Force balance, pore volume

A simple model for the pore volume or the void space in a porous material is to assume it to be composed of a collection of cylindrical pores of radius r. Then a volume of a liquid that does not wet the pore wall surfaces can be forced under pressure to fill the void space. This liquid is invariably mercury because it has a high surface tension, thus the Hg penetration (or porosimetry) method is used to determine pore volumes and the pore size distribution of larger pores, i.e., those with radii larger than about 10 nm. The relationship between pore size and applied pressure. Pap, is obtained by a force balance, that is, the force due to surface tension is equated to the applied force ... 

The particle and bulk densities are commonly used in mass balance equations, since the mass and the external volume of the particles are involved. On the other hand, the hydraulic density should be preferably used in hydrodynamic calculations, because buoyancy forces are involved, and so the total mass of the particle should be taken into account, including the fluid in the open pores. It is obvious that the particle density is equal to the skeletal and hydrodynamic density in the case of nonporous particles. Moreover, in the case of a porous solid in a gas-solid system, the gas density is much lower than the particle density, and tlius... 

The apparatus used was a non-commercial porosimeter which enabled us to make accurate measurements between 0.4 and 2000 bar corresponding to a pore radius between 2 10 and 3.6 nm. The porosimeter consists of a steel cylinder and a piston forced into the cylinder by a ram (ref. 2). The pressure and the volume change were measured accurately by a strain gauge and by the displacement of the piston respectively. Up to a pressure of 5 bar the mercury was forced into the porosimeter by an air pump and the amount of mercury was determined accurately by a balance (ref. 3). Fig. 1 shows schematically the... 

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