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Fractal Growth in Hydrodynamic Dispersion Through Random Porous Media.


pdf icon Fractal Growth in Hydrodynamic Dispersion Through Random Porous Media. (4501 K)
Martys, N. S.

Physical Review E, Vol. 50, No. 1, 335-342, July 1994.

Keywords:

dispersions; tracers; dyes; fluid flow; diffusion; scaling

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 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.