IDEAS home Printed from https://ideas.repec.org/a/eee/phsmap/v157y1989i1p524-528.html
   My bibliography  Save this article

Viscous fingers on fractals

Author

Listed:
  • Meir, Yigal
  • Aharony, Amnon

Abstract

We investigate the problem of flow in porous media near the percolation threshold by studying the generelized model of Viscous Fingering (VF) on fractal structures. We obtain analytic expressions for the fractal dimensions of the resulting structures, which are in excellent agreement with existing experimental results, and exact relations for the exponent Dt, which describes the scaling of the time it takes the fluid to cross the sample, with the sample size, in terms of geometrical exponents for various experimental situations. Lastly, we discuss the relation between the continuous viscous fingers model and stochastic processes such as dielectric breakdown model (DBM) and diffusion limited aggregation (DLA).

Suggested Citation

  • Meir, Yigal & Aharony, Amnon, 1989. "Viscous fingers on fractals," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 157(1), pages 524-528.
    • Handle: RePEc:eee:phsmap:v:157:y:1989:i:1:p:524-528
    DOI: 10.1016/0378-4371(89)90355-5
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/0378437189903555
    Download Restriction: Full text for ScienceDirect subscribers only. Journal offers the option of making the article available online on Science direct for a fee of $3,000
    File URL: https://libkey.io/10.1016/0378-4371(89)90355-5?utm_source=ideas
    LibKey link: if access is restricted and if your library uses this service, LibKey will redirect you to where you can use your library subscription to access this item
    ---><---

    As the access to this document is restricted, you may want to search for a different version of it.

    References listed on IDEAS

    as
    1. Den Nijs, M.P.M., 1979. "The Kadanoff lowerbound renormalization transformation for the q-state Potts model," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 95(3), pages 449-472.
    2. Joseph Aharony & Sasson Bar†Yosef, 1987. "Tests of the impact of LIFO adoption on stockholders: A stochastic dominance approach," Contemporary Accounting Research, John Wiley & Sons, vol. 3(2), pages 430-444, March.
    Full references (including those not matched with items on IDEAS)

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. Chame, Anna & Tsallis, Constantino, 1990. "Criticality of the discrete N-vector ferromagnet in a cubic lattice with a free surface," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 165(1), pages 41-63.
    2. Bourbonnais, Roch & Benoît, Alain & Maynard, Roger, 1989. "Computer simulation of localization effects on Euclidean and fractal lattices," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 157(1), pages 37-41.
    3. Woon†Oh Jung, 1989. "Strategic choice of inventory accounting methods," Contemporary Accounting Research, John Wiley & Sons, vol. 6(1), pages 1-25, September.
    4. Kim, Doochul, 1984. "Self-dual transfer matrix renormalization for the triangular Potts model," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 123(2), pages 577-585.
    5. Giona, Massimiliano & Eduardo Roman, H., 1992. "Fractional diffusion equation for transport phenomena in random media," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 185(1), pages 87-97.
    6. Snarskii, A.A. & Buda, S.I., 1997. "Effective conductivity of nonlinear two-phase media near the percolation threshold," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 241(1), pages 350-354.
    7. Barta, Štefan, 1994. "Anomalous diffusion on percolating clusters," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 203(2), pages 163-174.
    8. Blöte, H.W.J & Nightingale, M.P, 1982. "Critical behaviour of the two-dimensional Potts model with a continuous number of states; A finite size scaling analysis," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 112(3), pages 405-465.
    9. Mariz, A.M. & Nobre, F.D. & de Souza, E.S., 1991. "Criticality of the bond-diluted Z(4) ferromagnet on the square lattice," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 178(2), pages 364-375.
    10. Taggart, G.Bruce, 1982. "Correlated effective field approximation for the dilute Ising ferromagnet," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 116(1), pages 34-44.
    11. Aharony, Amnon & Entin-Wohlman, O. & Brooks Harris, A., 1993. "Was superlocalization observed on a fractal?," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 200(1), pages 171-178.
    12. Horiguchi, T. & Gonçalves, L.L., 1985. "Mixed spin Ising models with two-spin interactions and three-spin interactions of the diced lattice," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 133(3), pages 460-472.
    13. Barta, Štefan & Dieška, Peter, 1995. "A computer-simulation study of anomalous diffusion on percolating clusters near to the critical point," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 215(3), pages 251-260.
    14. Bouchaud, J.P. & Georges, A., 1989. "The diffusion front on fractals and superlocalization from linear response requirements," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 157(1), pages 535-538.
    15. Aharony, Amnon & Harris, A.Brooks, 1994. "Superlocalization of wave functions on fractal networks," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 205(1), pages 335-341.

    More about this item

    Statistics

    Access and download statistics

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:eee:phsmap:v:157:y:1989:i:1:p:524-528. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: Catherine Liu (email available below). General contact details of provider: http://www.journals.elsevier.com/physica-a-statistical-mechpplications/ .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.