  We introduce a simple and predictive model for determining the phase
stability of ternary phospholipid-cholesterol mixtures. Assuming that
competition between the liquid and gel order of the phospholipids is the main
driving force behind lipid segregation, we derive a Gibbs free-energy of
mixing, based on the thermodynamic properties of the lipids main transition. A
numerical approach was devised that enable the fast and efficient determination
of the ternary diagrams associated with our Gibbs free-energy. The computed
phase coexistence diagram of DOPC/DPPC/cholesterol reproduces well known
features for this system at 10\circ C, as well as its evolution with
temperature.
