Effect of turbulence intensity and surface tension on the emulsification process and its stationary state-A numerical study

We study turbulent emulsions and the emulsification process in homogeneous isotropic turbulence (HIT) using direct numerical simulations (DNS) in combination with the volume of fluid method (VOF). For generating a turbulent flow field, we employ a linear forcing approach augmented by a proportional-integral-derivative (PID) controller, which ensures a constant turbulent kinetic energy for two phase flow scenarios and accelerates the emulsification process. For the simulations, the density ratio of dispersed and carrier phases is chosen to be similar to that of oil and water (0.9), representing a typical application. We vary the turbulence intensity and the surface tension coefficient. Thus, we modulate those parameters that directly affect the Hinze scale, which is expected to be the most stable maximum droplet diameter in emulsions in HIT. The considered configurations can be characterized with Taylor Reynolds numbers in the range of 100-140 and Weber numbers, evaluated with the velocity fluctuations and the integral length scale, of 4-70. Using the 3-D simulation results, we study the emulsification process as well as the emulsions at a statistically stationary state. For the latter, droplet size distributions are evaluated and compared. We observe a Hinze scale similarity of the size distributions considering a fixed integral length scale, that is, similar Hinze scales obtained at different turbulence intensities or for different fluid properties result in similar distributions.