Geometry, dielectric response and scaling in porous media

Abstract

Local porosity distributions and local percolation probabilities have been proposed as well defined and experimentally observable geometric characteristics of general porous media. Based on these concepts the dielectric response is analysed using the effective medium approximation and percolation scaling theory. The theoretical origin of static and dynamic scaling laws for the dielectric dispersion and enhancement including Archie's law in the low porosity limit are elucidated. These well known experimental facts are unified within a theoretical framework based on a quantitative characterization of the pore space geometry. In the high porosity limit the zero frequency real dielectric constant is predicted to diverge as ε'(0) ∝ (1 − ϕ)-m' where ϕ denotes porosity and m' is analogous to the cementation exponent.