FRACTAL VISCOUS FINGERING AND ITS SCALING STRUCTURE IN RANDOM SIERPINSKI CARPET

Viscous fingering (VF)in the random Sierpinski carpet is investigated by means of the successive over-relaxation technique and under the assumption that bond radii are of Rayleigh distribution. In the random Sierpinski network, the VF pattern of porous media in the limit M\to \infty (M is the viscosity ratio and equals \eta_2/\eta_1 where \eta_1 and \eta_2 are the viscosities of the injected and displaced fluids, respectively) is found to be similar to the diffusion-limited aggregation (DLA) pattern. The interior of the cluster of the displacing fluid is compact on long length scales when M=1, and the pores in the interior of the cluster have been completely swept by the displacing fluid. For finite values of M, such as M\geq10,the pores in the interior of the cluster have been only partly swept by the displacing fluid on short length scales. But for values of M in 1