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In this paper the evolution of a binary mixture in a thin-film geometry witha wall at the top and bottom is considered. By bringing the mixture into itsmiscibility gap so that no spinodal decomposition occurs in the bulk, a slightenergetic bias of the walls towards each one of the constituents ensures thenucleation of thin boundary layers that grow until the constituents have movedinto one of the two layers. These layers are separated by an interfacial regionwhere the composition changes rapidly. Conditions that ensure the separationinto two layers with a thin interfacial region are investigated based on aphase-field model. Using matched asymptotic expansions a correspondingsharp-interface problem for the location of the interface is established.  It is then argued that this newly created two-layer system is not at itsenergetic minimum but destabilizes into a controlled self-replicating patternof trapezoidal vertical stripes by minimizing the interfacial energy betweenthe phases while conserving their area. A quantitative analysis of thismechanism is carried out via a thin-film model for the free interfaces, whichis derived asymptotically from the sharp-interface model.

Controlled topological transitions in thin film phase separation