Optimal substrate shape for vesicle adhesion on a curved substrate

When pulling a vesicle adhered on a substrate, both the force-displacement profile and the maximum force at pull-off are sensitively dependent upon the substrate shape. Here we consider the adhesion between a two-dimensional vesicle and a rigid substrate via long-range molecular interactions. For a given contact area, the theoretical pull-off force of the vesicle is obtained by multiplying the theoretical strength of adhesion and the contact area. It is shown that one may design an optimal substrate shape to achieve the theoretical pull-off force.