[Paper Review] Droplet breakup in homogeneous and isotropic turbulence

Federico Toschi, Prasad Perlekar+2 more|arXiv (Cornell University)|Oct 8, 2010

Particle Dynamics in Fluid Flows3 citations

TL;DR

This study investigates droplet breakup in homogeneous and isotropic turbulence using a multicomponent lattice-Boltzmann method to simulate droplets with the same density as the surrounding fluid. The key finding is that the simulated critical droplet diameter ($d_c^{LBM} = 25 \pm 2$) closely matches the theoretical Kolmogorov-Hinze estimate ($d_c \approx 24.16$), validating the model for studying turbulent breakup dynamics under varying viscosity contrasts and Reynolds numbers.

ABSTRACT

This fluid dynamics video shows the breakup of a droplet in a stationary homogeneous and isotropic turbulent flow. We consider droplets with the same density of the transporting fluid. The droplets and the fluid are numerically modelled by means of a multicompo- nent Lattice-Boltzmann method. The turbulent fluid is maintained through a large scale stirring force and the radius of stable droplets, for the parameters in our simulation, is larger than the Kolmogorov scale. Events of droplet deformation, break-up and aggregation are clearly visible from the movie. With the present database droplet evo- lution can be studied from both an Eulerian and Lagrangian point of view. The Kolmogorov-Hinze criteria for droplets break-up can be tested also by means of simulations with different viscosity contrast between the two components.

Motivation & Objective

• To investigate the dynamics of droplet deformation, breakup, and coalescence in homogeneous and isotropic turbulence.
• To test the Kolmogorov-Hinze criterion for droplet breakup under varying viscosity ratios and Reynolds numbers.
• To quantify the statistical properties of droplet size distribution and stress-induced deformation in turbulent flows.
• To provide a high-resolution numerical database for both Eulerian and Lagrangian analysis of droplet evolution.
• To validate theoretical estimates of critical droplet diameter using direct numerical simulation.

Proposed method

• Numerical simulation of droplet dynamics using a multicomponent lattice-Boltzmann method (MCLB) with a Shan-Chen model for phase separation.
• Turbulence is sustained via large-scale forcing with periodic boundary conditions to maintain homogeneous and isotropic flow.
• The system starts with a single spherical droplet at rest, which is deformed and broken up as turbulence develops over ~1–2 large eddy turnover times.
• The critical droplet diameter is estimated using the Weber number condition $We(d) \sim 1$, leading to $d_c \propto \left(\sigma / \rho_c\right)^{3/5} \varepsilon^{-2/5}$.
• Simulations are conducted at low Reynolds number ($R_\lambda = 29$) to ensure the interface thickness is smaller than the viscous scale.
• Statistical analysis of droplet size, deformation, and breakup events is performed post-simulation to assess intermittency and fluctuation effects.

Experimental results

Research questions

• RQ1 How does the simulated critical droplet diameter compare to the theoretical Kolmogorov-Hinze estimate under K41 turbulence assumptions?
• RQ2 What is the role of viscosity contrast between the dispersed and continuous phases in droplet breakup dynamics?
• RQ3 How do turbulent velocity fluctuations induce intermittent deformation and fragmentation events in droplets larger than the Kolmogorov scale?
• RQ4 What are the statistical properties of droplet size distribution during the stationary phase of breakup and coalescence?
• RQ5 To what extent do Eulerian and Lagrangian perspectives reveal distinct features of droplet evolution in turbulent flows?

Key findings

• The simulated critical droplet diameter ($d_c^{LBM} = 25 \pm 2$) is in excellent agreement with the theoretical estimate ($d_c \approx 24.16$), confirming the validity of the Kolmogorov-Hinze criterion in this setup.
• Droplet breakup occurs via a cascade of fragmentation events following initial stretching, with the system reaching a statistically stationary state after approximately 1–2 large eddy turnover times.
• The simulation captures continuous cycles of deformation, breakup, and coalescence in the final stationary phase, driven by turbulent fluctuations.
• The model successfully maintains a droplet interface thickness smaller than the viscous dissipation scale due to the low Reynolds number ($R_\lambda = 29$) configuration.
• The database enables both Eulerian and Lagrangian analysis of droplet trajectories and dynamics, supporting multi-scale study of emulsification processes.
• Fluctuations in turbulent stresses induce measurable deviations from the mean stable droplet size, highlighting the role of intermittency in breakup events.