ABSTRACT
Figure 1 shows how DLA grows. The black particle in the center is the nucleation core here called seed I. A dozen of particles has attached to it to form a cluster with a radius of rmax. At a random location on the circle with radius rmax+5, a new particle S1 appears and then goes randomly in the horizontal matrix in the direction decided by a random number the computer produce between 0 and 1. For example the number in 0∼0.25 decides a step up and the number in 0.25∼0.5 decides a step down etc.. After several steps in t1 it would walk in the vicinity of the central cluster (see the dashed grid) until it stops walking and becomes a part of the cluster. To save time, any particle K which goes outside of 3rmax in t2 will be neglected because it needs to walked many steps to attach the central cluster. Afterwards the particles born in the distance will repeat the aforesaid steps until a big enough DLA cluster forms. So the growth-up of the DLA cluster is a result of surface nucleation
1 INTRODUCTION
Viscous fingering is one of the important phenomena during multi-phase flow (Jia et al. 2001a,b), especially in the environment where low viscosity fluid displaces high viscosity fluid. It exists commonly in the processes like oil displacement and the non-equilibrium growth. On this point, the pore structure complexity (Qin 2012, Yao 2012, Qin 2013, Wu 2014a, b) is the internal factor to cause such viscous fingering while the differences of physical properties among multi-phase fluids act as the external factors. To analyze the viscous fingering mechanism in porous media, some researchers tried to change the properties of injected fluids to produce viscous fingering patterns which have been restricted by the experiment conditions and scale.
