Similarity Hypothesis for Capillary Hysteresis in Porous Materials

A quantitative description of the capillary hysteresis properties of a porous material is developed through bivariate distribution density function ƒ(α, β), where α and β are wetting and drying potentials. This is formally equivalent to the independent domain theory of Poulovassilis. The similarity hypothesis (implying, loosely, that the distribution of geometrical relationships between wetting and drying meniscus curvatures is independent of ‘pore size’) holds fairly well for Poulovassilis' experimental data. The corresponding h functions are found and the ƒ(α, β) are mapped. In general, the establishment of ƒ(α, β) is a laborious process. However, with (A), ƒ(α, β) may be found from only the (routinely observed) drying and wetting boundary curves. Equation A yields the integral equation where j and g are known from the boundary curves and Ψ0 is the minimum potential, h is the unknown function. Equation B is solved with the aid of the Faltung theorem of the Laplace transformation. It follows that, when (A) holds, h, and hence ƒ(α, β), is uniquely determined by the boundary curves. The solution of (B) is not necessarily physically acceptable, however. By adopting (A) plus an arbitrary, but plausible, form for h, we may roughly estimate the whole hysteresis character of the medium from a single boundary curve. Further experimental work is needed to establish the area of applicability of (A). (A) may apply also to hysteresis processes other than sorption in porous materials.