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DY: Dynamik und Statistische Physik

DY 33: Ferrofluids and Liquid Crystals

DY 33.1: Talk

Monday, March 7, 2005, 14:00–14:15, TU H2032

Band structure of surface waves on periodic fluid ridges resulting from the Rosensweig instability — •Rene Friedrichs — ABB AG, Corporate Research Center Germany, Wallstadter Str. 59, 68526 Ladenburg

Parallel fluid ridges can be generated on the free surface of a magnetic fluid by means of a tilted magnetic field [1]. Though the surface deformations resulting from this so called ”Rosensweig instability” are static, surface waves can propagate on the periodic deformations since the developed structures remain liquid.

Based on a weakly nonlinear analysis of the static ridge pattern [2], we derive a closed equation for the dynamics of the free fluid surface. We calculate the dispersion relation of the surface waves in dependence on the amplitude of the periodic fluid ridges. The resulting band structure of the surface waves can be controlled easily by the external magnetic field. This is in contrast to other hydrodynamic systems such as waves on a fluid with periodic surface tension [3] or over a periodic bottom [4].

[1] Y. D. Barkov and V. G. Bashtovoi, Magnetohydrodynamics 13, 497 (1977)

[2] R. Friedrichs and A. Engel, Europhys. Lett. 63 (6), 826 (2003)

[3] T. Chou, J. Fluid Mech. 369, 333 (1998)

[4] M. Torres, et al., Phys. Rev. E 63, 011204 (2000)