How does a patchy network affect the structure of invading percolation patterns?

Abstract

Invasion percolation with trapping (TIP) is studied on two kinds of pore networks. The first class of them is the one generated through the dual site bond model [I. Kornhauser, R.J. Faccio, J.L. Riccardo, F. Rojas, A.M. Vidales, G. Zgrablich, Structure characterization of disordered porous media, Fractals 5 (3) (1997) 355–377; S. Cordero, I. Kornhauser, A. Dominguez, C. Felipe, J.M. Esparza, F. Rojas, R.H. Lopez, A.M. Vidales, J.L. ´ Riccardo, G. Zgrablich, Site–bond network modeling of disordered porous media, Part. Part. Syst. Charact. 21 (2004) 101–116] (DSBM). This model allows different strengths of correlations among the elements of the lattice in such a way that patches of sites and bonds with similar sizes are structured as correlations are set up. The typical size of these patches depends on the strength of correlations. The other class is a set of networks with a chessboard-like structure, i.e., patches are the “black” and “white” squares of a chessboard. Each square is made with bonds of similar sizes sampled from the same bond distribution. Black squares have sites sampled from the lower half part of the site distribution and sites in white squares belong to the other half. When a network is built, both models have the constraint imposed by a construction principle (CP) that forbids a bond to be greater than any of the sites to which it is connected. This is a common used assumption in modeling porous networks. The aim of this paper is to find whether the global patchy structure is responsible of the patterns found in TIP, or it is the local constraint imposed by the CP, which prevails. To this end, we measure different quantities, such as fractal dimensions, trapped fluid island distributions and invaded volume ratio, among others.