Adhesive contact of a fluid-filled membrane driven by electrostatic forces

Adhesion of a particle with a substrate in presence of electrostatic interaction is an appealing area of research because of its significance in many biological and industrial applications. In this work, we study an interesting problem in which a charged flexible particle located in an electrolytic environment adheres to an oppositely charged rigid substrate due to the electrostatic attraction between them. The particle is a membrane filled with incompressible fluid and can undergo large deformation. Continuum theories are used to model the mechanics of the membrane and the electric potential in the electrolytic solution. The developed model allows us to examine the nature of the coupling between the electrostatic interaction and the deformation of the membrane. In particular, the deformation of the membrane causes non-uniform distribution of charges on its surface and significant electrostatic repulsion between these charges. This repulsion is most pronounced within and near the contact zone and provides a source of resistance to its further deformation and contact formation. As a result, the coupling between electrostatics and deformation is most significant for moderate deformation and becomes weaker for very large deformation. The relation between the total electrostatic adhesive force and the contact area shows similar scaling ( F ∼ a n , where n = 3 ) to the classical Hertz theory of contact at small deformation, but the value of n increases as deformation increases. The dependence of this relation on the Debye length of the solution and the initial fluid pressure in the membrane is also investigated.