  A phase-separation front will leave in its wake a phase-separated morphology
that differs markedly from homogeneous phase-separation morphologies. For a
purely diffusive system such a front, moving with constant velocity, will
generate very regular, non-equilibrium structures. We present here a numerical
study of these fronts using a lattice Boltzmann method. In two dimensions these
structures are regular stripes or droplet arrays. In general the kind and
orientation of the selected morphology and the size of the domains depends on
the speed of the front as well as the composition of the material overtaken by
the phase-separation front. We present a survey of morphologies as a function
of these two parameters. We show that the resulting morphologies are initial
condition dependent. We then examine which of the potential morphologies is the
most stable. An analytical analysis for symmetrical compositions predicts the
transition point from orthogonal to parallel stripes.
