Estimation of size from capillary pressure—A correction factor for a two menisci capillary

Abstract

Extrusion of a liquid from a single vertical glass capillary, forming two menisci, by the application of air pressure is studied, to obtain a correct estimate of the capillary radius from the measured capillary pressure. Experimental measurements of critical extrusion pressure demonstrate the conditions under which the same capillary system can exhibit significantly different extrusion pressures. The absolute value of capillary radius is obtained by optical microscopy. Comparison of the estimated radius from capillary pressure measurements and optical microscopy show that the single meniscus-based capillary pressure equation results in a radius estimate that is smaller than the optically measured radius by 35%. This may be expected since the single meniscus-based capillary pressure equation is not applicable for the two menisci capillary. A theoretical analysis of the two menisci system, is presented, which leads to a new factor, β, in the single meniscus capillary pressure equation. This correction factor is estimated by solving the coupled Young–Laplace equations for the two menisci shapes. This “coupled menisci shape factor” is first estimated for a known capillary radius, and is subsequently used to predict capillary radius in capillaries of unknown radii of the same material. The use of the above correction factor leads to an estimate of the capillary radius, which differs from the optically estimated radius by less than 7%. Hence the two menisci-based capillary pressure equation developed in this paper results in a significant improvement, when the above liquid extrusion, from a capillary containing two menisci, is used for capillary pressure measurement.