General Description

Relationship between Pore Radii and Intrusion Pressure. Mercury porosimetry is based on the capillary rise phenomenon whereby an excess pressure is required to cause a nonwetting liquid to enter a narrow capillary. The pressure difference across the interface is given by the equation of Young (Ref 31) and Laplace (Ref 32), and its sign is such that the pressure is less in the liquid than in the gas (or vacuum) phase if the contact angle 01S greater than 90° or more if 0is less than 90°. If the capillary is circular in cross section, and not too large in radius, the meniscus will be approximately hemispherical. The curvature of the meniscus can be related to the radius of the capillary, and the Young-Laplace equation reduces to the Washburn equation (Ref 33):

This is the Young-Laplace and Washburn equation where 7[V is the surface tension of the liquid (e.g., for mercury, 0.485 N/m), r, and r2 are mutually perpendicular radii of a surface segment. The angle Wis the angle of contact between the liquid and the capillary walls and is always measured within the liquid (Fig. 11). rP is the capillary radius.

Fig. 11 Contract angle (i0) of a liquid in a capillary

Equipment Fundamentals. The sample is placed into the penetrometer assembly; it is then evacuated to a set vacuum level for a specific time, before the sample cell is filled with mercury. Air is admitted to the low-pressure chamber, and the increasing pressure forces the mercury to penetrate the largest pores of the sample. The amount or volume of mercury penetrating into the sample is recorded at each pressure (or pore size) point; the first reading usually is taken at a pressure of 0.5 psi (0.003 MPa), although readings at a pressure of 0.1 psi (0.7 x 10-4 MPa) are possible. The pressure is then increased to 1 atm, or in some instruments the pressure is actually increased to a slight overpressure (up to 50 psi in some cases). After the low-pressure run is finished, the penetrometer is then inserted into a high-pressure port and surrounded with a special grade of high-pressure oil; it is special with respect to the dielectric constant and viscosity of the oil under high-pressure conditions. The pressure is increased up to a final pressure of 60 ksi (400 MPa). Commercial instruments work either in an incremental or continuous mode. In the former, the pressure is increased in steps and the system allowed to stabilize at each pressure point before the next step. In the continuous mode, the pressure is increased continuously at a predetermined rate. Schematics of low-pressure and high-pressure systems are shown in Fig. 12 and 13, respectively (Ref 34).

Fig. 12 Low-pressure mercury porosimeter. Source: Ref 34
Fig. 13 Micromeritics high-pressure mercury porosimeter
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