Using Gibbs method of dividing surfaces, the condition of equilibrium of a sessile drop on a flat non-deformable solid substrate is investigated. The dependence of the line tension on the curvature radius of the dividing three-phase contact line is found. It has been derived a relationship between the partial derivative of the line tension with respect to the curvature radius of the three-phase contact line (which stands in the generalized Young equation) and the total derivative of the line tension with respect to the same radius along the equilibrium states. Various approximated formulas of the generalized Young equation used in the literature are analyzed.

Using the chemical potential of a solid in a dissolved state or the corresponding component of the chemical potential tensor at equilibrium with the solution, a new concept of grand thermodynamic potential for solids has been suggested. This allows generalizing the definition of Gibbs' quantity  (surface work often called the solid-fluid interfacial free energy) at a planar surface as an excess grand thermodynamic potential per unit surface area that (1) does not depend on the dividing surface location and ( 2) is common for fluids and solids.In its development (see, e.g., surveys 1,2 ), the surface thermodynamics of solids seems to become more and more complicated as compared with the thermodynamics of fluids. Concerning

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