The Surface Topography of a Magnetic Fluid -- a Quantitative Comparison between Experiment and Numerical Simulation

Abstract

The normal field instability in magnetic liquids is investigated experimentally by means of a radioscopic technique which allows a precise measurement of the surface topography. The dependence of the topography on the magnetic field is compared to results obtained by numerical simulations via the finite element method. Quantitative agreement has been found for the critical field of the instability, the scaling of the pattern amplitude and the detailed shape of the magnetic spikes. The fundamental Fourier mode approximates the shape to within 10% accuracy for a range of up to 40% of the bifurcation parameter of this subcritical bifurcation. The measured control parameter dependence of the wavenumber differs qualitatively from analytical predictions obtained by minimization of the free energy.

21 pages, 16 figures; corrected typos, added reference to Kuznetsov and Spector(1976), S.J. Fortune(1995) and Harkins&Jordan (1930). Figures revised

References in corpus (8)

• Two-dimensional solitons on the surface of magnetic fluids
• Pattern and wavenumber selection in ferrofluids
• Wave Number of Maximal Growth in Viscous Magnetic Fluids of Arbitrary Depth
• Amplitude measurements of Faraday waves
• Nonlinear Dynamics of a Single Ferrofluid-Peak in an Oscillating Magnetic Field
• Non-Monotonic Dispersion of Surface Waves in Magnetic Fluids
• Parametrically excited surface waves in magnetic fluids: observation of domain structures
• Scaling Behaviour of the Maximal Growth Rate in the Rosensweig Instability

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