Effective conductivity in isotropic heterogeneous media using a strong-contrast statistical continuum theory

The strong-contrast formulation is used to predict the effective conductivity of a porous material. The distribution, shape and orientation of the two phases are taken into account using two- and three-point probability distribution functions. A new approximation for the three-point probability function appropriate for two-phase media is proposed and discussed. Computed results for the effective conductivity using the strong-contrast formulation are compared to the Voigt and the Hashin-Shtrikman upper-bound estimates. These results show that the predicted effective conductivity is lower than both Voigt and Hashin-Shtrikman bounds. Compared to previous results using the weak-contrast formulation, the strong-contrast formulation seems to provide a better estimate for the effect of the microstructure on the conductivity.