Gravity-Driven Assembly Dynamics of Liquid Metal Microdroplets for Functional Composite Films

Liquid metal (LM) microdroplets have emerged as versatile building blocks for soft and stretchable electronics, enabling compliant conductors, multilayer architectures, and reconfigurable systems. Among the manufacturing strategies used to structure these composites, gravitational settling in liquid-phase polymer films offers a scalable pathway for directed assembly; however, the mechanics and kinetics governing this process remain poorly understood. Here we create an experimental platform and quantitative image-analysis framework to measure the gravitational settling dynamics of highly packed LM microdroplets in liquid-phase polymer resin films. By systematically varying LM microdroplets size ( $\sim 50-500$ $\mu m$ diameter), resin viscosity ( $\sim 100-5000$ mPa s), and the geometry of the film system ( $\sim 300-1600$ $\mu m$ thick), we elucidate the process-structure relationships of gravitational settling of LM in confined films. Settling time decreases with droplet diameter following an inverse-square Stokes-type scaling and increases linearly with resin viscosity, which dominates the assembly rate. In contrast, film and saturated layer thicknesses exert only minor influence due to confinement effects. These relationships translate directly to a multilayer assembly process for soft interlayer via fabrication, establishing a predictive framework for scalable gravity-directed LM assembly.