Macroscopic wettability based on an interfacial jump condition

Young's equation, describing an interfacial equilibrium condition of a liquid droplet on a smooth solid surface, raises issues concerning the existence of a sine term which has not yet been resolved theoretically and continues to be discussed to the present day. From a thermodynamics viewpoint, the equilibrium condition arises by minimizing the total free energy of the system while intensive parameters are kept constant. In the derivation, variations in the virtual work in both horizontal and vertical directions of the droplet on the smooth solid are considered. From a hydrodynamics viewpoint, there is a momentum jump condition at the gas-liquid interface that is derived based on a mechanical balance. Using standard mathematical procedures such as Stokes' theorem and differential geometry, a test volume is considered across the interface between two continuous phases from which the jump condition is derived. In the present paper, Young's equation is revisited from the point of view of the momentum jump condition at the two-phase interface and a modified Young's equation is derived. The analytical solution derived from the modified Young's equation is then used to compare theory with experimental data. The line tension and contact angle for a lens droplet are also discussed on the basis of this model.