| Issue |
Europhys. Lett.
Volume 63, Number 6, September 2003
|
|
|---|---|---|
| Page(s) | 826 - 832 | |
| Section | Electromagnetism, optics, acoustics, heat transfer, classical mechanics, and fluid dynamics | |
| DOI | https://doi.org/10.1209/epl/i2003-00605-7 | |
| Published online | 01 November 2003 | |
Non-linear analysis of the Rosensweig instability
1
ITP, Otto-von-Guericke-Universität - Postfach 4120, 39016 Magdeburg, Germany
2
ABB AG, Corporate Research Center - Wallstadter Str. 59 68526 Ladenburg, Germany
Received:
6
February
2003
Accepted:
10
July
2003
We derive a closed equation for the shape of the free surface of a magnetic fluid subject to an external magnetic field. The equation is non-local due to the long-range character of the magnetic interaction. We develop a systematic multiple-scale perturbation expansion with a non-local linear operator involving the Hilbert transform of the surface profile. The resulting amplitude equation describing the slow modulation of the basic pattern is shown to remain local.
PACS: 47.20.Ma – Interfacial instability / 47.20.Lz – Secondary instability / 75.50.Mm – Magnetic liquids
© EDP Sciences, 2003
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