Droplet dynamics in homogeneous and isotropic turbulence

Emulsions are a major class of multiphase flows, crucial in industrial process (e.g. food and drug production) and ubiquitous in environmental flows (e.g. oil spilling in maritime environment). Already at volume fractions of few precents, the dispersed phase interacts with pre-existing turbulence created at large scale, yet the interaction between phases and the turbulent energy transport across scales is not yet fully understood.

In this work, we use Direct Numerical Simulation to study emulsions in homogeneous and isotropic turbulence, where the Volume of Fluid (VoF) method is used to represent the complex features of the liquid-liquid interface.

We consider a mixture of two matching-density phases, where we vary volume fraction, viscosity ratio and large-scale Weber number aiming at understanding the turbulence modulation and the observed droplet size distributions.  The analysis, based on the spectral scale-by-scale analysis, reveals that energy is consistently transported from large to small scales by the interface, and no inverse cascade is observed. We find that the total surface is directly proportional to the amount of energy transported, and that the energy transfer in the inertial range provides information about the droplet dynamics. We observe the -10/3 and -3/2 scaling on droplet size distributions, suggesting that the dimensional arguments which led to their derivation are verified in HIT conditions and denser conditions. Finally, we discuss the highly intermittent behaviour of the multiphase flow, which can be directly related to the polydisperse nature of the flow.

The study provides some significant observations towards a more comprehensive understanding of multiphase turbulence, opening new questions for future studies.