Curved Fluid Interfaces. II. The Generalized Neumann Formula

Following an analysis of the phenomenological concept of surface stress, the confluence properties of three fluid phases are examined from the molecular point of view. The detailed theory leads to a generalization of the Neumann surface tension triangle, which provides a boundary condition for the Laplace equations describing the surfaces of a fluid lens. It is found that the classical equation must be supplemented by a thermodynamic length parameter which, however, does not contribute to the Archimedean equilibrium of the lens. As in the preceding investigation, the first-order correction terms of the theory again provide criteria for the breakdown of thermodynamic concepts.