Local thermodynamic derivation of Young's equation

A derivation of Young's equation based on the energy balance near the contact line is presented. Our proposal is rigorous and avoids the errors identified in the usual local derivation. It is valid under very general conditions (for any geometry, in a gravitational field and for compressive fluids). Deviations of the contact angle from Young's equation are discussed in several cases: surfaces of high curvature and line tension. Finally, the relationship between surface tensions and surface energies comes as an additional, natural result. Our derivation also provides a new physical insight into the equilibrium of forces acting near the contact line. Its local character makes the recourse to integral analysis unnecessary, which results in a great simplification when compared to other general treatments.