Resolving Capillary Mode Transitions in Microparticles at Fluid Interfaces

Abstract

Capillarity-driven self-assembly at fluidic interfaces offers a scalable route to large, reconfigurable materials. Microscale particles with high horizontal-to-vertical aspect ratios become attractive building blocks for shape-directed organization, but the capillary rules governing their assembly remain incompletely understood. Here, we combine experiments and theory to explain the transition between two capillary regimes: monopolar interactions arising from millimeter-scale curved interfaces, and quadrupolar interactions arising from local contact-line distortions. We show that the conventional Bond number is insufficient to predict this transition because it omits key material and surface-topography effects. Instead, we identify a new dimensionless parameter that captures the coupled roles of particle size, density, surface roughness, contact angle, and quadrupolar strength. This criterion correctly predicts when gravitationally induced monopolar attraction or surface-pinning-induced quadrupolar attraction dominates, providing a general design rule for interfacial particle assembly. The resulting model explains how particles self-organize across length scales and offers guiding principles for engineering next-generation interfacial materials from miniaturized particulate building blocks.