Fluctuations, viscous fingering, and diffusion-limited aggregation

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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.