Hyperuniformity of driven suspensions

An arrangement of particles is said to be "hyperuniform" if its density fluctuations over large distances are strongly suppressed relative to a random configuration. Crystals, for example, are hyperuniform. Recently, several disordered materials have been found to be hyperuniform. Examples are sheared suspensions and emulsions, and, possibly, random close packings of particles. We show that externally driven particles in a liquid suspension (as in sedimentation, for example) self-organize hyperuniformly in certain directions relative to the external force. This dynamic hyperuniformity arises from the long-range coupling, induced by the force and carried by the fluid, between the concentration of particles and their velocity field. We obtain the general requirements, which the coupling should satisfy in order for this phenomenon to occur. Under other conditions (e.g., for certain particle shapes), the coupling can lead to the opposite effect -- enhancement of density fluctuations and instability. We confirm these analytical results in a simple two-dimensional simulation.