Meniscus model for noncontacting and contacting sphere-on-flat surfaces including elastic-plastic deformation

Abstract

Single asperity adhesive contact is a fundamental problem in physics and mechanics and a significant body of research works have been published on capillary adhesion of noncontacting and contacting spheres and surfaces in general. The existing works, however, do not specifically consider the change of the projected meniscus area due to the solid asperity deformation when contacting with the flat solid surface. In this paper, accounting for the effects of both elastic and plastic deformations, we present an improved meniscus model for a deformable sphere on a rigid flat surface covering a large range of interference values from noncontact to a fully plastic contact. For elastic contact, the real contact area, the deformed sphere profile, and the projected meniscus area were determined by the Hertzian solution. For elastic-plastic contact, a finite element-based spherical solution was used to calculate the real wetted area and meniscus force. The model predicts that due to the spherical deformation, the meniscus force increases with increasing interference. The effects of asperity radius, humidity level, and different liquid environments, as well as the valid range of the model, were also discussed.