Phase transitions in equilibrium systems: microscopic models and mesoscopic free energies

We describe the derivation of mesoscopic free energy functionals for systems with long-range Kac potentials and analyse them in the presence of phase transitions. This yields information about the arrangement of phases in some binary mixtures as well as explicit criteria for the stability of liquid droplets in a one-component fluid described by a Cahn-Hilliard type of free energy functional.