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Surface shape stability analysis of a magnetic fluid in the field of an electromagnet

  • T. I. Becker (a1), V. A. Naletova (a2) (a3), V. A. Turkov (a3) and K. Zimmermann (a1)


Static surface shapes of a magnetic fluid volume between two plates in a non-uniform magnetic field are investigated theoretically and experimentally. Abrupt changes and hysteresis of the magnetic fluid surface shape are observed in the experiments when the current in the coil increases and decreases quasi-statically. The necessary and sufficient conditions for a local minimum of the energy functional are derived theoretically. A method to find stable/unstable surface shapes is developed. The ambiguity in the determination of the magnetic fluid surface shape at the same value of the current is shown. It is found that the experimentally observed surface shapes of the given magnetic fluid volume coincide with the shapes obtained numerically, and practically all of them satisfy the derived necessary and sufficient conditions of the minimum energy. The stability curves of the magnetic fluid bridge between the plates are determined experimentally and theoretically.


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Abou, B., Wesfreid, J.-E. & Roux, S. 2000 The normal field instability in ferrofluids: hexagonsquare transition mechanism and wavenumber selection. J. Fluid Mech. 416, 217237.
Afkhami, S., Tyler, A. J., Renardy, Y., Renardy, M., Pierre, T. G. St., Woodward, R. C. & Riffle, J. S. 2010 Deformation of a hydrophobic ferrofluid droplet suspended in a viscous medium under uniform magnetic fields. J. Fluid Mech. 663, 358384.
Arkhipenko, V. I., Barkov, Yu. D. & Bashtovoi, V. G. 1980 Behavior of a drop of a magnetizable liquid in magnetic fields. Magnetohydrodynamics 16, 221227.
Bacri, J.-C., Frenois, C., Perzynski, R. & Salin, D. 1988 Magnetic drop-sheath wetting transition of a ferrofluid on a wire. Rev. Phys. Appl. 23, 10171022.
Bacri, J.-C. & Salin, D. 1982 Instability of ferrofluid magnetic drops under magnetic field. J. Phys. Lett. 43, 649654.
Barkov, Yu. D. & Berkovskii, B. M. 1980 Breakup of a drop of magnetic fluid. Magnetohydrodynamics 16, 228230.
Cowley, M. D. & Rosensweig, R. E. 1967 The interfacial stability of a ferromagnetic fluid. J. Fluid Mech. 30, 671688.
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.
Gelfand, I. M. & Fomin, S. V. 2000 Calculus of Variations. Dover Publications.
de Gennes, P. G. 1985 Wetting: statics and dynamics. Rev. Mod. Phys. 57, 827863.
John, T., Rannacher, D. & Engel, A. 2007 Influence of surface tension on the conical meniscus of a magnetic fluid in the field of a current-carrying wire. J. Magn. Magn. Mater. 309, 3135.
Kiryushin, V. V. & Bin, C. Z. 1980 Figures of equilibrium of a magnetizable fluid in a magnetic field. Fluid Dyn. 15, 573578.
Landau, L. D. & Lifshitz, E. M. 1980 Electrodynamics of Continuous Media. Pergamon.
Naletova, V. A., Kiryushin, V. V., Reks, A. G. & Suvchuk, E. 2008 Hysteresis of a shape of a magnetic fluid volume near a line conductor. Magnetohydrodynamics 44, 167174.
Naletova, V. A., Turkov, V. A., Pelevina, D. A., Rozin, V. A., Zimmermann, K., Popp, J. & Zeidis, I. 2012 Behavior of a free surface of a magnetic fluid containing a magnetizable cylinder. J. Magn. Magn. Mater. 324, 12531257.
Plateau, J. 1863 Experimental and theoretical researches on the figures of equilibrium of a liquid mass withdrawn from the action of gravity. In Annual Report of the Board of Regents of the Smithsonian Institution, pp. 207285. Government Printing Office.
Polevikov, V. & Tobiska, L. 2005 Instability of magnetic fluid in a narrow gap between plates. J. Magn. Magn. Mater. 289, 379381.
Richter, R. & Lange, A. 2009 Surface instabilities of ferrofluids. In Colloidal Magnetic Fluids: Basics, Development and Application of Ferrofluids (ed. Odenbach, S.), Lect. Notes Phys., vol. 763, pp. 157247. Springer.
Rosensweig, R. E. 1985 Ferrohydrodynamics. Cambridge University Press.
Rosensweig, R. E., Elborai, S., Lee, S.-H. & Zahn, M. 2005 Ferrofluid meniscus in a horizontal or vertical magnetic field. J. Magn. Magn. Mater. 289, 192195.
Rothert, A. & Richter, R. 1999 Experiments on the breakup of a liquid bridge of magnetic fluid. J. Magn. Magn. Mater. 201, 324327.
Vinogradova, A. S., Naletova, V. A., Turkov, V. A. & Reks, A. G. 2013 Influence of apex angles of limiting conic surfaces on the hysteresis of the shape of a magnetic fluid drop on a line conductor. Magnetohydrodynamics 49, 350354.
Volkova, T. I. & Naletova, V. A. 2014 Instability of the magnetic fluid shape in the field of a line conductor with current. Fluid Dyn. 49, 310.
Volkova, T. I., Naletova, V. A. & Turkov, V. A. 2013 Magnetic fluid volume between horizontal plates in the field of an electromagnetic coil. Magnetohydrodynamics 49, 386390.
Yildirim, O. E. & Basaran, O. A. 2001 Deformation and breakup of stretching bridges of newtonian and shear-thinning liquids: comparison of one- and two-dimensional models. Chem. Engng Sci. 56, 211233.
Zahn, M. 2001 Magnetic fluid and nanoparticle applications to nanotechnology. J. Nanopart. Res. 3, 7378.
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Surface shape stability analysis of a magnetic fluid in the field of an electromagnet

  • T. I. Becker (a1), V. A. Naletova (a2) (a3), V. A. Turkov (a3) and K. Zimmermann (a1)


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