Europhys. Lett., 63 (6) , pp. 826-832 (2003)
Non-linear analysis of the Rosensweig instabilityR. Friedrichs1, 2 and A. Engel1
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 in final form 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.
47.20.Ma - Interfacial instability.
47.20.Lz - Secondary instability.
75.50.Mm - Magnetic liquids.
© EDP Sciences 2003