Casimir Interaction between Polydisperse Colloids Trapped at a Fluid Interface

Abstract

We investigate the effect of polydispersity on fluctuation-induced interactions between colloids trapped at a fluid interface. Using the scattering-matrix formalism, we calculate the interaction energy in two- and three-body systems under three mechanical boundary conditions. We find that size asymmetry can either suppress or enhance the many-body interaction compared to a monodisperse system, with the outcome depending on colloids mobility and separation. For fixed colloids, the interaction is suppressed at short separations but enhanced at large separations. In contrast, for mobile colloids, the interaction is predominantly enhanced at large distances but exhibits a competitive behavior in the near-field. This culminates in a large, multi-order-of-magnitude amplified sensitivity {to size asymmetry} for bobbing and tilting colloids at long range, highlighting a complex interplay between geometry and colloids mobility with significant implications for self-assembly.