### 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 direct numerical simulations (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 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 critical capillary number can be predicted based on the large deviation theory
for the largest finite-time Lyapunov exponent quantifying the chaotic separation of
particle trajectories. Also, for subcritical capillary numbers near the critical value,
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. The
results also underscore the usefulness of large deviation theory to model these highly complex couplings and fluctuations in turbulence that result from time integrated effects of fluid deformations.

Original language | English |
---|---|

Pages (from-to) | 184-207 |

Number of pages | 24 |

Journal | Journal of fluid mechanics |

Volume | 754 |

DOIs | |

Publication status | Published - 2014 |

### Keywords

- METIS-308154
- IR-95042

## Fingerprint Dive into the research topics of 'Deformation statistics of sub-Kolmogorov-scale ellipsoidal neutrally buoyant drops in isotropic turbulence'. Together they form a unique fingerprint.

## Cite this

Biferale, L., Meneveau, C., & Verzicco, R. (2014). Deformation statistics of sub-Kolmogorov-scale ellipsoidal neutrally buoyant drops in isotropic turbulence.

*Journal of fluid mechanics*,*754*, 184-207. https://doi.org/10.1017/jfm.2014.366