Clusters in sedimentation equilibrium for an experimental hard-sphere-plus-dipolar Brownian colloidal system

In this work, we use structure and dynamics in sedimentation equilibrium, in the presence of gravity, to examine, $via$ confocal microscopy, a Brownian colloidal system in the presence of an external electric field. The zero field equation of state (EOS) is hard sphere without any re-scaling of particle size, and the hydrodynamic corrections to the long-time self-diffusion coefficient are quantitatively consistent with the expected value for hard spheres. Care is taken to ensure that both the dimensionless gravitational energy, which is equivalent to a Peclet number $Pe_g$, and dipolar strength $\Lambda$ are of order unity. In the presence of an external electric field, anisotropic chain-chain clusters form; this cluster formation manifests itself with the appearance of a plateau in the diffusion coefficient when the dimensionless dipolar strength $\Lambda \sim 1$. The structure and dynamics of this chain-chain cluster state is examined for a monodisperse system for two particle sizes.