A general stability criterion for droplets on structured substrates

Wetting morphologies on solid substrates, which may be chemically or topographically structured, are studied theoretically by variation of the free energy which contains contributions from the substrate surface, the fluid–fluid interface and the three-phase contact line. The first variation of this free energy leads to two equations—the classical Laplace equation and a generalized contact line equation—which determine stationary wetting morphologies. From the second variation of the free energy we derive a general spectral stability criterion for stationary morphologies. In order to incorporate the constraint that the displaced contact line must lie within the substrate surface, we consider only normal interface displacements but introduce a variation of the domains of parametrization.