Forced detachment of a vesicle in adhesive contact with a substrate

We consider the forced detachment of a thin-walled vesicle bonded to a substrate for two particular cases. In both cases, the configuration is three-dimensional and the bonding is assumed to occur under conditions of axial symmetry for which the adhered area is always circular. Detachment is driven by a force applied to the top of the vesicle in a direction normal to the substrate surface. The first case is the static or time-independent situation of a vesicle for which bonding is the result of nonspecific interactions between the vesicle and substrate surfaces. For this case, it is shown that the radius of the adhesion patch is determined implicitly by the pulling force F. The maximum pulling force F cr, beyond which the adhered configuration is unstable and the detachment proceeds spontaneously, can also be calculated implicitly. For the particular case of weak adhesion, all significant parameters of the detachment process can be determined explicitly. The second case studied is the time-dependent debonding of a vesicle for which adhesion with the substrate is the result of specific interactions between binders on the two surfaces, typical of biological materials for which the binders are ligand–receptor protein pairs. By treating the detachment process as a result of the debonding of the protein pairs at the edge of the circular adhesion patch, the governing equation for the radius of the adhesion patch is obtained. If a constant force is suddenly applied, it is found that the elapsed time to full detachment is proportional to the magnitude of this force to the power −1.1; alternatively, if the force applied to the vesicle increases linearly in time, it is found that the value of the force at complete detachment is proportional to the applied loading rate F ˙ to the power 0.39, in agreement with recent experimental observations.