The contact angle for a droplet on homogeneous and spherical concave surfaces

Wetting of droplets on homogeneous and spherical concave rough surfaces is investigated based on thermodynamics. In this study, neglecting the droplet gravity and the thickness of the precursor film of the liquid vapor interface, the three-phase system is divided into six parts using Gibbs concept of dividing surface. The system Helmholtz free energy is established based on thermodynamics. Supposing the temperature and chemical potential to be constant, a new generalized Young's equation of the equilibrium contact angle for a spherical droplet on a spherical concave rough surfaces is obtained including the line tension effects. Under certain conditions, this generalized Young's equation is the same as the Rusanov's equation.