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 (\emph{J. Fluid Mech.} 78, 227-241 (1998)) to track the shape evolution and orientation of approximately $10^5$ ellipsoidal droplets. By varying the capillary number $Ca$ and viscosity ratio $\hat{\mu }$ of the droplets we find that the droplets deform more with increasing capillary number $Ca$ and this effect is more pronounced in the boundary layer regions. This indicates that along with a 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 stream-wise direction and the extensional strain rate eigen direction in the boundary layer region while the distribution is highly isotropic in the bulk. 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.

References in corpus (7)

• High Reynolds number Taylor-Couette turbulence
• Rotation Rate of Rods in Turbulent Fluid Flow
• Shape-dependence of particle rotation in isotropic turbulence
• Measurements of the coupling between the tumbling of rods and the velocity gradient tensor in turbulence
• Numerical simulations of aggregate breakup in bounded and unbounded turbulent flows
• Deformation statistics of sub-Kolmogorov-scale ellipsoidal neutrally buoyant drops in isotropic turbulence
• Drag reduction in numerical two-phase Taylor-Couette turbulence using an Euler-Lagrange approach

Cited by in corpus (6)

• A parallel interaction potential approach coupled with the immersed boundary method for fully resolved simulations of deformable interfaces and membranes
• Suspensions of finite-size neutrally-buoyant spheres in turbulent duct flow
• Deformable ellipsoidal bubbles in Taylor-Couette flow with enhanced Euler-Lagrange tracking
• Lattice Boltzmann simulations of droplet dynamics in time-dependent flows
• Sub-Kolmogorov droplet dynamics in isotropic turbulence using a multiscale lattice Boltzmann scheme
• Droplets in isotropic turbulence: deformation and breakup statistics