Skip to main content Accessibility help

The surface topography of a magnetic fluid: a quantitative comparison between experiment and numerical simulation



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.



Hide All
Abou, B., Wesfreid, J.-E. & Roux, S. 2001 The normal field instability in ferrofluids: hexagon-square transition mechanism and wavenumber selection. J. Fluid Mech. 416, 217237.
Bacri, J.-C. & Salin, D. 1984 First-order transition in the instability of a magnetic fluid interface. J. Phys. Lett. (Paris) 45, L559L564.
Boudouvis, A. G., Puchalla, J. L., Scriven, L. E. & Rosensweig, R. E. 1987 Normal field instability and patterns in pools of ferrofluid. J. Magn. Magn. Mater. 65, 307310.
Browaeys, J., Bacri, J.-C., Flament, C., Neveu, S. & Perzynski, R. 1999 Surface waves in ferrofluids under vertical magnetic field. Eur. Phys. J. B 9, 335341.
Cowley, M. D. & Rosensweig, R. E. 1967 The interfacial stability of a ferromagnetic fluid. J. Fluid Mech. 30, 671688.
Cross, M. C. & Hohenberg, P. C. 1993 Pattern formation outside of equilibrium. Rev. Mod. Phys. 65, 8511112.
Fortune, S. J. 1995 Voronoi diagrams and Delaunay triangulations. In Computing in Euclidean Geometry (ed. Du, D.-Z. & Hwang, F.), Lecture Notes Series on Computing, vol. 1. World Scientific.
Friedrichs, R. 2002 Low symmetry patterns on magnetic fluids. Phys. Rev. E 66, 066215-1-7.
Friedrichs, R. & Engel, A. 2001 Pattern and wave number selection in magnetic fluids. Phys. Rev. E 64, 021406-1-10.
Gailitis, A. 1969 A form of surface instability of a ferromagnetic fluid. Magnetohydrodynamics 5, 4445.
Gailitis, A. 1977 Formation of the hexagonal pattern on the surface of a ferromagnetic fluid in an applied magnetic field. J. Fluid Mech. 82, 401413.
Harkins, W. D. & Jordan, H. F. 1930 A method for the determination of surface and interfacial tension from the maximum pull on a ring. J. Am. Chem. Soc. 52, 17471750.
John, V. & Matthies, G. 2004 MooNMD – a program package based on mapped finite element methods. Comput. Vis. Sci. 6, 163170.
Kuznetsov, E. A. & Spektor, M. D. 1976 Existence of a hexagonal relief on the surface of a dielectric fluid in an external electrical field. Sov. Phys., J. Exp. Theor. Phys. 44, 136.
Lange, A. 2001 Scaling behaviour of the maximal growth rate in the Rosensweig instability. Europhys. Lett. 55, 327.
Lange, A., Reimann, B. & Richter, R. 2000 Wave number of maximal growth in viscous magnetic fluids of arbitrary depth. Phys. Rev. E 61, 55285539.
Lange, A., Reimann, B. & Richter, R. 2001 Wave number of maximal growth in viscous ferrofluids. Magnetohydrodynamics 37, 261.
Lange, C. G. & Newell, A. C. 1971 The post buckling problem for thin elastic shells. SIAM J. Appl. Maths, 21, 605629.
Lavrova, O., Matthies, G., Mitkova, T., Polevikov, V. & Tobiska, L. 2003 Finite Element Methods for Coupled Problems in Ferrohydrodynamics. Lecture Notes in Computer Science and Engineering, vol. 35, pp. 160183. Springer.
Mahr, T. & Rehberg, I. 1998a Nonlinear dynamics of a single ferrofluid-peak in an oscillating magnetic field. Physica D 111, 335346.
Mahr, T. & Rehberg, I. 1998b Parametrically excited surface waves in magnetic fluids: observation of domain structures. Phys. Rev. Lett. 81, 89.
Mahr, T., Groisman, A. & Rehberg, I. 1996 Non-monotonic dispersion of surface waves in magnetic fluids. J. Magn. Magn. Mater. 159, L45L50.
Matthies, G. & Tobiska, L. 2005 Numerical simulation of normal-field instability in the static and dynamic case. J. Magn. Magn. Mater. 289, 346349.
Megalios, E., Kapsalis, N., Paschalidis, J., Papathanasiou, A. & Boudouvis, A. 2005 A simple optical device for measureing free surface deformations of nontransparent liquids. J. Colloid Interface Sci. 288, 505512.
Peinke, J., Parisi, J., Rössler, O. E. & Stoop, R. 1992 Encounter with Chaos: Self-Organized Hierarchical Complexity in Semiconductor Experiments. Springer.
Perlin, M., Lin, H. & Ting, C.-L. 1993 On parasitic capillary waves generated by steep gravity waves: an experimental investigation with spatial and temporal measurements. J. Fluid Mech. 255, 597.
Prigogine, I. 1988 Vom Sein zum Werden. Zeit und Komplexität in den Naturwissenschaften, 1st edn. Piper.
Rehberg, I., Bodenschatz, E., Winkler, B. & Busse, F. H. 1987 Forced phase diffusion in a convection experiment. Phys. Rev. Lett. 59, 282284.
Reimann, B., Richter, R., Rehberg, I. & Lange, A. 2003 Oscillatory decay at the Rosensweig instability: experiment and theory. Phys. Rev. E 68, 036220.
Richter, R. & Barashenkov, I. 2005 Two-dimensional solitons on the surface of magnetic liquids. Phys. Rev. Lett. 94, 184503.
Richter, R. & Bläsing, J. 2001 Measuring surface deformations in magnetic fluid by radioscopy. Rev. Sci. Instrum. 72, 17291733.
Rosensweig, R. E. 1985 Ferrohydrodynamics. Cambridge University Press.
Sauer, K. D. & Allebach, J. P. 1987 Iterative reconstruction of multidimensional signals from nonuniformly spaced samples. IEEE Trans. CAS 34, 14971506.
Shipman, P. D. & Newell, A. C. 2004 Phylotactic patterns on plants. Phys. Rev. Lett. 92, 168102.
Taylor, G. I. 1933 The buckling load for a rectangular plate with four clamped edges. Z. Angew. Math. Mech. 13, 147152.
Taylor, G. I. & McEwan, A. D. 1965 The stability of a horizontal fluid interface in a vertical electric field. J. Fluid Mech. 22, 115.
Wernet, A., Wagner, C., Papathanassiou, D., Müller, H. W. & Knorr, K. 2001 Amplitude measurements of Faraday waves. Phys. Rev. E 63, 036305.
MathJax is a JavaScript display engine for mathematics. For more information see

Related content

Powered by UNSILO

The surface topography of a magnetic fluid: a quantitative comparison between experiment and numerical simulation



Full text views

Total number of HTML views: 0
Total number of PDF views: 0 *
Loading metrics...

Abstract views

Total abstract views: 0 *
Loading metrics...

* Views captured on Cambridge Core between <date>. This data will be updated every 24 hours.

Usage data cannot currently be displayed.