Capillary Adhesion of Microbeams: Finite Deformation Analysis

Capillary force may cause adhesion of devices at micro- and nano-scales.
Considering the fact that large deformation is often involved in adhesion of microbeams, we analysed the capillary adhesion of two beams using finite deformation elasticity theory. The critical adhesion condition can be obtained from the present method as a function of the bending stiffness, Young's contact angle, the spacing of the two beams as well as the surface tensions of the solid and liquid phases. The solution for the capillary adhesion of a beam with a rigid substrate is also given. The results from the finite deformation analysis are compared with that of infinitesimal deformation method in order to show the necessity of accounting for the nonlinear effect associated with large deflection. The method adopted in this study can also be used to solve other adhesion problems associated with van der Waals force or electrostatic force.