Local stability for a general wetting functional

We compute the second variation of a general energy functional describing a drop of incompressible liquid in contact with a fluid environment and a rigid substrate structurally inhomogeneous and arbitrarily curved. Both surface and line tensions, residing on the drop’s interfaces and along its contact line, contribute to the energy functional. Our method is purely intrinsic, as it does not resort to any representation of the drop’s shape. From the energy’s second variation we also derive a criterion for the local stability of an equilibrium configuration of the drop.