Abstract
A high-curvature generalization of the Laplace equation of capillarity and the Young equation of capillarity (including line tension) is developed for an axisymmetric solid-liquid-fluid system. The most general expressions for the Laplace and Young equations do not assume a particular form for the specific surface free energy. However, when a particular form, i.e., ω (A) = γ (A) ∞+ C J J+ C k K, which is related to Gibbs' expression for a highly curved menisci, 1 is assumed to hold for the specific surface free energy then we are able to recover the expected simplified form of the Laplace equation. The corresponding high-curvature Young equation includes a couple which balances the surface moments at the contact line. Unfortunately, the effect of this couple could be confused with the effect of line tension in experiments which attempt to measure the dependence of the contact angle on the contact line radius.
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