TECHNICAL MECHANICS
ISSN (Print): 1561-9184, ISSN (Online): 2616-6380

English
Russian
Ukrainian
Home > Journal Issues > 2 (2016) Technical mechanics > 8
___________________________________________________

UDC 537.84

Technical mechanics, 2016, 2, 71 - 84

STABILITY OF FREE SURFACE OF VISCOUS FERROFLUID LAYER EXPOSED TO VARIABLE MAGNETIC FIELD AND MECHANICAL VIBRATIONS

N. F. Patsegon, S. I. Potseluev

      ABSTRACT

      The stability of a layer of a viscous nonlinearly magnetizing ferrofluid in the non-stationary uniform magnetic field oriented arbitrary to a free surface is considered with provision for the mechanical vibrations of the layer. In case of the magnetic field composing of a constant portion and a harmonically time-varied portion, pro- viding the rationality of relations between electromagnetic frequencies and those of the vibratory effects, the problem reduces to the study of an infinite system of the linear equations for the Fourier series of the amplitude of disturbances of a free surface of the ferrofluid. The matrix of this system is a square bunch of the known matrices whose parameter is the amplitude of the parametric effects. The problem is reduced to a linear spectral problem in which the amplitude of the parametric effects is the eigenvalue. Neutral curves of the stability are found. It is established that variations in angle of orientation of the magnetic field and an increase in its stationary component may result in the bicritical points and the transfer from the harmonic oscillation to the subharmonic oscillation. The effects of the stationary inclined magnetic field on a critical amplitude of the mechanical vibrations are non- monotonic and depend on not only the orientation of the magnetic field but on the thickness of the fluid layer. A decrease in the thickness of the ferrofluid layer can result in an increase in the threshold of the initiation of a parametric instability and excitation of waves of a lower length at its surface when losing the stability. Distinctions of the vibratory and electromagnetic mechanisms in evolution of the parametric instability of a free surface resulted from two-frequency modulation of the magnetic field are studied. Pdf (English)







      KEYWORDS

parametric resonance, oscillating magnetic field, mechanical vibrations, magnetic fluid.

      FULL TEXT:

Pdf (English)









      REFERENCES

1. Colloidal Magnetic Fluids: Basics, Development and Application of Ferrofluids / S. Odenbach, W. Beiglbock, J. Ehlers et al. - Berlin : Springer, 2009. - 430 p.

2. Faraday M. On the forms and states assumed by fluids in contact with vibrating elastic surfaces / M. Faraday // Phil. Trans. of the Royal Society of London. - 1831. - Vol. 121. - . 319 - 346.

3. Ibrahim R. A. Liquid Sloshing Dynamics: Theory and Applications / R. A. Ibrahim. - Cambridge University Press, 2005. - 947 p.

4. Kumar K. Linear Theory of Faraday Instability in Viscous Fluids. / K. Kumar // Proc. Roy. Soc. London. - 1996. - Vol. 452, No1948. - . 1113 - 1126.

5. Heat and Mass Exchange and Vibration (in Russian) / Prisnyakov V., Bondarenko S., Lutsenko V. et al. - Odessa: Neptun-Tekhnogia, 2001. - 208 p

6. Rosensweig R. Ferrohydrodynamics (in Russian) / R. Rosensweig, Translated from English by V. V. Kiryushin. - Moscow : Mir, 1989. - 356 p.

7. Tarapov I. E. Surface waves and the stability of the free surface of a magnetizable fluid / I. E. Tarapov // J. Appl. Mech. and Techn. Phys. - 1974. - Vol. 15, No 4. - . 465 - 469.

8. Muller H. W. Parametrically driven surface waves on viscous ferrofluids / H. W. Muller // Phys. Rev.E. - 1998. - Vol. 58, No 5. - . 6199 - 6205.

9. Mekhonoshin V. V. Faraday instability on viscous ferrofluids in a horizontal magnetic field: Oblique rolls of arbitrary orientation. / V. V. Mekhonoshin, A. Lange // Phys. Rev. E. - 2002. - Vol. 65. - . 061509-1 - 061509-7.

10. Bashtovoi V. G. Excitation and study of subcritical waves on a magnetic fluid surface / V. G. Bashtovoi, R. E. Rosensweig // J. Magn. Magn. Mater. - 1993. - Vol. 122, No 1 - 3. - . 234 - 240.

11. Blum E. Ya. Magnetic Fluids (in Russian) / E. Ya. Blum, M. M. Mayorov, A. O. Tsebers. - Riga : Zinatne, 1989. - 386 p.

12. Bajaj R. Parametric instability of the interface between two viscous magnetic fluids / R. Bajaj, S. K. Malik // J. Magn. Magn. Mater. - 2002. - Vol. 253, No 1 - 2. - P. 35 - 44.

13. Hennenberg M. On the Hill Equation Describing Oscillations of a Ferrofluid Free Surface in a Vertical Magnetic Field / M. Hennenberg, S. Slavtchev, G.Valchev // Microgravity Sci. Technol. - 2010. - Vol. 22, No 3. - . 455 - 460.

14. Tarapov I. Ye. Mechanics of Continuum Medium. In 3 parts. Part 2: General Laws of Kinematics and Dynamics (in Russian) / I. Ye. Rarapov. - Kharkov : Zolotye Stranitsy, 2002. - 516 p.

15. Patsegon N. F. Stability of free surface of a viscous magnetizing fluid exposed to multiple parametric excitation (in Russian) / N. F. Patsegon, S. I. Potseluev // Prikladnaya Gidromekhanika. - 2014. - Vol. 16, No 3. - P. 36 - 51.

16. Patsegon N. F. The volumetric parametric resonance in magnetizable medium / N. F. Patsegon, S. I. Potseluiev // Visnyk Kharkivskogo Natsionalnogo Universitetu imeni Karamzina. Seria Matematyka, Prykladna Matematyka ta Mekhanika. - 2015. - Vol. 81. - . 12 - 27.





Copyright () 2016 N. F. Patsegon, S. I. Potseluev

Copyright 2014-2018 Technical mechanics


____________________________________________________________________________________________________________________________
GUIDE
FOR AUTHORS
Guide for Authors