Wave-mediated capillary assembly on a fluid interface

In the last few years, wave-propelled particles at an air-fluid interface have been shown to exhibit a host of both static and dynamic collective states, with even the two-body problem admitting multiple stable equilibria for a fixed set of experimental parameters. The interaction between such particles is governed by a combination of a static capillary attractive force, colloquially known as the "Cheerios Effect" and a dynamic wave-mediated force that oscillates from attractive to repulsive over a length scale set by the wavelength. Here, we consider the simple problem of the dynamics of interacting "point sources" (small superhydrophobic spheres) that sit atop a vibrating fluid interface. We find that the spheres admit multiple stable equilibria, quantized by the wavelength, with the existence and stability of the equilibria being a function of driving and fluid parameters. A previously established quasi-potential model, which provides predictions for both the wavefield and the resulting wave-mediated force law, is compared with experimental results, allowing for direct verification of the stable equilibrium spacing as a function of system parameters. With an understanding of the pairwise interaction, stable assemblies of objects are formed, with lattice constants and structure capable of being dynamically manipulated by the driving parameters of the forcing itself.