FRACTAL VISCOUS FINGERING AND ITS SCALING STRUCTURE IN RANDOM SIERPINSKI CARPET |
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Authors: | Tian Ju-ping and Yao Kai-lun |
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Affiliation: | Department of Physcis, Huazhong University of Science and Technology, Wuhan 430074, China; China Center of Advanced Science and Technology (CCAST) (World Laboratory), P.O. Box 8730, Beijing 100080, China; International Center for Material Physics, Chines; Department of Physics, Wuhan Institute of Science and Technology, Wuhan 430073,} China; Department of Physics, Huazhong University of Science and Technology, Wuhan 430074, China |
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Abstract: | Viscous fingering (VF) in random Sierpinski carpet is investigated by means of 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→∞ (M is the viscosity ratio and equals to η2/η1 where η1 and η2 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≥10, 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 1f(α) sites have velocites scaling as L-α; and the scaling function f(α) is measured and its variation with M is found. |
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Keywords: | viscous fingering fractal construction Sierpinski carpet |
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