Critical path analysis of the relationship between permeability and electrical conductivity of three-dimensional pore networks

The critical path analysis (CPA) of Ambegaokar et al. [1971] suggests that transport in random systems with a broad enough distribution of conductances is dominated by a controlling conductance of a critical magnitude. The present short, yet systematic, study provides a test of the applicability of the CPA to determine the relationship between two different transport properties of three-dimensional pore networks. Two characteristic transport properties are examined: viscous (hydraulic) permeability and electrical conductivity, and the three-dimensional pore networks are represented by diluted simple-cubic lattices of different average coordination numbers and broadness of a positively skewed pore size distribution. The prediction of the critical path analysis is good for small coordination numbers as the flow is largely through resistances in series and it diverges from the correct permeability-electrical conductivity relationship as the coordination number increases, especially for moderate broadness of the pore size distribution. The critical path analysis is also applicable to the relationships between other transport properties, for example, molecular and Knudsen diffusivities, and also to various pore shapes, other then cylindrical and slit-shaped, referred to in this study.