A novel strategy for determining line tension from the shape of a liquid meniscus near a stripwise heterogeneous wall

Abstract

According to the classical theory of capillarity, which does not consider the influence of line tension, a liquid meniscus in contact with a stripwise, heterogeneous wall will experience a high curvature situation at the ends of the four-phase (i.e., solid-solid-liquid-vapour) contact line. For capillary systems with finite line tension the effect on the contact line will be most pronounced at those locations where the curvature is large. Using these basic physical ideas, a strategy is proposed for using a stripwise, heterogeneous wall to evaluate the magnitude of the line tension based on the shape of the contact line. The strategy uses a combination of incremental loading coupled with the Newton-Raphson method to generate a series of non-zero line tension solutions from an initial analytical solution that corresponds to the zero line tension case.