Interactions and Pattern Formation in a Macroscopic Magnetocapillary SALR System

Interaction potentials defined by Short-range Attraction and Long-range Repulsion (SALR), frequently arise in the modeling of colloidal systems. Here, we introduce a new SALR potential that combines capillary attraction and repulsive magnetic forces and can be realized in an accessible tabletop experiment. We develop a simplified model of the pairwise interaction potential that predicts a variety of regimes, including the possibility of a local minimum energy configuration for certain parameters. Experiments confirm that a minimum energy configuration corresponding to a finite equilibrium spacing is possible for a pair of millimetric magnetic floating disks. Quasi-1D experiments and simulations show that beyond a critical packing fraction, the uniform lattice state becomes unstable and localized clusters spontaneously form. Finally, we explore pattern formation at high packing fractions in the two-dimensional magnetocapillary system which exhibits behaviors that are reminiscent of microscopic colloidal systems.