Figure 11: Example of the intrusion of a non-wetting fluid (color) into the empty pore space (black) around the solid (fixed) circles (white). Left: low pressure intrusion, right: high pressure intrusion.
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A simple simulation of injection of a non-wetting fluid has been developed in 2-D [76] and 3-D [77,78]. The results can be compared with mercury porosimetry experiments. The idea is to apply the "equivalent sphere" concept to digital images in the following way [79]. For a given injection pressure P, there is a corresponding pore radius R, P ~ 1 / R. In 3-D, a sphere with radius R is put into the image from the outside, and moved around to cover much volume as possible without overlapping the solid. As the injection pressure is increased, the size of the sphere is decreased. The amount of additional volume swept out at each progressively smaller value of R is the pore space assigned to that pore size or to its equivalent pressure [10,76], just like in mercury injection porosimetry. In 2-D, this technique is fairly accurate, as there is only one radius of curvature for a meniscus, and it is reasonably approximated by a circular arc. In 3-D, however, there are two principal radii of curvature at any point on the surface of a liquid meniscus. So using a sphere to simulate the meniscus is much less reliable. Mathematical morphology techniques can also be utilized in simulating these processes in porous media [80].
Figure 11 shows a simulation of mercury intrusion (color) in a material in which the solid frame is made up of randomly placed, rigid overlapping monosize circles (white) [76]. The uninvaded pores are in black. The lefthand side is for a lower pressure, where only surface intrusion has occurred. The righthand side shows the intrusion that occurrs at higher injection pressure, where the non-wetting fluid can get into smaller pores. Clearly, there are large pores that are not invaded because they are only acessible by small throats . This is the well-known "ink-bottle" effect [81].
Figure 11: Example of the intrusion of a non-wetting fluid (color) into the empty pore space (black) around the solid (fixed) circles (white). Left: low pressure intrusion, right: high pressure intrusion.
Moisture absorption is important in the study and use of porous materials in atmospheric conditions (see Chapter 3). A typical quantity measured is the sorption isotherm, which is the amount of moisture absorbed as a function of the partial pressure of the absorbing vapor, at a fixed temperature. A simple variation of the mercury injection simulation can be made so as to simulate the moisture absorption-desorption processes in any digital image of a porous material in 2-D or 3-D [75,78,80].