Skip to main content
SpringerLink
Log in

Viscous Fingering Patterns in Ferrofluids

  • Published:
Journal of Statistical Physics Aims and scope Submit manuscript

Abstract

Viscous fingering occurs in the flow of two immiscible, viscous fluids between the plates of a Hele–Shaw cell. Due to pressure gradients or gravity, the initially planar interface separating the two fluids undergoes a Saffman–Taylor instability and develops fingerlike structures. When one of the fluids is a ferrofluid and a perpendicular magnetic field is applied, the labyrinthine instability supplements the usual viscous fingering instability, resulting in visually striking, complex patterns. We consider this problem in a rectangular flow geometry using a perturbative mode-coupling analysis. We deduce two general results: viscosity contrast between the fluids drives interface asymmetry, with no contribution from magnetic forces; magnetic repulsion within the ferrofluid generates finger tip-splitting, which is absent in the rectangular geometry for ordinary fluids.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Similar content being viewed by others

REFERENCES

  1. P. G. Saffman and G. I. Taylor, Proc. R. Soc. London Ser. A 245:312 (1958).

    Google Scholar 

  2. For recent reviews on this fascinating subject see K. V. McCloud and J. V. Maher, Phys. Rep. 260:139 (1995); A. A. Sonin, Rivista del Nuovo Cimento 14:1 (1991); P. G. Saffman, IMA J. Appl. Math. 46:137 (1991); D. Bensimon, L. P. Kadanoff, S. Liang, B. I. Shraiman, and C. Tang, Rev. Mod. Phys. 58:977 (1986).

    Google Scholar 

  3. R. E. Rosensweig, Ferrohydrodynamics (Cambridge University Press, Cambridge, 1985).

    Google Scholar 

  4. R. Perzynski et al. (unpublished).

  5. D. P. Jackson, R. E. Goldstein, and A. O. Cebers, Phys. Rev. E 50:298 (1994).

    Google Scholar 

  6. A. O. Cebers, Magnetohydrodynamics 17:113 (1981).

    Google Scholar 

  7. B. A. Dubrovin, A. T. Fomenko, and S. P. Novikov, Modern Geometry-Methods and Applications, Part 1 (Springer-Verlag, New York, 1984).

    Google Scholar 

  8. I. S. Gradshteyn and I. M. Ryzhik, Table of Integrals, Series, and Products (Academic Press, New York, 1994).

    Google Scholar 

  9. A. O. Tsebers, Magnetohydrodynamics 16:236 (1980).

    Google Scholar 

  10. J. A. Miranda and M. Widom, Int. J. Mod. Phys. B 12:931 (1998).

    Google Scholar 

  11. J. A. Miranda and M. Widom, Physica D 120:315 (1998).

    Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Department of Physics, Carnegie Mellon University, Pittsburgh, Pennsylvania, 15213

    Michael Widom & José A. Miranda

  2. Departamento de Fisica, Universidade Federal de Pernambuco, Recife, PE 50670-901, Brazil

    José A. Miranda

Authors
  1. Michael Widom
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. José A. Miranda
    View author publications

    You can also search for this author in PubMed Google Scholar

Rights and permissions

Reprints and permissions

About this article

Cite this article

Widom, M., Miranda, J.A. Viscous Fingering Patterns in Ferrofluids. Journal of Statistical Physics 93, 411–426 (1998). https://doi.org/10.1023/B:JOSS.0000033156.44251.15

Download citation

  • Issue Date:

  • DOI: https://doi.org/10.1023/B:JOSS.0000033156.44251.15

Search

Navigation