Lateral capillary forces of cylindrical fluid menisci: a comprehensive quasi-static study

Capillarity is pivotal to many important technologies, including capillary self-alignment and self-assembly for heterogeneous microsystem integration and packaging. Lateral capillary forces ensuing from perturbed fluid menisci were the object of substantial theoretical and numerical modeling in recent years. Anyway, those studies were so far unsatisfactorily supported by direct experimental inspections. In this paper we present a comprehensive quasi-static study of lateral capillary forces arising from a constrained cylindrical fluid meniscus subjected to small lateral perturbations. We describe the novel experimental apparatus that we designed to accurately characterize such a fundamental system. We then reproduce our experimental data on lateral meniscus forces and stiffnesses by means of both a finite element and a novel analytical model. The agreement between our measurements and models, while confirming earlier reports, provides a solid foundation for the applications of lateral capillary forces to microsystem assembly. Moreover, our experimental apparatus may enable the exploitation of Gibbs' inequality to measure the advancing contact angles of liquids, and it may be used as a reference testbed for further experimental investigations on constrained fluid menisci.