Inside vesicle adhesion between two vesicles in 2-D case

A theoretic model is proposed to study the adhesion behavior of a vesicle adhering inside another vesicle in 2-D case. The equilibrium shape equations and boundary conditions are investigated. With zero pressure, the integral case of the shape equations with dimensionless parameters is derived. When a soft vesicle adheres inside a rigid ring, the bifurcation between two phases is revealed, the critical adhesion condition and phase diagram are obtained. The finite element method (FEM) is used to study the deformation processes induced by the change of work of adhesion and bending rigidity. The relationships between the energy, adhesion length, cell volume, bending rigidity and work of adhesion are obtained