Surface Shape of a Magnetic Fluid with a Ferromagnetic Cylinder in a Uniform Magnetic Field

Purpose. To investigate the surface shape of a flat layer of a magnetic fluid with a ferromagnetic cylindrical body in a uniform magnetic field

Methods. Magnetic fluids based on transformer oil MMT-44 and MMT-10 with saturation magnetization of 43.8 and  9.6 kA/m, respectively, were used in the experiments. A flat layer of magnetic fluid was formed by filling a non-magnetic rectangular cell 57x102 mm in size. The source of a uniform magnetic field is Helmholtz coils with a cylindrical working area 0.2 m in diameter and 0.2 m high. Deviations of the magnetic field strength do not exceed 0.2% in the area where the cell with the magnetic fluid is located. Distortions of a uniform magnetic field were created by a steel rod 10 mm in diameter placed in a magnetic fluid. A study was made of the deformation of the surface of a magnetic fluid in fields of different directions in the range of intensity up to 30 kA/m.

Results. Above a cylindrical ferromagnetic body immersed in a magnetic fluid, the fluid surface was studied under the action of a uniform external magnetic field. Also identified experimental dependences of the deformation amplitude of the free surface of liquids with different saturation magnetization on the magnitude of the acting external field in different directions. The phenomenon of hysteresis of the shape of the free surface of a ferromagnetic fluid is established when the direction of the change in the magnetic field changes. The range of critical fields in which the hysteresis of the free surface shape was observed was established.

Conclusion. The results of the study show that the shape of the free surface of a magnetic fluid with a cylindrical ferromagnetic rod is determined by the nature of the distortion of the uniform magnetic field introduced by the rod. The nature of the field distortion depends on the orientation of the rod relative to the field. The saturation magnetization, as well as the thickness of the liquid layer above the body, affects the shape of the liquid surface in addition to the orientation of the body. The results are of interest in the development of magnetically controlled heat exchange technologies, in vibration protection systems, as well as for control and measuring systems.

1. Rosensweig R. E. Ferrohydrodynamics. Cambridge, USA, Cambridge University Press, 1985. 344 p.

2. Bashtovoy V. G., Berkovskiy B. M., Vislovich A. N. Vvedenie v termomekhaniku magnitnykh zhidkostei [Introduction to Thermomechanics of Magnetic Fluids]. Moscow, IVTAN SSSR Publ., USA, 1985. 188 p.

3. Berkovskiy B. M., Medvedev V. F., Krakov M. S. Magnitnye zhidkosti [Magnetic Fluids: Engineering Applications]. Moscow, Khimiya Publ., 1989. 240 p.

4. Magnetic fluids and Applications Handbook; editor-in-chief B. Berkovski; ed. V. Bashtovoi. New York, USA, Begell House Inc. Publishers, 1996. 851 p.

5. Reks A. G. Nekotoryye voprosy mekhaniki magnitozhidkostnykh sistem so svobodnoy poverkhnost'yu [Some aspects of the mechanics of magnetic fluid systems with a free surface]. Minsk, Belarusian National Technical Univ. Publ., 2005. 256 p.

6. Simonovskii A. Ya. Teploperenos pri zakalochnom okhlazhdenii v magnitnoi zhidkosti [Heat transfer during quench-cooling in a magnetic field]. Magnitnaya gidrodinamika = Magnetohydrodynamics, 1988, vol. 24, no. 2, pp. 67–72.

7. Bashtovoi V. G., Krakov M. S., Taits E. M. Upravlenie teploobmenom v sistemakh s granitsei razdela magnitnoi i nemagnitnoi zhidkostei [Controlling the exchange of heat in systems with a boundary of separation between]. Magnitnaya gidrodinamika = Magnetohydrodinamics, 1989, vol. 25, no. 4, pp. 60–66.

8. Bashtovoi V. G., Volkova O. Yu., Reks A. G. [Influence of magnetic field orientation on the heat transfer process during boiling of magnetic liquids]. Magnitnaya gidrodinamika = Magnetohydrodynamics, 1992, vol. 28, no. 2, pp. 27–31.

9. Gogosov V. V., Kiryushin V. V., Simonovskii A. Ya. Upravlenie teplo- i massoperenosom v magnitnykh zhidkostyakh [Control of the heat and mass transfer in magnetic fluids]. Magnitnaya gidrodinamika = Magnetohydrodynamics, 1994, vol. 30, no. 2, pp. 163–170.

10. Landau L. D., Lifshits Ye. M. Teoreticheskaya fizika [Theoretical physics]. 4th ed. Moscow, Fizmatlit Publ., 2005, vol. 8. 656 p.

11. Gogosov V. V., Grishanina O. A., Kiryushin V. V., Simonovskii A. Ya. Eksperimental'noe issledovanie form svobodnoi poverkhnosti magnitnoi zhidkosti, okruzhayushchei namagnichivayushchuyusya plastinu, vo vneshnem magnitnom pole [Experimental investigations of the free surface of a magnetic fluid, surrounding a magnetizable plane in an external magnetic field]. Magnitnaya gidrodinamika = Magnetohydrodynamics, 1998, vol. 34, no. 1, pp. 40–49.

