Classical phase field models for lipid phase separation tend to minimize the interface energy, ending up with large domains after separation. A biologically more relevant scenario is the formation of local lipid domains, centered around proteins or not, called lipid rafts, which can not be reproduced by using the classical lipid phase separation models. Here we introduce an energy penalizing the mismatch of different lipid species at their contact interface and represent this energy using the geodesic curvature on arbitrarily curved membrane surfaces. We successfully simulated the formation of local lipid domains for various lipid compositions. Our results will provide a solid mathematical foundation for simulating the ras proteins localization at the boundary of micro lipid domains.