Modulation of homogeneous and isotropic turbulence in emulsions

Abstract

We present a numerical study of emulsions in homogeneous and isotropic turbulence (HIT) at $Re_\lambda =137$ . The problem is addressed via direct numerical simulations, where the volume of fluid is used to represent the complex features of the liquid–liquid interface. We consider a mixture of two iso-density fluids, where fluid properties are varied with the goal of understanding their role in turbulence modulation, in particular the volume fraction ( $0.03<\alpha <0.5$ ), viscosity ratio ( $0.01<\mu _d/\mu _c<100$ ) and large-scale Weber number ( $10.6< We_\mathcal {L}<106.5$ ). The analysis, performed by studying integral quantities and spectral scale-by-scale analysis, reveals that energy is transported consistently from large to small scales by the interface, and no inverse cascade is observed. Furthermore, the total surface is found to be directly proportional to the amount of energy transported, while viscosity and surface tension alter the dynamic that regulates energy transport. We also observe the $-10/3$ and $-3/2$ scaling on droplet size distributions, suggesting that the dimensional arguments that led to their derivation are verified in HIT conditions.