SCALING BEHAVIOR OF PERMEABILITY AND CONDUCTIVITY ANISOTROPY NEAR THEPERCOLATION-THRESHOLD

We use the finite-size scaling method to estimate the critical exponen t lambda that characterizes the scaling behavior of conductivity and p ermeability anisotropy near the percolation threshold p(c). Here lambd a is defined by the scaling law k(l)/k(t) - 1 approximately (p - p(c)l ambda, where k(l) and k(t) are the conductivity or permeability of the system in the direction of the macroscopic potential gradient and per pendicular to this direction, respectively. The results are lambda(d = 2) congruent-to 0.819 +/- 0.011 and lambda(d = 3) congruent-to 0.518 +/- 0.001. We interpret these results in terms of the structure of per colation clusters and their chemical distance. We also compare our res ults with the predictions of a scaling theory for lambda due to Strale y, and propose that lambda(d = 2) = t - beta(B), where t is the critic al exponent of the conductivity or permeability of the system, and bet a(B) is the critical exponent of the backbone of percolation clusters.