General Equations for the Equilibrium Shape of a Fluid Interface and for Its Angle of Contact with a Solid

Abstract

Abstract The classical equations of Young-Laplace (equilibrium shape of a fluid interface in a uniform gravitational field) and Young (angle of contact of the fluid interface with a solid) are generalized to take into account: (i) the presence of externally applied fields of any type; (ii) the variation of the interfacial tensions from point to point; (iii) the variation of the fluid interfacial tension with its orientation in space. The general equations are deduced simultaneously by a variational method, which allows the determination of the minimum Helmholz energy configuration of a system comprising the two fluids and the solid. An axially symmetric geometry is assumed. The equations so derived clarify the difficulties that have been found in the application of the classical equations-particularly Young's equation-to actual systems. Both equations, in their general form, contain terms that may be interpreted as representing the interaction between the three interfaces near their line of contact, and such an interaction cannot be ignored in actual systems.