Deformation statistics of sub-Kolmogorov-scale ellipsoidal neutrally buoyant drops in isotropic turbulence

Abstract

Small droplets in turbulent flows can undergo highly variable deformations and orientational dynamics. For neutrally buoyant droplets smaller than the Kolmogorov scale, the dominant effects from the surrounding turbulent flow arise through Lagrangian time histories of the velocity gradient tensor. Here we study the evolution of representative droplets using a model that includes rotation and stretching effects from the surrounding fluid, and restoration effects from surface tension including a constant droplet volume constraint, while assuming that the droplets maintain an ellipsoidal shape. The model is combined with Lagrangian time histories of the velocity gradient tensor extracted from DNS of turbulence to obtain simulated droplet evolutions. These are used to characterize the size, shape and orientation statistics of small droplets in turbulence. A critical capillary number, $C{a}_c$ is identified associated with unbounded growth of one or two of the droplet's semi-axes. Exploiting analogies with dynamics of polymers in turbulence, the $C{a}_c$ number can be predicted based on the large deviation theory for the largest Finite Time Lyapunov exponent. Also, for sub-critical $Ca$ the theory enables predictions of the slope of the power-law tails of droplet size distributions in turbulence. For cases when the viscosities of droplet and outer fluid differ in a way that enables vorticity to decorrelate the shape from the straining directions, the large deviation formalism based on the stretching properties of the velocity gradient tensor loses validity and its predictions fail. Even considering the limitations of the assumed ellipsoidal droplet shape, the results highlight the complex coupling between droplet deformation, orientation and the local fluid velocity gradient tensor to be expected when small viscous drops interact with turbulent flows.

References in corpus (2)

• Rotation Rate of Rods in Turbulent Fluid Flow
• Lyapunov exponents of heavy particles in turbulence

Cited by in corpus (10)

• Bubble puzzles: From fundamentals to applications
• On the effects of membrane viscosity on transient red blood cell dynamics
• Numerical simulations of aggregate breakup in bounded and unbounded turbulent flows
• Micromechanics of liquid-phase exfoliation of a layered 2D material: A hydrodynamic peeling model
• Large deviations in chaotic systems: exact results and dynamical phase transition
• Polymer scission in turbulent flows
• 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
• Remarkable similarities in distributions of dynamical observables in chaotic systems