Quantitative comparison of mean field mixing laws for conductivity and dielectric constants of porous media

Exact numerical solution of the electrostatic disordered potential problem is carried out for four fully discretized three-dimensional experimental reconstructions of sedimentary rocks. The measured effective macroscopic dielectric constants and electrical conductivities are compared with parameter-free predictions from several mean field type theories. All these theories give agreeable results for low contrast between the media. Predictions from local porosity theory, however, match for the entire range of contrast.