Resolving Capillary Mode Transitions in Micro-DiscInterfacial Particle Assembly

Capillarity-induced self-assembly at fluidic interfaces is a powerful strategy for fabricating large-scale, complex materials. Microscale particles with high horizontal-to-vertical aspect ratios have recently drawn attention as building blocks for controlled two-dimensional self-assembly thanks to the well-defined interfacial deformations they induce. Nevertheless, the underlying dynamics governing lateral capillary interactions at these scales remain incompletely understood. Here, we integrate experimental and theoretical approaches to elucidate the interplay among gravitational forces, wetting, and contact line undulations that give rise to curvature-mediated interparticle potentials. We focus on the transition between two capillarity regimes—monopolar and quadrupolar—using sub-millimeter, disc-shaped micro-particles at fluidic interfaces. By systematically reducing the lateral dimensions of the micro-discs, we probe the limits of the Bond number (Bo) in predicting this transition. Our results reveal that Bo alone is insufficient, as it omits key material parameters such as particle density and surface topography. We identify and experimentally validate a coupled set of parameters that, below a critical threshold, reliably predict the emergence of quadrupolar capillarity, driven by topography-induced meniscus undulations in the absence of gravitational deformation. This study provides the first direct experimental demonstration of the monopolar-to-quadrupolar transition in a particle system without altering material composition. Our validated theoretical model maps the governing parameter space and enables the controlled assembly of hierarchical two-dimensional super-structures with tunable phase behavior. These insights offer design principles for next-generation interfacial materials, particularly in applications requiring capillarity-driven assembly of increasingly miniaturized particulate building blocks.