Discussion on Young's Equation Based on Interfacial Jump Condition

Abstract

The Young's equation describes the interfacial equilibrium condition of a liquid droplet on a smooth solid surface. This relation is derived by Thomas Young in 1805. It has been discussed until today after his work. In general, the Young's equation is discussed from the viewpoint of thermo-dynamics. However, there is no answer which elucidates the normal force balance σlg sin θ in the Young's equation. From the hydrodynamics point of view, there is a momentum jump condition at a gas-liquid interface. This jump condition is derived based on mechanical balance by using mathematical procedure such as Stoke's theorem and the differential geometry. In this study, we reconsider the Young's equation from this momentum jump condition point of view. Finally, we dynamics. However, there is no answer which elucidates the normal force balance σlg sin θ in the Young's equation. From the hydrodynamics point of view, there is a momentum jump condition at a gas-liquid interface. This jump condition is derived based on mechanical balance by using mathematical procedure such as Stoke's theorem and the differential geometry. In this study, we reconsider the Young's equation from this momentum jump condition point of view. Finally, we derive the revised Young's equation in which there is the normal force term (σlg sin θ). Then, we evaluate the revised Young's equation by comparing the analytical solution with the experimental data reported by Amirfazli. Moreover, we discuss on the line tension and the contact angle for a lens