Fractal growth in hydrodynamic dispersion through random porous media

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Abstract
Results from the numerical simulation of hydrodynamic dispersion in model random porous media are presented. The morphology of a spreading dye (or tracer), as a function of Peclet number, is studied. In the limit of infinite Peclet number, the dye pattern formed is fractal with fractal dimension close to that observed in diffusion-limited aggregation (DLA) in both two and three dimensions. Also, as in DLA, multifractal behavior is exhibited. At moderately high Peclet numbers the pattern formed by the dispersing dye in a two-dimensional porous medium is fractal over the width of the front as observed in experiment. In the low Peclet number regime contours of equal concentration are self-affine with an anomalously large roughness exponent. By comparison, we show that the pattern formed by a dilute ion concentration driven by an electric field, rather than a flow field, is also self-affine but with the usual roughness exponent of 0.5.