Viscous fingers on fractals

Yigal Meir, Amnon Aharony

Research output: Contribution to journalArticlepeer-review

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).

Original languageEnglish
Pages (from-to)524-528
Number of pages5
JournalPhysica A: Statistical Mechanics and its Applications
Volume157
Issue number1
DOIs
StatePublished - 1 May 1989

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