A More General Capillary Adhesion Model Including Shape Index: Single-Asperity and Multi-Asperity Cases

The capillary interaction between a sphere and a flat substrate has been widely investigated. Considering the complex shape of single asperities in real configurations, a more general model of capillary adhesion force including a power law shape index of asperities is developed. For the interaction between a single asperity with any axisymmetric power law shape profile and a flat substrate, the deformation originating from the adhesive force and the contact force is included in the model. Combining the single asperity capillary adhesion model and a statistical description of rough surfaces, the capillary adhesion between two rough surfaces is also studied. The simulation results show that the adhesive force between a single asperity and a flat surface increases gradually with increasing shape index at the same humidity level. For typical microelectromechanical systems surfaces, the adhesive force between rough surfaces also increases with the increased shape index of multi-asperities. Specifically, when the shape index varies from 1.8 to 2.4 at high humidity, the adhesive force between a single asperity and a plane may change remarkably, and the adhesion energy between rough surfaces may increase by several orders of magnitude at low humidity. These results show the necessity of including a shape index for modeling the capillary adhesion between single asperities, and a more detailed description of rough surfaces is also helpful to better quantify the capillary adhesion between rough surfaces.