Next: Permeability Length Scales
Up: Main
Previous: Main
Mercury is a non-wetting fluid at room temperature for most porous materials of technological interest. This fact led Washburn in 1921 [1] 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. [2]. The pressure P required to force a non-wetting fluid into a circular cross-section capillary of diameter d is given by:
is the surface tension of
the mercury, and 
is the contact angle of the
mercury on the material being intruded. By gradually increasing the pressure applied to a porous
sample immersed in a mercury bath, and monitoring the incremental volume of mercury intruded
for each new applied pressure, the pore-size distribution of the sample can be estimated in terms
of the volume of the pores intruded for a given diameter d. Of course, using eq. (1) to relate
intrusion pressure P and a pore diameter d assumes that the pores have circular cross-sections.
In two recent papers [3,4], Katz and Thompson have used the percolation theory
concepts of Ambegaokar, Halperin, and Langer [5], Shante [6], and Kirkpatrick
[7] 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 [8], and dc is the threshold pore diameter as
measured by mercury porosimetry, defined in the next section. Refs. [3] and [4] give
evidence for quantitative agreement, within experimental error, of eq. (2) with measurements on
sedimentary rocks that span over six decades of permeability [9]. 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 [8] 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 [10] 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.