Thermodynamic derivation of the Young-Dupré form equations for the case of two immiscible liquid drops resting on a solid substrate.

In this study a form of Young-Dupré equation has been derived for the case of a drop of a liquid (1) completely encapsulated by another drop of liquid (2) and both are resting on a solid substrate. The two liquids considered here are immiscible homogeneous phases. The derivation is mainly based on the powerful thermodynamics formalism with the help of geometrical considerations. The derivation yields two equations describing the equilibrium conditions of the two drops considered. In addition the equilibrium conditions for the four-phase merging along a single contact line is derived. The results show the advantages of thermodynamic formalism over mechanical considerations.