Meniscus curvatures in capillaries of uniform cross-section

Abstract

Menisci contained in capillaries of uniform cross-section can be broadly classed according to whether wedge-like liquid structures exist, as in triangular-section tubes, or do not exist, as in circular-section tubes. In tubes which form wedge menisci the liquid in the wedge adopts a form so that a section through the liquid surface is the arc of a circle. The volume of liquid per unit length of the wedge is constant along the tube. A non-wedging meniscus, however, is locally bounded by its tube and has a curvature inversely proportional to the hydraulic radius of the tube. Mayer and Stowe (J. Colloid Interface Sci., 1965, 20, 893) proposed an approximate method of determining the mean surface curvature of menisci in sphere packs. It was later applied independently by Princen (J. Colloid Interface Sci., 1969, 30, 60) to estimating capillary rise in spaces between parallel rods. The method, which incorporates the presence of wedges, is shown to be exact for determining mean surface curvatures in systems where the meniscus is undistorted by gravity. Experimental confirmation of the theoretical predictions to within 1.5% was obtained from measurements of capillary rise of a perfectly wetting liquid in tubes formed either by a rod and a square corner or by two rods and a plate. The conditions of pore geometry and contact angles which give rise to wedge menisci are discussed and illustrated by examples which include menisci in tubes of polygonal section.