In this talk we will consider phase separations on generalized hypersurfaces in Euclidean space. For a diffuse surface area (line tension) energy of Modica-Mortola type, we prove a compactness and lower bound estimate in the sharp interface limit. We use the concept of generalized BV functions over currents as introduced by Anzellotti et al. [Annali di Matematica Pura ed Applicata, 170, 1996] to give a suitable formulation in the limit and achieve the necessary compactness property. We also consider an application to phase separated biomembranes where a Willmore energy for the membranes is combined with a generalized line tension energy. For a diffuse description of such energies we give a lower bound estimate in the sharp interface limit. Joint work with Matthias Röger, TU Dortmund