Young, Boruvka–Neumann, Wenzel and Cassie–Baxter equations as the transversality conditions for the variational problem of wetting

The problem of wetting is discussed in the framework of the variational approach. It is shown that the Young, Boruvka–Neumann, Wenzel and Cassie–Baxter equations result from the transversality conditions for a drop placed on the solid substrate and exerted to the external field. Equilibrium (Young) and apparent contact angles are insensitive to external fields under very general assumptions concerning the nature of the field. Generalization of the developed approach to the line tension is discussed.