Relationship between pore radii and intrusion pressure

2 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 non-wetting liquid to climb up a narrow capillary. The pressure difference across the interface is given by the equation of Young and Laplace [3 sic] and its sign is such that the pressure is less in the liquid than in the gas (or 

If the capillary is circular in cross-section, and not too large in radius, the meniscus will be approximately hemispherical. The two radii of curvature are thus equal to each other and to the radius of the capillary. Under these conditions equation (4.1) reduces to the Washburn [4] equation  

Mercury porosimetry, in which the amount of mercury forced into a solid is determined as a function of pressure, is based on this equation. If one considers a powder in the evacuated state, Ap p, the absolute pressure required to force a non-wetting liquid into a pore of radius r. 

For non-wetting liquids (contact angles greater than 90°) the pressure difference is negative and the level of the meniscus in the capillary will be lower than the level in a surrounding reservoir of liquid. In this case Ap is the pressure required to bring the level of the liquid in the capillary up to the level in die surrounding liquid. 

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