Collective Dynamics of Long-Range Interacting Droplet Ensembles

Many-body systems with long-range interactions that are driven out of equilibrium are common in Nature. For example, stellar motion, charged particles in plasma and sedimentation of particles in a fluid under gravity. Yet, their complex behavior is hard to explain, since each constituent effectively interacts with all the others. I will present a study of the dynamics of microfluidic droplet ensembles flowing in a two-dimensional channel and governed by long-range hydrodynamic dipolar interactions1,2. While the ensemble is spatially disordered, the droplet velocities exhibit strong long-range correlations proportional to 1/r^2, with a four-fold angular symmetry3. The two-droplet correlation is explained by representing the entire ensemble as a third droplet. The velocity fluctuations amplitude is non-monotonous with the ensemble’s density owing to excluded-volume effects. The summation over the long-range interactions converges thanks to the low-dimensionality of the system facilitating a theoretical description of the velocity fluctuations and correlations in such a complicated system.
1.           Beatus, T., Tlusty, T. & Bar-Ziv, R. Phonons in a one-dimensional microfluidic crystal. Nat. Phys. 2, 743–748 (2006).
2.           Beatus, T., Bar-Ziv, R. H. & Tlusty, T. The physics of 2D microfluidic droplet ensembles. Phys. Rep. 516, 103–145 (2012).
3.           Shani, I., Beatus, T., Bar-Ziv, R. H. & Tlusty, T. Long-range orientational order in two-dimensional microfluidic dipoles. Nat. Phys. 10, 140–144 (2014).