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We consider the problem of viscous fingering in the presence of quencheddisorder that is both weak and short-range correlated. The two pointcorrelation function of the harmonic measure is calculated perturbatively, andis used in order to calculate the correction the the box-counting fractaldimension. We show that the disorder increases the fractal dimension, and thatits effect decreases logarithmically with the size of the fractal.

Viscous fingering in the presence of weak disorder