Deformation and orientation statistics of neutrally buoyant sub-Kolmogorov ellipsoidal droplets in turbulent Taylor–Couette flow

Abstract

The influence of the underlying flow topology on the shape and size of sub-Kolmogorov droplets dispersed in a turbulent flow is of considerable interest in many industrial and scientific applications. In this work we study the deformation and orientation statistics of sub-Kolmogorov droplets dispersed into a turbulent Taylor–Couette flow. Along with direct numerical simulations (DNS) of the carrier phase and Lagrangian tracking of the dispersed droplets, we solve a phenomenological equation proposed by Maffettone and Minale (J. Non-Newtonian Fluid Mech., vol. 78, 1998, pp. 227–241) to track the shape evolution and orientation of approximately $10^{5}$ ellipsoidal droplets. By varying the capillary number $Ca$ and viscosity ratio $\hat{\unicode[STIX]{x1D707}}$ of the droplets we find that they deform more with increasing capillary number $Ca$ and this effect is more pronounced in the boundary layer regions. This indicates that along with an expected capillary number effect there is also a strong correlation between spatial position and degree of deformation of the droplet. Regardless of the capillary number $Ca$, the major axis of the ellipsoids tends to align with the streamwise direction and the extensional strain rate eigendirection in the boundary layer region while the distribution is highly isotropic in the bulk due to the strong mixing provided by the large-scale vortical structures. When the viscosity ratio between the droplet and the carrier fluid is increased we find that there is no preferential stretched axis which is due to the increased influence of rotation over stretching and relaxation. Droplets in high viscosity ratio systems are thus less deformed and oblate (disk-like) as compared to highly deformed prolate (cigar-like) droplets in low viscosity ratio systems.