Invasion percolation in fractal fractures

Abstract

Invasion percolation (IP) with trapping was studied on two-dimensional substrates with a correlated distribution of invasion thresholds. The substrates represented the void spaces of variable-aperture fracture models that were formed by (2+1)-dimensional self-affine rough surfaces and their replicas, displaced relative to each other. Void spaces generated in this manner were self-affine on length scales less than the horizontal displacement r d , and uncorrelated on larger length scales. The geometry of the IP clusters reflected the void space geometry, with different scaling behavior on length scales below and beyond r d .