  In this paper the evolution of a binary mixture in a thin-film geometry with
a wall at the top and bottom is considered. By bringing the mixture into its
miscibility gap so that no spinodal decomposition occurs in the bulk, a slight
energetic bias of the walls towards each one of the constituents ensures the
nucleation of thin boundary layers that grow until the constituents have moved
into one of the two layers. These layers are separated by an interfacial region
where the composition changes rapidly. Conditions that ensure the separation
into two layers with a thin interfacial region are investigated based on a
phase-field model. Using matched asymptotic expansions a corresponding
sharp-interface problem for the location of the interface is established.
  It is then argued that this newly created two-layer system is not at its
energetic minimum but destabilizes into a controlled self-replicating pattern
of trapezoidal vertical stripes by minimizing the interfacial energy between
the phases while conserving their area. A quantitative analysis of this
mechanism is carried out via a thin-film model for the free interfaces, which
is derived asymptotically from the sharp-interface model.
