Mercury porosimetry is a widely used method of approximately measuring the pore-size distribution of porous materials [17]. Samples are first evacuated, and then surrounded by a mercury bath. Mercury is a non-wetting fluid for most porous materials of interest, so increasing pressure is required to force the mercury into smaller and smaller pores. In the porosimeter, an increase in pressure is made, and the additional volume of mercury that goes into the sample is monitored. This volume of mercury is then associated with a pore diameter that is determined by assuming a circular cylindrical pore geometry. As the pressure is increased, a wide range of pore sizes can be explored.
The algorithm for mercury, or non-wetting fluids in general, injection is a geometric method that works only for completely non-wetting fluid injection, in 2D, with a contact angle of 180o. The algorithm, described in detail by Garboczi and Bentz [18], begins by surrounding a porous image with a bath of fluid pixels. A pressure is implicitly chosen, via the Washburn equation, by selecting a diameter that is the smallest channel through which the fluid will be allowed to go. The fluid is then successively intruded from the outside by trying to place fluid circles of the chosen diameter, centered at previously intruded fluid pixels. The circular intruding shape gives approximately the correct meniscus, and the chosen diameter guarantees that the fluid will only go into allowed regions. By keeping track of how much pore area is intruded with each choice of pressure/pore diameter, an approximate pore-size distribution can be traced out.
An important quantity is the pore diameter, denoted dc, that is intruded just at the point when the mercury becomes continuous across the sample, or percolates. This parameter can be measured experimentally using commercial porosimeters. In the mercury intrusion algorithm, the value of dc is determined directly by intruding from one direction (top or left) only and finding if the intruded fluid has percolated to the other side (bottom or right). The value of dc is then the intruding fluid circle diameter at percolation, averaged between the left-right and up- down thresholds, which are not always the same due to finite-size effects.
Physically, the length scale dc can be thought of as the smallest member of a subset of the pore space containing the largest pores that form a continuous pathway through the pore space. The parameter dc is a key quantity in the Katz-Thompson fluid permeability theory [19], and basically sets the scale for permeability. Roughly, the permeability of a porous material is proportional to dc2.