Scaling behavior of permeability and conductivity anisotropy near the percolation threshold

We use the finite-size scaling method to estimate the critical exponent that characterizes the scaling behavior of conductivity and permeability anisotropy near the percolation thresholdp_c. Here is defined by the scaling lawk_l/k_t–1(p–p_c), wherek_t andk_t 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 (d=2)0.819±0.011 and (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 due to Straley, and propose that (d=2)=t-_B, wheret is the critical exponent of the conductivity or permeability of the system, and _B is the critical exponent of the backbone of percolation clusters.