Study on Interfacial Mechanical Balance Conditions
of a Sessile Drop on a Smooth Solid Surface

Abstract

Young's equation describes the interfacial equilibrium condition of a liquid droplet on a smooth solid surface. Young's equation is generally discussed from a thermodynamic perspective and derived by minimizing the total free energy of a system while keeping the intensive parameters in the total free energy constant (i.e., the variation of the total free energy is zero). In our previous study, we derived a modified Young's equation by using thermodynamics based on a new perspective. This equation was derived by considering the virtual work variation in the horizontal directions of the three phase contact line. However, in the conventional thermodynamic approach, the Young-Laplace equation is derived from the virtual work variation on the droplet surface. This point was not considered in our previous derivation. In this study, we give the complete derivation of the interfacial mechanical balance conditions of a liquid droplet on a smooth solid surface. We then derive both the modified Young's equation and the Young-Laplace equation from the virtual work variation of the droplet. Moreover, we consider the relationship between both equations.