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Viscous fingers on fractals

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  • 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
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    References listed on IDEAS

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    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.
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