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.

A lamellar pattern can form in a thin magnetic fluid layer when the applied electric field is above a critical value. A 2D simulation is performed to study the field-induced phase separation and the pattern by using the mass continuity equation. The simulation produces the similar structure in field but does not match the experimental growth law.

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