Generalization of the classical theory of capillarity

Gibbs’ concept of dividing surfaces is supplemented explicitly by the concepts of dividing lines and dividing points. The general forms of the fundamental equations for dividing surfaces and lines are established by considering the proper extensive geometric properties, in addition to area and length. The detailed description of the fluid part of a capillary system by these fundamental equations is used to obtain the general conditions of equilibrium. Proper generalizations of the Laplace equation, the Neumann relation, and the Young equation are derived.