Dynamic restructuring and ordering are prevalent in driven many-body systems with long-range interactions, such as sedimenting particles, dusty plasmas, flocking animals and microfluidic droplets. Yet, understanding such collective dynamics from basic principles is challenging because these systems are not governed by global minimization principles, and because every constituent interacts with many others. Here, we report long-range orientational order of droplet velocities in disordered two-dimensional microfluidic droplet ensembles. Droplet velocities exhibit strong long-range correlation as 1/r 2, with a four-fold angular symmetry. The two-droplet correlation can be explained by representing the entire ensemble as a third droplet. The correlation amplitude is non-monotonous with density owing to excluded-volume effects. Our study puts forth a many-body problem with long-range interactions that is solvable from first principles owing to the reduced dimensionality, and introduces new experimental tools to address open problems in many-body non-equilibrium systems.
Bibliographical noteFunding Information:
This work was supported by a Yeda-Sela Grant (R.H.B-Z). T.B. was supported by the Cross Disciplinary Postdoctoral Fellowship of the Human Frontier Science Program. T.T. is the Helen and Martin Chooljian Founders Circle Member in the Simons Center for Systems Biology of the Institute for Advanced Study, Princeton.