We investigate the collective motion of a two-dimensional disordered ensemble of droplets in a microfluidic channel far from equilibrium and at Reynolds number $\sim {10}^{-4}$. The ensemble carries ultraslow shock waves and sound, propagating at $\sim 100\mu \mathrm{m}{\mathrm{s}}^{-1}$ and superposed on diffusive droplets motion. These modes are induced by long-range hydrodynamic dipolar interactions between droplets, the result of the symmetry breaking flow. The modes obey the Burgers equation due to a local coupling between droplets velocity and number density. This stems from a singular effect of the channel sidewall boundaries upon summation of the hydrodynamic interaction in two dimensions.

• Received 6 April 2009

DOI:https://doi.org/10.1103/PhysRevLett.103.114502