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A simple model for the adhesion of vesicles to interfaces and membranes is introduced and theoretically studied. It is shown that adhering (or bound) vesicles can exhibit a large variety of different shapes. The notion of a contact angle governed by tension is found to be applicable only for a restricted subset of these shapes. Furthermore, the vesicle undergoes a nontrivial adhesion transition from a free to a bound state. This transition is governed by the balance between the overall bending and adhesion energies, and occurs even in the absence of shape fluctuations.
Seifert et al. (Mon,) studied this question.