Capillary properties of model pores

Liquid menisci in small pores exhibit a curved surface across which there is a significant pressure difference. The capillary properties of such surfaces are important in many areas of science and technology. Pores of uniform section can be broadly classified according to whether the perimeter is smooth (as in cylindrical tubes) or angular (as in triangular tubes). A meniscus that is entirely bounded by the pore walls has a curvature that is inversely proportional to the tubes' hydraulic radius. A meniscus in an angular tube, however, has liquid wedges in the corners and this reduces the effective area of the pore. In the past it has been difficult to calculate the curvatures, of this class of menisci. Some recent studies have shown that a relatively straightforward, but hitherto neglected, method originated by Mayer & Stowe (1965) and Princen (1969a) can be applied to analyse wedging menisci. However, the method has lacked a comprehensive experimental verification. This investigation follows on from the previously limited studies. A standardised method for the application of the analysis is described, the results from which are compared to observations made using modified experimental procedures. The behaviour of the capillary surfaces formed in several model pores are analysed with the method. The model systems studied are rectangular ducts, the pores formed by a rod in an angled corner, by two contacting rods and a plate and the space between a rod and a plate. For the latter two shapes the analysis is extended to include systems of mixed wettability which have a particular bearing on enhanced oil recovery operations. Experiments in which curvatures are inferred from observations of capillary rise, are performed using two comparative techniques. An involved procedure confurns predictions of meniscus curvature to within 0.3%. Use of a more straightforward, though less accurate, technique enables variations of curvature with tube shape or contact angle(s) to be conveniently studied. Results obtained are excellent and confmn the theory within the determined experimental errors. In addition the analysis has been extended to predict more complex meniscus behaviour. The tubular space formed by three rods and a plate gives rise to a whole family of meniscus shapes. With certain geometries a capillary surface regards the tube as a pore doublet where the behaviour in one neighbouring pore depends on that in the other. The capillary properties of this model system shed light on the behaviour of adjacent pores in a porous medium undergoing drainage (ordesorption). Experiments show excellent agreement with predictions of meniscus shapes, curvatures and, most interestingly, points of spontaneous transition from one meniscus shape to another. The system also has a potential future application because one panicular arrangement of rods produces a meniscus with a curvature virtually independent of the geometry. This makes it suitable for producing a standard meniscus of known curvature.