Volumes and Surface Areas of Pendular Rings

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Abstract
A packing of spheres is taken as a suitable model of porous media. The packing may be regular and the sphere size may be uniform, but in general, both should be random. Approximations are developed to give the volumes and surface areas of pendular rings that exist at points of sphere contact. From these, the total free volume and interfacial specific surface area are derived as expressive of the textural character of the packing. It was found that the log-log plot of volumes and surface areas of pendular rings vary linearly with the angle made by the line joining the sphere centers and the line from the center of the largest sphere to the closest edge of the pendular ring. The relationship, moreover, was found not to be very sensitive to variation in the size ratio of the spheres in contact. It also was found that the addition of pendular ring material to various sphere packings results in an unexpected decrease in the surface area of the boundaries that confine the resulting pore space.

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