Dynamical and structural transitions in periodically-driven emulsions: Reversibility loss and random hyper-unifom organization

We present experiments and numerical simulations of a microfluidic echo process, in which a large number of droplets interact in a periodically driven viscous fluid [Jeanneret \& Bartolo, Nature Comm. {\bf 5}, 3474 (2013)]. Upon increasing the driving amplitude we demonstrate the collective reversibility loss of the droplet dynamics. In addition we show that this genuine dynamical phase transition is associated with a structural one: at the onset of irreversibility the droplet ensemble self-organises into a random hyperuniform state. Numerical simulations evidence that the purely reversible hydrodynamic interactions together with hard-core repulsion account for most of our experimental findings. Hyperuniformity is relevant for the production of large-band-gap materials, but are difficult to construct both numerically and experimentally. The hydrodynamic echo-process may provide a robust, fast, and simple way to produce hyper uniform structures over a wide range of packing fractions.