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

Abstract

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.

Modeling capillary forces for large displacements

“…Note that for R 1 | 0<u<h the small displacement values F 1 = −2γL u h and k 1 = 2γ L h of linear elastic models are recovered 9,12,20,29 . Conversely, the absence of elastic work in R 3 is evidenced by the null constant value of k 3 .…”

“…Thereby the focus has mainly been on sub-millimetric components actuated by droplets of similar size, and correspondingly on displacements from equilibrium of relatively small magnitude. Elastic models accurately capture the response of the capillary system to such small lateral displacements 9,12,[20][21][22] . In this type of models the restoring capillary forces arise exclusively from the shear deformation of liquid interfaces pinned to bounding solid surfaces.…”

Dynamics of capillary self-alignment for mesoscopic foil devices

“…The thickness h and the surface tension c of the liquid layer directly affect the lateral capillary forces driving the alignment process. 10 The thickness of the water layer was calculated from the dispensed water volume and the area of the sites. It was optimized to consistently achieve accurate registration of the dies upon SA (%30 lm, as limited by laser dicing tolerance, to be compared with the centimetric dies dimensions).…”

Experimental characterization of Drobot: Towards closed-loop control

“…A new design should include sharper edges or more hydrophobic materials to better confine the spreading, low-surface-tension ionic liquid. The liquid bridge is not sufficiently constrained by the geometry of the substrate [22], and the ionic liquid overflows and spreads onto the platform.…”