Scale effects on the (pore scale) electrical conductivity as a function of saturation in anisotropic media

It has been shown that the hydraulic conductivity can exhibit a "scale" effect (more precisely a system shape effect) in anisotropic media due to a cross-over in effective dimensionality of the conduction, from 1D at small sizes to 3D at large sizes. The "scale effect then arises from the effects on a "bottleneck" resistance of a change in the effective percolation probability from 1 at small sizes to near zero at large sizes. The electrical conductivity, however, is much less sensitive to the pore size distribution and is dominated by issues of connectivity/tortuosity over most of the range of saturations. As a consequence the issue of scale effects on the electrical conductivity for non-equidimensional systems (or anisotropy) is related more simply to finite-size scaling from percolation theory and universal expressions will usually apply.