Revista UIS Ingenierías

Vol. 11 No. 2 (2012): Revista UIS Ingenierías
Articles

Numerical analysis for the ferrofluid flow in the annular gap between two concentric cylinders

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  • Víctor Peña C.,
  • Arlex Chaves-Guerrero,
  • David Fuentes-Diaz
Víctor Peña C.
Universidad Industrial de Santander
Bio
Arlex Chaves-Guerrero
Universidad Industrial de Santander
Bio
David Fuentes-Diaz
Universidad Industrial de Santander
Bio

Published 2012-12-15

Keywords

  • Ferrofuid,
  • structured fluid,
  • ferrohyrodynamics

How to Cite

Peña C., V., Chaves-Guerrero, A., & Fuentes-Diaz, D. (2012). Numerical analysis for the ferrofluid flow in the annular gap between two concentric cylinders. Revista UIS Ingenierías, 11(2), 145–153. Retrieved from https://revistas.uis.edu.co/index.php/revistauisingenierias/article/view/145-153
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Abstract

This paper presents a numerical-analytic solution for the fow of a ferrofuid in the annular gap between two concentric cylinders induced by a rotating magnetic feld. Unlike analytical solutions presented in the literature,  this analysis takes into account the effect of the terms ω×M and in the magnetization equation which are  commonly disregarded in order to decouple the magnetic hydrodynamic problem obtaining in this way an analytical  solution. However, it was found that its effect is negligible under the assumption that the magnetization vector of the  ferrofuid is proportional to magnetic feld vector. The numerical results show a good agreement with the asymptotic  solution reported by Chaves et al. 2010. We also review the range of application of this analysis and others reported  in the literature made under assumption of proportionality of the vectors of magnetization and magnetic feld.

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References

  1. R. E. Rosensweig, Ferrohydrodynamics. Mineola, NY: Dover Publications, 1997.
  2. K. Raj, B. Moskowitz, and R. Casciari, “Advances in ferrofluid technology,” Journal of Magnetism and Magnetic Materials, vol. 149, pp. 174-180, 1995.
  3. C. Barrera, A. P. Herrera, N. Bezares, E. Fachini, R. Olayo-Valles, J.P. Hinestroza and C. Rinaldi, “Effect of poly(ethylene oxide)-silane graft molecular weight on the colloidal properties of iron oxide nanoparticles for biomedical applications”. Journal of Colloid and Interface Science. vol. 377, pp. 40-50, 2012.
  4. J. P. Mctague, “Magnetoviscosity of Magnetic Colloids,” The Journal of Chemical Physics, vol. 51, pp. 133, 1969.
  5. C. Rinaldi, F. Gutman, X. He, A. D. Rosenthal, and M. Zahn, “Torque measurements on ferrofluid cylinders in rotating magnetic fields,” Journal of Magnetism and Magnetic Materials, vol. 289, pp. 307-310, 2005.
  6. M. I. Shliomis and K. I. Morozov, “Negative viscosity of ferrofluid under alternating magnetic field,” Physics of Fluids, vol. 6, pp. 2855-2861, 1994.
  7. R. Moskowitz and R. E. Rosensweig, “Nonmechanical torque-driven flow of a ferromagnetic fluid by an electromagnetic field,” Applied Physics Letters, vol. 11, pp. 301-303, 1967.
  8. A. Chaves, C. Rinaldi, S. Elborai, X. He, and M. Zahn, “Bulk flow in ferrofluids in a uniform rotating magnetic field,” Physical Review Letters, vol. 96, pp. 194501(1-4), 2006.
  9. V. M. Zaitsev and M. I. Shliomis, “Entrainment of ferromagnetic suspension by a rotating field,” Journal of Applied Mechanics and Technical Physics, vol. 10, pp. 696-700, 1969.
  10. A. F. Lehlooh, S. H. Mahmood, and J. M. Williams, “On the particle size dependence of the magnetic anisotropy energy constant,” Physica B, vol. 321, pp. 159-162, 2002.
  11. A. Chaves, F. Gutman and C. Rinaldi, “Torque and bulk flow of ferrofluid in an annular gap subjected to a rotating magnetic Field,” Journal of Fluids Engineering, vol. 129 pp. 412-422, 2007.
  12. C. Rinaldi, “Continuum modeling of polarizable systems,” vol. Ph.D. Boston, USA: Massachusetts Institute of Technology, 2002.
  13. S. Feng, A. L. Graham, J. R. Abbott, and H. Brenner, “Antisymmetric stresses in suspensions: vortex viscosity and energy dissipation,” Journal of Fluid Mechanics, vol. 563, pp. 97-122, 2006.
  14. A. Chaves, I. Torres, and C. Rinaldi, “Flow of ferrofluid in an annular gap in a rotating magnetic field,” Physics of Fluids, vol. 22, pp. 092002, 2010.
  15. I. Torres and C. Rinaldi, “Ferrofluid flow i the annular gap of a multipole rotating magnetic field,” Physics of Fluids, vol. 23, pp. 082001-1, 2011.
  16. R. E. Rosensweig, J. Popplewell, and R. J. Johnston, “Magnetic fluid motion in rotating field,” Journal of Magnetism and Magnetic Materials, vol. 85, pp. 171-180, 1990.
  17. A. Chaves, M. Zahn, and C. Rinaldi, “Spinup flow of ferrofluids: Asymptotic theory and experimental measurements,” Physics of Fluids, vol. 20, pp. 053102, 2008.
  18. B. A. Finlayson, “Modeling a Ferrofluid in a Rotating Magnetic Field,” presented at Comsol Conference, Boston, Massachusetts, 2007.
  19. S. M. Elborai, “Ferrofluid surface and volume flows in uniform rotating magnetic field,” in Department of electrical engineering and computer science, vol. Doctor of Phylosophy. Boston: Massachusetts Institute of Technology, 2006, pp. 260.
  20. S. Khushrushahi, A. Chaves Guerrero, C. Rinaldi, and M. Zahn, “An analysis of spin diffusion dominated ferrofluid spin-up flows in uniform rotating magnetic field,” presented at COMSOL COMFERENCE, Boston, USA, 2011.
  21. J. S. Dahler and L. E. Scriven, “Theory of structured continua. I. General considerations of angular momentum and polarization," Proceedings of the Royal Society of London, Series A, vol. 275, pp. 504-527, 1963.
  22. D. W. Condiff and J. S. Dahler, “Fluid mechanical aspects of antisymmetric stress,” The Physics of Fluids, vol. 7, pp. 842-854, 1964.
  23. J. S. Dahler and L. E. Scriven, “Angular momentum of continua,” Nature, vol. 192, pp. 36-37, 1961.
  24. H. Brenner, “Rheology of a dilute suspension of dipolar spherical particles in an external field,” Journal of Colloid and Interface Science, vol. 32, pp. 141-158, 1970.
  25. M. I. Shliomis, “Effective viscosity of magnetic suspensions,” Sov. Phys. JETP, vol. 34, pp. 1291- 1294, 1972.
  26. M. I. Shliomis, “Concerning one gyromagnetic effect in a liquid paramagnet,” Sov. Phys. JETP, vol. 39, pp. 701-704, 1974.
  27. J. R. Melcher, Continuum Electromechanics. Cambridge, MA: MIT Press, 1981.