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# Introduction

Mercury is a non-wetting fluid at room temperature for most porous materials of technological interest, including cementitious materials. This fact led Washburn in 1921 [1] to propose that mercury injection into a porous material could be used to measure pore-size distributions. Ref. [2] gives an excellent review of the modern technique of mercury porosimetry (MP). The pressure P required to force a non-wetting fluid into a circular cross-section capillary of diameter d is given by:

where is the mercury's surface tension, and is the contact angle of the mercury on the material being intruded. This equation is called the Washburn equation. 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 increase in applied pressure, the pore-size distribution of the sample can be estimated in terms of the volume of pores intruded for a given diameter d, by converting an intrusion pressure into a pore diameter via eq. (1). The identification of a pore diameter d with an injection pressure P depends on the assumptions made for the pore geometry, which is taken to be cylindrical in eq. (1). Also, larger pores that are only accessible through smaller pores will wrongly be counted with the smaller pores when the mercury is able to pass through the smaller pores. This is often known as the ink-bottle pore effect [2].

Much of the information contained in a mercury intrusion curve is not used, as only median or average pore diameters are usually quoted by practitioners. A model that could simulate a mercury intrusion experiment on a well-characterized pore space could bring much-needed insight into real experimental results. That is one motivation for the work described in this paper.

In two recent papers [3,4], Katz and Thompson have used the percolation concepts of Ambegaokar, Halperin, and Langer [5], Shante [6], and Kirkpatrick [7] applied to laminar flow in porous media to develop a new prediction for the ratio of the permeability k to the electrical conductivity of a porous material, which is based on MP measurements. Their main result is the prediction that

where o is the electrical conductivity of the pore- saturating fluid, dc is the threshold diameter (as measured by a MP experiment), the diameter of the pore that just completes a continuous pathway consisting only of pores with diameter
d > dc, and c is a constant on the order of 0.01 [8]. Refs. [3] and [4] give evidence for quantitative agreement, within experimental error, of the Katz-Thompson (KT) theory with measurements on sedimentary rocks spanning over six orders of magnitude of permeability [9]. This is an impressive result, especially since the theory has no adjustable parameters.

The dependence of the parameter dc on pore structure is extremely important to analyze, in order to understand why porous materials in general, and cementitious materials in particular, have their characteristic permeabilities. That is the second motivation for the work described in this paper.

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