Elastocapillary coalescence of plates and pillars

Abstract

When a fluid-immersed array of lamellae or filaments that is attached to a substrate is dried, evaporation leads to the formation of menisci on the tips of the plates or pillars that bring them together. Similarly, when hair dries it clumps together due to capillary forces induced by the liquid menisci between the flexible hairs. Building on prior experimental observations, we use a combination of theory and computation to understand the nature of this instability and its evolution in both the two-dimensional and three-dimensional setting of the problem. For the case of lamellae, we explicitly derive the interaction torques based on the relevant physical parameters. A Bloch-wave analysis for our periodic mechanical system captures the critical volume of the liquid and the 2-plate-collapse eigenmode at the onset of instability. We study the evolution of clusters and their arrest using numerical simulations to explain the hierarchical cluster formation and characterize the sensitive dependence of the final structures on the initial perturbations. We then generalize our analysis to treat the problem of pillar collapse in 3D, where the fluid domain is completely connected and the interface is a surface with the uniform mean curvature. Our theory and simulations capture the salient features of both previous experimental observations and our own in terms of the key parameters that can be used to control the kinetics of the process.