Two-dimensional modelling of a freely suspended smectic film

We present a two-dimensional model for a smectic film suspended horizontally between two thin electrodes attached to glass plates. The film is bordered vertically by air and is subject to an electric field. Our two-dimensional model allows for spatial variations in the electric field, and predicts the existence of anticlinic or synclinic equilibrium director profiles. Governing equations describing the equilibrium behaviour of the electric potential and the director have been derived by minimizing the free energy of the system. The equations have been solved numerically, and for a fixed set of parameters we are able to obtain two different types of solution profile for our system, corresponding to anticlinic and synclinic configurations.