12. Gogosov V. V., Grishanina O. A., Kiryushin V. V., Simonovskii A. Ya. Teoreticheskoe opisanie form svobodnoi poverkhnosti magnitnoi zhidkosti, okruzhayushchei namagnichivayushchuyusya plastinu, vo vneshnem magnitnom pole [Theoretical description of a free surface shapes of a magnetic fluid. Surrounding a magnetizable plate in an external magnetic field]. Magnitnaya gidrodinamika = Magnetohydrodynamics, 1998, vol. 34, no. 1, pp. 50–57.

13. Gogosov V. V., Iskanderov Kh. D., Kiryushin V. V., Simonovskii A. Ya. Raspredelenie polya temperatur na poverkhnosti i vnutri namagnichivayushchegosya shara pri ego okhlazhdenii v magnitnoi zhidkosti v prilozhennykh magnitnykh polyakh. Eksperimenty i chislennye resheniya [Temperature distribution on the surface and in the interior of a magnetizable sphere during cooling in a magnetic fluid in applied magnetic fields. Experiments and numerical solutions]. Magnitnaya gidrodinamika = Magnetohydrodynamics, 1999, vol. 35, no. 2, pp. 184–194.

14. Bashtovoi V., Motsar А., Reks A. Energy dissipation in a finite volume of magnetic fluid. Journal of magnetism and magnetic materials, 2017, vol. 431, pp. 245–248.

15. Gogosov V. V., Simonovskii A. Ya., Shaposhnikova G. A. Gidrodinamika magnitnykh zhidkostey. Nekotoryye modeli i primery ikh primeneniy [Hydrodynamics of Magnetic Fluids. Some models and examples of their applications]. Trudy matematicheskogo instituta im. A. Steklova = Proceedings of the Mathematical Institute A. Steklov, 1989, vol. 186, pp. 140– 149. (In Russ.)

16. Zimmermann K., Zeidis I., Naletova V., Turkov V., Goncharov P. Surface of magnetic fluid containing a spherical body in the uniform magnetic field. The 15th Riga and 6th PAMIR conference on fundamental and applied MHD, 2005, vol. 1, pp. 373–376.

17. Zimmermann K., Naletova V. A., Zeidis I., Turkov V. A., Pelevina D. A., Bohm V., Popp J. Surface of magnetic fluid containing magnetizable bodies in an applied uniform magnetic field. Magnetohydrodynamics, 2008, vol. 44, no 2, pp. 175–181.

18. Naletova V. A., Pelevina D. A., Turkov V. A. Statika magnitnoy zhidkosti, soderzhashchey kontsentratory magnitnogo polya [Static of a magnetic fluid containing magnetic field concentrators]. Izvestiya RAN. Mekhanika zhidkosti i gaza = Proceedings of the Russian Academy of Sciences. Fluid and gas mechanics, 2009, no. 6, pp. 3–10.

19. Naletova V. A., Turkov V. A., Pelevina D. A., Rozin A. V., Zimmermann K., Popp J., Zeidis I. Behavior of a free surface of a magnetic fluid containing a magnetizable cylinder. J. of Magnetism and Magnetic Materials, 2012, vol. 324, pp. 1253–1257.

20. Bashtovoi V., Motsar А., Naletova V., Reks A., Pelevina D. Free surface of magnetic fluid with a spherical ferromagnetic body in uniform magnetic field. Magnetohygrodynamics, 2013, vol. 49, no. 3-4, pp. 592–595.

21. Pelevina D., Naletova V., Bashtovoi V., Motsar A., Reks A. Magnetic fluid with a spherical ferromagnetic body in a uniform magnetic field. Theory and experiment. Magnetohygrodynamics, 2014, vol. 50, no. 1, pp. 83–90.

22. Bashtovoi V. G., Motsar A. A., Naletova V. A., Reks A. G. The shape of the magnetic fluid surface above a magnetizable sphere in a uniform magnetic field. Technical physics, 2015, vol. 60, no. 10, pp. 1437–1442. http://doi.org/10.1134/S1063784215100060

23. Pelevina D. A., Sharova O. A., Merkulov D. I., Turkov V. A., Naletova V. A. Spherical magnetizable body partially immersed in a magnetic fluid in a uniform magnetic field. Journal of Magnetism and Magnetic Materials. 2019, vol. 494, pp. 165751. http://doi.org/1016/j.jmmm.2019.165751

24. Ryapolov P. A., Polunin V. M., Postnikov E. B., Bashtovoi V. G., Reks A. G., Sokolov E. A. The behaviour of gas inclusions in a magnetic fluid in a non-uniform magnetic field. Journal of Magnetism and Magnetic Materials, 2020, vol. 497, pp. 165925. http://doi.org/10.1016/j.jmmm.2019.165925.