Determination of surface tension and contact angle from the shapes of axisymmetric fluid interfaces

Abstract

A general, yet user-oriented scheme is provided to determine liquid—fluid interfacial tensions and contact angles from the shapes of axisymmetric menisci, i.e., from sessile as well as pendant drops. The strategy employed is to construct an objective function which expresses the error between the physically observed and a theoretical Laplacian curve, i.e., a curve representing a solution of the Laplace equation of capillarity. This objective function is minimized numerically using the method of incremental loading in conjunction with the Newton—Raphson method. This strategy is necessary as the otherwise powerful Newton-Raphson method depends on a good initial approximation to the true curve. Incremental loading provides a scheme of approaching the solution from a remote situation. A spherical meniscus, i.e., the case of infinite interfacial tension, is chosen here as the simple, unloaded solution. The method is set up from the point of view of user convenience: Apart from local gravity and densities of liquid and fluid phases the only input information required to determine the liquid-fluid interfacial tension is information on meniscus shape, typically several coordinate points in a coordinate system the origin of which may be placed at will. Specifically it is not necessary to identify the apex of the drop profile, the drop width, or drop height. For determinations of contact angles, the vertical coordinate of the three-phase line needs to be specified. As an illustration, “synthetic” drops, simulating physical drop profiles, are investigated. Sessile drops are generated with the aid of the tables of Bashforth and Adams and pendant drops with the aid of the tables of Fordham. The results show that the technique, which is an absolute one independent of any tables, is fully functional. A computer program implementing the method may be purchased from the authors.