Adhesion of Multi-component Vesicle Membranes

In this work, we study the adhesion of multi-component vesicle membrane to both flat and curved substrates, based on the conventional Helfrich bending energy for multi-component vesicles and adhesion potentials of different forms. A phase field formulation is used to describe the different components of the vesicle. For the axisymmetric case, a number of representative equilibrium vesicle shapes are computed and some energy diagrams are presented which reveal the dependence of the calculated shapes and solution branches on various parameters including both bending moduli and spontaneous curvatures as well as the adhesion potential constants. Our computation also confirms a recent experimental observation that the adhesion effect may promote phase separation in two-component vesicle membranes.