Burgers Shock Waves and Sound in a 2D Microfluidic Droplets Ensemble

Abstract

We investigate the collective motion of a two-dimensional disordered ensemble of droplets in a microfluidic channel far from equilibrium and at Reynolds number similar to 10(-4). The ensemble carries ultraslow shock waves and sound, propagating at similar to 100 mu ms(-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.