Invasion percolation in fractal fractures

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 rd, 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 rd.