CAPILLARY RISE IN SANDS OF UNIFORM SPHERICAL GRAINS

Abstract

Uniform spheres packed in regular array form a non‐cylindrical cyclic capillary, characterized by a maximum and minimum capillary rise with intermediate positions of possible equilibrium. In practice spheres may be packed to a variety of porosities P thus requiring a mixture of regular and irregular pilings arranged in a very distorted pattern. However the meniscus is also distorted to conform in a general way with the distortions of the lattice. Accordingly positions of maximum and minimum rise may be expected. The meniscus for maximum rise tends to pass through the plane of centers of neighboring spheres. Slight deviations from this condition due to the rise at sphere contacts are shown to be of minor importance. Any piling may be treated statistically as a hexagonal array with a spacing 2r+d where d is computed to give the observed porosity. In such a system three types of cell occur with a definite frequency, and these cell types are assumed present in the meniscus with the same frequency distribution. Hence it is possible to evaluate pr/a = ρghr/σ where p = perimeter, r = grain radius, a = area of pore opening, g = acceleration of gravity, σ = surface tension, ρ = density and h = capillary rise. The final formula so derived reduces to $$\frac{\mathrm{pr}}{a}=\frac{\mathrm{\rho ghr}}{\sigma }=\frac{2}{{\text{[0.9590/(1−P)}}^{\text{2/3}}\text{]−1}}.$$ This agreed with experiments made with several sizes of grains, porosities, and liquids. The minimum rises were also determined but a satisfactory interpretation in terms of a model has not been effected.