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 coexistence 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
