Scaling behavior of permeability and conductivity anisotropy near the percolation threshold

Abstract

We use the finite-size scaling method to estimate the critical exponent λ that characterizes the scaling behavior of conductivity and permeability anisotropy near the percolation thresholdpc. Here λ is defined by the scaling lawkl/kt−1∼(p−pc)λ, wherekt andkt are the conductivity or permeability of the system in the direction of the macroscopic potential gradient and perpendicular to this direction, respectively. The results are λ(d=2)≃0.819±0.011 and λ(d=3)≃0.518±0.001. We interpret these results in terms of the structure of percolation clusters and their chemical distance. We also compare our results with the predictions of a scaling theory for λ due to Straley, and propose that λ(d=2)=t-βB, wheret is the critical exponent of the conductivity or permeability of the system, and βB is the critical exponent of the backbone of percolation clusters.