Fractal Growth in Hydrodynamic Dispersion Through Random Porous Media.
Fractal Growth in Hydrodynamic Dispersion Through Random
Martys, N. S.
Physical Review E, Vol. 50, No. 1, 335-342, July 1994.
dispersions; tracers; dyes; fluid flow; diffusion;
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