Self-Assembly of Lamellae by Elastocapillarity in the Presence of Gravity: Experiments and Modeling

Elastocapillarity describes the self-organization of elastic structures under liquid surface forces, for applications to micro-and nanoscale self-Assembly. It has recently become evident that precise prediction of elastocapillary self-Assembly is challenged by the various phenomena arising due to fluid flow. In this study, we present experiments and a corresponding reduced-order model for the dynamic coalescence of flexible lamellae arrays. Vertical arrays of elastomeric lamellae attached to a substrate at the bottom are fabricated using 3D-printed molds. The lamellae have sub-mm thickness and a few millimeters height, a size scale that cannot be achieved by traditional microfabrication. The gaps between the elastic lamellae are filled with liquid while the tips of the lamellae, which are at the top with respect to gravity, are initially fixed, and then, they are released which leads to their spontaneous bending and coalescence. We study the cluster size as a function of system variables both experimentally and numerically. The solid lamellae are modeled as discrete rigid elements connected by torsional springs to the substrate, while the fluid flow uses lubrication theory and capillarity. Importantly, the model incorporates the gravitational forces to effectively capture the systems' behavior ranging from the microscale with negligible gravity effect to the macroscale where gravity significantly influences the dynamics. We further derive a linearized continuum model from our nonlinear formulation, providing an analytical universal scaling law for the lamellae cluster size. This work is relevant for new polymorphic fins and lamellae devices, capillary self-folding and origami.