Capillary force in high aspect-ratio micropillar arrays

Abstract

High aspect-ratio (HAR) micropillar arrays are important for many applications including, mechanical sensors and actuators, tunable wetting surfaces and substrates for living cell studies. However, due to their mechanical compliance and large surface area, the micropillars are susceptible to deformation due to surface forces, such as adhesive force and capillary force. In this thesis we have explored the capillary force driven mechanical instability of HAR micropillar arrays. We have shown that when a liquid is evaporated off the micropillar arrays, the pillars bend and cluster together due to a much smaller capillary meniscus interaction force while still surrounded by a continuous liquid body, rather than due to often reported Laplace pressure difference because of isolated capillary bridges. We have studied both theoretically and experimentally, the capillary force induced clustering behavior of micropillar arrays as a function of their elastic modulus. To this end, we have developed a modified replica molding process to fabricate a wide range of hydrogel micropillar arrays, whose elastic modulus in the wet state could be tuned by simply varying the hydrogel monomer composition. By minimizing the sum of capillary meniscus interaction energy and bending energy of the pillars in a cluster, we have derived a critical micropillar cluster size, which is inversely proportional to elastic modulus of micropillars. The estimated cluster size as a function of elastic modulus agrees well with our experimental observation. We have also explored the utility of the clustered micropillar arrays as ultrathin whitening layers mimicking the structural whitening mechanism found in some insects in nature. Finally, we have theoretically studied the capillary force induced imbibition of a liquid droplet on a model rough surface consisting of micropillar arrays. Our theoretical model suggests that due to shrinking liquid droplet, the imbibition dynamics does not follow the diffusive Washburn dynamics but progressively becomes slower with time