Modeling capillary bridge dynamics and crack healing between surfaces of nanoscale roughness

Capillary bridge formation between adjacent surfaces in humid environments is a ubiquitous phenomenon. It strongly influences tribological performance with respect to adhesion, friction and wear. Only a few studies, however, assess effects due to capillary dynamics. Here we focus on how capillary bridge evolution influences crack healing rates. Experimental results indicated a logarithmic decrease in average crack healing velocity as the energy release rate increases. Our objective is to model that trend. We assume that capillary dynamics involve two mechanisms: capillary bridge growth and subsequently nucleation followed by growth. We show that by incorporating interface roughness details and the presence of an adsorbed water layer, the behavior of capillary force dynamics can be understood quantitatively. We identify three important regimes that control the healing process, namely bridge growth, combined bridge growth and nucleation, and finally bridge nucleation. To fully capture the results, however, the theoretical model for nucleation time required an empirical modification. Our model enables significant insight into capillary bridge dynamics, with a goal of attaining a predictive capability for this important microelectromechanical systems (MEMS) reliability failure mechanism.