Deformation of ellipsoidal droplets in homogeneous and isotropic turbulence

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 ${\tau }_{\eta }$.