Next: Permeability Length Scales
Mercury is a non-wetting fluid at room temperature for most porous materials of technological interest. This fact led Washburn in 1921  to propose that mercury injection into a porous material could be used to measure pore-size distributions. An excellent review of the modern technique of mercury porosimetry is given in Ref. . The pressure P required to force a non-wetting fluid into a circular cross-section capillary of diameter d is given by:
In two recent papers [3,4], Katz and Thompson have used the percolation theory concepts of Ambegaokar, Halperin, and Langer , Shante , and Kirkpatrick  applied to laminar flow in porous media to develop a new mercury porosimetry-based prediction for the ratio of the fluid permeability k to the electrical conductivity of a porous material. Their main result is the prediction that
where o is the electrical conductivity of the pore-saturating fluid, c is a calculated constant on the order of 0.01 that depends weakly on the assumptions made for the relationship between pore length and pore diameter , and dc is the threshold pore diameter as measured by mercury porosimetry, defined in the next section. Refs.  and  give evidence for quantitative agreement, within experimental error, of eq. (2) with measurements on sedimentary rocks that span over six decades of permeability . This is an impressive result, especially since the theory has no adjustable parameters.
Recently, critiques of Katz and Thompson's approach have appeared. Banavar and Johnson  remark that the parameter dc is "well-defined only when the porous medium can be modelled as a distribution of cylindrical pores on a lattice." This statement is true. Le Doussal  raised the question of the effect of the assumption of circular cylindrical pore geometry on the determination of dc, which is a reasonable criticism. The purpose of this paper is to address these points by setting forth a conceptual framework for the use of mercury porosimetry in the prediction of fluid permeability using Katz and Thompson's approach.