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

Published online by Cambridge University Press:  29 September 2017

T. I. Becker Open the ORCID record for T. I. Becker [Opens in a new window] ,
V. A. Naletova ,
V. A. Turkov  and
K. Zimmermann
T. I. Becker*
Affiliation:
Technical Mechanics Group, Faculty of Mechanical Engineering, Technische Universität Ilmenau, Max-Planck-Ring 12, 98693 Ilmenau, Germany
V. A. Naletova
Affiliation:
Department of Hydromechanics, Faculty of Mechanics and Mathematics, Lomonosov Moscow State University, Leninskiye Gory, 119991 Moscow, Russia Insitute of Mechanics, Lomonosov Moscow State University, Michurinskiy pr. 1, 119192 Moscow, Russia
V. A. Turkov
Affiliation:
Insitute of Mechanics, Lomonosov Moscow State University, Michurinskiy pr. 1, 119192 Moscow, Russia
K. Zimmermann
Affiliation:
Technical Mechanics Group, Faculty of Mechanical Engineering, Technische Universität Ilmenau, Max-Planck-Ring 12, 98693 Ilmenau, Germany
*
†Email address for correspondence: [email protected]
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Abstract

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.

JFM classification

Interfacial Flows (free surface): Liquid bridges MHD and Electrohydrodynamics: Magnetic fluids Mathematical Foundations: Variational methods
Type
Papers
Information
Journal of Fluid Mechanics , Volume 830 , 10 November 2017 , pp. 326 - 349
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Copyright
© 2017 Cambridge University Press 

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