  An electric-field-induced phase transition and pattern formation in a binary
dielectric fluid layer are studied using a coarse-grained free energy
functional. The electrostatic part of the free energy is a nonlinear functional
of the dielectric function, which depends in turn on the local colloidal
concentration. We determine the phase co-existence curve and find that beyond a
critical electric field the system phase separates. Accompanying the phase
separation are patterns similar to those observed in a spinodal decomposition
of an ordinary binary fluid. The temporal evolution of the phase separating
patterns are discussed both analytically and numerically by integrating a
Cahn-Hilliard type of equation.
