(2007)
Heft 1
.
- S. 4140025-4140026.
ISSN 1617-7061
DOI: https://doi.org/10.1002/pamm.200700969
Abstract
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 step like 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 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.