Continuum percolation theory for natural porous media

The ratio of the solute diffusion constant in a porous medium to the product of its value in water and the moisture content of the medium is equal to the difference of the moisture content and a critical value of the moisture content at which the diffusion vanishes. A phenomenological relationship for the critical moisture content was obtained in experiments. Continuum percolation theory predicts the observed relationship, an approximate value for the critical moisture content, and the hydraulic conductivity as a function of saturation. Deviations in the fractal scaling of the pressure-saturation curves both at the wet end and at the dry end set on at moisture contents closely related to the critical value for percolation. Hysteresis in pressure-saturation is also predicted using the percolation result for the fraction of sites accessible to the infinite cluster (for imbibition). The values of the parameters extend across major solid types, and even country of origin of the soil. Thus it is claimed that the best ray to represent natural porous media is through truncated random fractals, and the best way to try to understand their behavior is within the context of percolation theory.