Oil Droplet Size Distribution on the Free Surface of Turbulent Water

Understanding droplet dynamics in turbulent flows is crucial across numerous fields, ranging from environmental sciences to chemical processing and industrial applications.

In this work, we experimentally investigate the breakup and coalescence of oil droplets populating the surface of a water layer stirred into quasi-two-dimensional turbulence by electromagnetic forces. Through high-speed imaging, we characterize the droplet size distributions along with breakup and coalescence frequencies. We systematically vary the oil properties, the turbulent intensity, and the initial droplet size distribution. At steady state, we observe a robust bimodal droplet size distribution, dividing the drops into four distinct classes: tracer droplets, intermediate-size droplets, condensates near a critical/cutoff scale, and giant droplets exceeding this critical scale. The latter plays an analogous role as the Kolmogorov-Hinze scale in three-dimensional turbulence. Furthermore, we propose scaling laws associated with the tracer and cutoff regimes, highlighting the interplay between turbulence intensity and droplet size distribution.

The present results provide new insights into droplet behavior under the influence of turbulence and interfacial forces, towards a better understanding of fundamental processes in free-surface oil transport as well as in general turbulent multiphase flows and emulsions.