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A simple computer model of viscous fingering in a porous medium is presented, together with experimental results for fingering of oil into glycerine in etched-glass networks. The model treats the medium as a square lattice of connected tubes with randomly chosen radii. By Monte Carlo simulation it is demonstrated that for a narrow size distribution of tubes the fingers form ordered patterns (dendrites) with growth mostly along the coordinate axes, but for a wide size distribution the fingers form a chaotic structure with a fractal dimension around 1.72. Qualitatively similar behavior is seen in the experiments.
Chen et al. (Mon,) studied this question.