Stability of droplets and channels on homogeneous and structured surfaces

Wetting of structured or imprinted surfaces which leads to a variety of dif ferent morphologies such as droplets, channels or thin films is studied the oretically using the general framework of surface or interface thermodynami cs. The first variation of the interfacial free energy leads to the well-kn own Laplace equation and a generalized Young equation which involves spatia lly dependent interfacial tensions. Furthermore, we perform the second vari ation of the free energy for arbitrary surface patterns and arbitrary shape of the wetting morphology in order to derive a new and general stability c riterion. The latter criterion is then applied to cylindrical segments or c hannels on homogeneous and structured surfaces.