Droplet-Induced Budding Transitions of Membranes
  Motivated by recent experiments on biomimetic membranes exposed to several aqueous phases, we theoretically study the morphology of a membrane in contact with a liquid droplet formed via aqueous phase separation. We concentrate on membranes with negligible spontaneous curvature. At small droplet volume, bending energy dominates and the droplet is only partially wrapped by the membrane. At large volume, this configuration can become unstable and undergo a discontinuous transition to a state, in which the droplet is (almost) completely wrapped by the membrane. A morphology diagram, showing the parameter region where such budding transition occurs, is constructed as a function of the membrane tension and the intrinsic contact angle of the liquid with the membrane. The effects of spontaneous curvature are discussed qualitatively. 
Halim Kusumaatmaja and Reinhard Lipowsky
cond-mat.soft physics.bio-ph