A Micro-Scale Liquid Bridge Between Two Elastic Spheres: Deformation and Stability

Abstract

A recent study showed that for a liquid bridge of volume Vo interposed between two half-spaces and originally separated by uniform gap H, the interface stability was determined by a single dimensionless parameter. When the parameter exceeds a certain value, the interface loses stability and the solid surfaces come into contact. Further, once contact is made, the contact zone will continue to spread without bound. In the present work, the interaction between two curved elastic bodies coupled via a small liquid bridge is investigated. The equilibrium configurations are determined by minimizing the total free energy stored in the interface among all provisional equilibrium configurations; i.e., those configurations consistent with the equations of elasticity and capillarity. In the case of curved bodies, the stability of the interface is governed by the above parameter as well as by a dimensionless ratio involving the liquid volume (Vo), the composite radius (R) and the original (undeformed) minimum sphere–sphere separation (H). When the interface becomes unstable, solid–solid separation cannot be sustained and contact ensues. The resulting solid–solid contact radius is found to depend on the above parameters as well as on the ratio of solid–liquid and liquid–air surface energies. Based on the numerical calculations, simple relations are found between the contact radius and the other relevant parameters.