Capillary collapse of a micro-double cantilever beam: a rigorous study

Abstract

High-aspect-ratio microstructures have been found, in the literature, to collapse due to capillary forces of liquids. In this paper, mathematical models are developed to study the collapse of a microstructure represented by a double cantilever beam (DCB) with a liquid droplet located at the free end. Formulations are presented using the classical Bernoulli–Euler beam theory as well as an analysis that accounts for geometrical nonlinearity. The models introduce rigorous coupling between the DCB deformation, the capillary forces, and the meniscus position, and have predicted interesting nonlinear behaviors that previous models could not. Parameters governing the capillary collapse of the DCB are identified, and their influence is discussed. A single dimensionless number that controls the condition for collapse is proposed and validated against numerical results. Comparison between the linear and nonlinear beam analyses shows that linear analysis generally suffices for the description of capillary collapse of microstructures.