Percolation and anomalous conduction on fractals in fluid-saturated porous media

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Abstract
At low frequency the conductivity of fluid-saturated porous media varies with porosity as phi m where m is Archie's exponent. At higher frequencies, the real part of the conductivity exhibits a dispersive (non-Gaussian) behaviour characterised by the power law sigma '( omega ) varies as omega x. The real part of the dielectric constant, which can attain a very large value at low frequency, varies in the dispersive region as epsilon '( omega ) varies as omega -y with x+y=1. The authors obtained the values of these exponents from data on brine-saturated porous alumina ceramics presented in previous papers and they determine the values of t and s, the usual conductivity and superconductivity exponents. They agree with the latest theoretical estimations. The conclusion of the authors' analysis is that the low-frequency conductivity of porous alumina ceramics saturated with saline water yields a value for Archie's exponent compatible with the theory of percolation while the dielectric constant and the conductivity frequency exponents in the dispersive region are consistent both with percolation theory and with an interpretation in terms of anomalous conduction on fractals.