Deformation of ellipsoidal droplets in homogeneous and isotropic turbulence

TL;DR

This paper compares phenomenological ellipsoidal models with detailed simulations to understand how neutrally buoyant droplets deform in homogeneous isotropic turbulence, focusing on the influence of the capillary number.

Contribution

It evaluates the accuracy of ellipsoidal models against fully resolved simulations for droplet deformation in turbulence across different capillary numbers.

Findings

Ellipsoidal models can approximate droplet deformation under certain conditions.

The models' accuracy varies with the capillary number.

Simulation data provides ground truth for model validation.

Abstract

We study the statistics of deformation of neutrally buoyant droplets in homogeneous isotropic turbulence (HIT), wherein the characteristic droplet size $R$ is smaller than the characteristic Kolmogorov scale $\eta$ of the turbulent flow. We systematically focus on the characterization of droplet statistics obtained with various phenomenological ellipsoidal models (EMs) -- assuming that the droplet preserves the ellipsoidal shape at all times - with the droplet moving as a passive tracer in the turbulent flow. The predictions of the EMs are compared with ground-truth data obtained with three-dimensional fully resolved simulations (FRSs) without any ad-hoc assumption on the droplet shape. Our work helps in elucidating the applicability of the EMs in describing droplet deformation in HIT at changing the capillary number $\text{Ca}=\tau_{\sigma}/\tau_{\eta}$, weighting the relative importance of the droplet characteristic time $\tau_{\sigma}$ with respect to the turbulent flow characteristic time $\tau_{\eta}$.