Fluctuations, viscous fingering, and diffusion-limited aggregation

Derek Y. C. Chan, Barry D. Hughes, and Lincoln Paterson
Phys. Rev. A 34, 4079 – Published 1 November 1986
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Abstract

A physical interpretation of the diffusion-limited-aggregation (DLA) algorithm for simulating viscous fingering during fluid displacement in a porous medium is given in terms of the material properties of the porous medium. In one dimension, the flow patterns generated by a DLA simulation correspond to a simple exponential distribution of ‘‘fluid capacity.’’ Also, for any given distribution of fluid capacity, it is possible to establish a corresponding stochastic algorithm for the moving fluid interface. The discussion of this paper places the DLA simulation of viscous fingering on a physical basis and, more generally, establishes the mathematical equivalence of two models of stochastic interface evolution.

  • Received 25 July 1986

DOI:https://doi.org/10.1103/PhysRevA.34.4079

©1986 American Physical Society

Authors & Affiliations

Derek Y. C. Chan and Barry D. Hughes

  • Department of Mathematics, University of Melbourne, Parkville, Victoria, Australia 3052

Lincoln Paterson

  • Division of Geomechanics, Commonwealth Scientific and Industrial Research Organization, P.O. Box 54, Mount Waverley, Victoria, Australia 3149

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Issue

Vol. 34, Iss. 5 — November 1986

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