Correlation of Occupation Profiles in Invasion Percolation

Abstract

We study theoretically and by simulation the spatial correlation of the fluctuations of the transversely averaged fraction of the invading phase in invasion percolation. For an uncorrelated lattice, the profile has the correlation structure of the trace of fractional Brownian motion (FBM) with Hurst exponent $H=D\ensuremath{-}2$ for 3D percolation and $H=D\ensuremath{-}1.5$ for 2D percolation, where $D$ is the fractal dimension of the percolation cluster. Extension to correlated percolation shows similar results, with the FBM signal displaying persistent correlations ($H>0.5$) in 3D and antipersistent correlations ($H<0.5$) in 2D percolation. Experiments of nonwetting fluid invasion in porous media confirm the theory in 3D.