Modulation of homogeneous and isotropic turbulence in emulsions

TL;DR

This study uses DNS with VOF to explore how emulsions affect turbulence, revealing energy transfer mechanisms, the influence of fluid properties, and droplet size scaling in isotropic turbulence.

Contribution

It provides new insights into turbulence modulation by emulsions, including the role of interface dynamics and the effects of fluid property variations.

Findings

Energy is transported from large to small scales without inverse cascade.

Total surface area correlates with energy transport.

Droplet size distributions follow specific scaling laws (-10/3 and -3/2).

Abstract

We present a numerical study of emulsions in homogeneous and isotropic turbulence at $Re_\lambda=137$. The problem is addressed via Direct Numerical Simulations (DNS), where the Volume of Fluid (VOF) 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 consistently transported 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 which led to their derivation are verified in HIT conditions.