Phase separation of a binary mixture with an external force field

The objective of this work is to simulate the phase separation of a regular binary mixture in the presence of an external force field. In general, when a partially miscible binary mixture is brought from the stable, single phase region of its phase diagram to the unstable region, it separates into two coexisting phases, corresponding to a minimum of the free energy of the mixture. As the mass of each chemical species is conserved, phase transition consists of a reordering process, called spinodal decomposition. Now, assume that an external force field is applied to the mixture, and that its effects on the species composing the mixture are different from each other. For example, the force field can be gravity, applied to a mixture of fluids having different densities. Or, it can be an electric field, applied to a mixture of ionic species having different electric charges. In all these cases, the external force will enhance demixing: for example, gravity will tend to increase the concentration of the heavier species in the bottom of the container and the electric field will tend to separate the two species along the direction of the force field. Here we show that the non-homogeneity of the composition field induced by the external field may cause, locally, a phase transition even when, globally, the system is in a metastable, and even a stable, thermodynamic condition.