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Numerical determination of the surface and composition profiles for a film of binary mixture on a solid substrate

We numerically study the static structures resulting from the coupled demixing and dewetting of a film of binary liquid on a solid substrate. The model corresponds to the static limit of the diffuse interface model describing the phase separation process for a binary liquid (model-H), when supplemented by boundary conditions at the evolving free surface. The resulting variational problem is discretized using the Finite Element Method. We obtain the dependence of the static surface shape of a symmetric droplet on surface tension and discuss its relation to the corresponding sharp interface solutions and solutions in the limit of large surface tension. The effective interface tension of the diffuse interface is determined by several independent means. Finally, we observe changes in the droplet geometry due to preferential attraction of one component of the binary liquid to the substrate. Our results elucidate the structure of nanodroplets when the phase separation is strongly influenced by boundary effects.