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A numerical approach is developed to gain fundamental insight in liquid‐liquid dispersion formation under well‐controlled turbulent conditions. The approach is based on a free energy lattice Boltzmann equation method, and relies on detailed resolution of the interaction of the dispersed and continuous phase at the microscopic level, including drop breakup and coalescence. The capability of the numerical technique to perform direct numerical simulations of turbulently agitated liquid‐liquid dispersions is assessed. Three‐dimensional simulations are carried out in fully periodic cubic domains with grids of size . The liquids are of equal density. Viscosity ratios (dispersed phase over continuous phase) are in the range 0.3–1.0. The dispersed phase volume fraction varies from 0.001 to 0.2. The process of dispersion formation is followed and visualized. The size of each drop in the dispersion is measured in‐line with no disturbance of the flow. However, the numerical method is plagued by numerical dissolution of drops that are smaller than 10 times the lattice spacing. It is shown that to mitigate this effect it is necessary to increase the resolution of the Kolmogorov scales, such as to have a minimum drop size in the range 20–30 lattice units [lu]. Four levels of Kolmogorov length scale resolution have been considered , 2.5, 5, and 10 [lu]. In addition, the numerical dissolution reduces if the concentration of the dispersed phase is increased. © 2015 American Institute of Chemical Engineers AIChE J, 61: 2618–2633, 2015

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The motion of an n-butanol drop in water under the influence of gravity was numerically studied using a diffuse interface free energy lattice Boltzmann method. A pure two-liquid system without mass transfer between the phases was considered. A range of drop diameters of 1.0–4.0 mm covered the flow conditions. Most calculations were carried out in a moving reference frame. This allowed studying of long-term drop behavior in a relatively small computational domain. The capability of the method to capture the drop shape especially in the oscillating regime was demonstrated. For each drop diameter the evolution of the drop velocity in time, the terminal rise velocity and drop's shape were determined. The results were compared to experimental and numerical results and to semi-empirical correlations. The deviation of the simulated terminal velocity from other results is within 5% for smaller drops and up to 20% for large oscillating drops. It was shown that beyond the onset of shape oscillations the binary system converges towards a constant capillary number of 0.056.