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. 2D experiments and simulations show that beyond a critical packing fraction, the uniform lattice state becomes unstable and localized clusters spontaneously form which is reminiscent of microscopic colloidal systems. Finally, we show that the state of the system can be controlled by tuning the capillary force via an external magnetic force.