Variational approach to wetting problems: Calculation of a shape of sessile liquid drop deposited on a solid substrate in external field

Analysis of the shape of sessile drops pinned to a solid substrate and exposed to the external potential is presented. Explicit expressions describing the drops' shape are obtained with a calculus of variations for 2D and 3D wetting problems. The presented approach is applicable for analysis of electrowetting problems, the study of vibrated and centrifuged drops.