FRACTAL VISCOUS FINGERING AND ITS SCALING STRUCTURE IN RANDOM SIERPINSKI CARPET
Tian Ju-ping (田巨平)ab, Yao Kai-lun (姚凯伦)cde
a Department of Physics, Wuhan Institute of Science and Technology, Wuhan 430073, China; b Department of Physcis, Huazhong University of Science and Technology, Wuhan 430074, China; c Department of Physcis, Huazhong University of Science and Technology, Wuhan 430074, China; d China Center of Advanced Science and Technology (CCAST) (World Laboratory), P.O. Box 8730, Beijing 100080, China; e International Center for Material Physics, Chinese Academy of Sciences, Shenyang 110015, China
Abstract 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 $1<M \leq5$, the pores in the interior of the cluster have been completely swept by the displacing fluid on short length scales. The symmetry of the growth of VF is broken by randomizing the positions of the holes. The fractal dimension for VF in fractal space is calculated. However,the sweep efficiency of the displacement processes mainly depends upon the length of the network system and also on the viscosity ratio $M$. The fractal dimension $D$ can be reasonably regarded as a useful parameter to evaluate the sweep efficiencies. The topology and geometry of the porous media have a strong effect on the structure of VF and the displacement process. The distribution of velocities normal to the interface has been studied by means of multifractal theory.Results show that the distribution is consistent with the hypothesis that, for a system of size $L$, $L^{f(\alpha)}$ sites have velocities scaling as $L^{-\alpha}$; and the scaling function $f(\alpha)$ is measured and its variation with $M$ is found.
Received: 15 March 2000
Revised: 13 September 2000
Accepted manuscript online:
Fund: Project supported by the National Natural Science Foundation of China (Grant No. 19774023) and by the National High Performance Computing Foundation of China (Grant No. 984050).
Cite this article:
Tian Ju-ping (田巨平), Yao Kai-lun (姚凯伦) FRACTAL VISCOUS FINGERING AND ITS SCALING STRUCTURE IN RANDOM SIERPINSKI CARPET 2001 Chinese Physics 10 128
Altmetric calculates a score based on the online attention an article receives. Each coloured thread in the circle represents a different type of online attention. The number in the centre is the Altmetric score. Social media and mainstream news media are the main sources that calculate the score. Reference managers such as Mendeley are also tracked but do not contribute to the score. Older articles often score higher because they have had more time to get noticed. To account for this, Altmetric has included the context data for other articles of a similar age.
