The surface and the linear tension and the contact angle of a small drop under isothermal conditions

A small lying drop is investigated considering the linear tension at the three-phase boundary under thermodynamic and mechanical equilibrium. Formulas for the surface tension at the liquid-vapor interface, the linear tension, and the contact angle are found by the Gibbs dividing surface method. It is shown that the surface tension and the contact angle decrease while the absolute value of the linear tension increases with decreasing radius of the surface curvature. Comparison of theoretical predictions with experimental data obtained by atomic-force microscopy shows a satisfactory agreement and evidences that the linear tension must be negative.