Variational framework for defining contact angles: a general thermodynamic approach

The paper surveys the variational thermodynamic approach, enabling defining and predicting equilibrium contact angles. The approach enables considering 1D, 2D and 3D contributions to the free energy of the sessile droplet. 3D components of free energy such as contributions due to external fields or heat release do not influence equilibrium contact angles. In the situation when 1D (line tension) contributions to the free energy are neglected the equilibrium contact angle depends only on the intensive thermodynamic parameters of the system and it turns out to be the intensive thermodynamic parameter of the system. This is true for droplets placed on rough and chemically heterogeneous surfaces. Actually, the Young, Wenzel and Cassie equilibrium contact angles represent the transversality conditions of the variational problem of wetting. The analysis of the role of the substrate area adjacent to the triple line in constituting equilibrium contact angles is presented.