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The thermodynamics and mechanics of the surface of a deformable body arestudied here, following and refining the general approach of Gibbs. It is firstshown that the 'local' thermodynamic variables of the state of the surface areonly the temperature, the chemical potentials and the surface strain tensor(true thermodynamic variables, for a viscoelastic solid or a viscous fluid). Anew definition of the surface stress is given and the corresponding surfacethermodynamics equations are presented. The mechanical equilibrium equation atthe surface is then obtained. It involves the surface stress and is similar tothe Cauchy equation for the volume. Its normal component is a generalization ofthe Laplace equation. At a (body-fluid-fluid) triple contact line, twoequations are obtained, which represent: (i) the equilibrium of the forces(surface stresses) for a triple line fixed on the body; (ii) the equilibriumrelative to the motion of the line with respect to the body. This last equationleads to a strong modification of Young's classical capillary equation.

Surface thermodynamics, surface stress, equations at surfaces and triple lines for deformable bodies