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This paper aims to demonstrate the capabilities of a diffuse interface free energy lattice Boltzmann method to perform direct numerical simulations of liquid–liquid dispersions in a well-controlled turbulent environment. The goal of this research study is to develop numerical techniques that can visualize and quantify drop interaction with the turbulent vortices. The obtained information will be used for the development of sub-models of drop breakup for multi-scale simulations.

A pure binary liquid system is considered that is subject to fully developed statistically stationary turbulent flow field in a cubic fully periodic box with the edge size of 300 lattice units. Three turbulent flow fields with varying energy input are examined and their coherent structures are visualized using a normalized Q-criterion. The evolution of the liquid–liquid interface is tracked as a function of time. The detailed explanation of the numerical method is provided with a highlight on a choice of the numerical parameters.

Drop breakup mechanisms differ depending on energy input. Drops break due to interaction with the vortices. Quantification of turbulent structures shows that the size of vortices increases with the decrease of energy input. Drop interacts simultaneously with multiple vortices of the size comparable to or smaller than the drop size. Vortices of the size smaller than the drop size disturb drop interface and pinch off the satellites. Vortices of the size comparable to the drop size tend to elongate the drop and tear it apart producing daughter drops and satellites. Addition of the second phase enhances turbulent dissipation at the high wavenumbers. To obtain physically realistic two-phase energy spectra, the multiple-relaxation-time collision operator should be used.

Detailed information of drop breakup in the turbulent flow field is crucial for the development of drop breakup sub-models that are necessary for multi-scale numerical simulations. The improvement of numerical methods that can provide these data and produce reliable results is important. This work made one step towards a better understanding of how drops interact with the turbulent vortices.