Self-assembly of ferrofluid droplets at a curved surface

We produce a monodisperse 2D raft of ferrofluid droplets at a meniscus. At short length scales, these droplets are attracted to each other via the depletion interaction. When we apply a magnetic field we can induce a tunable repulsive force between the droplets. As the repulsive force between the droplets is increased, the droplet raft transitions from a dense closely packed crystalline structure, to an intermediate filamentary structure, to a low-density dispersed structure. We see sharp transitions between these regimes and explain the phenomenon with a simple model and simulations