(371d) Determination of Drop Size Distribution in Turbulently Agitated Liquid-Liquid Dispersion Using Numerical Simulations

Liquid-liquid dispersion and emulsion properties, such as apparent viscosity, rheology, stability, interfacial area available for heat and mass transfer, are determined by the size of droplets in the system. Accurate prediction and control of the drop size distribution (DSD) can be vital for practical applications.

In the present study, direct numerical simulations were utilized to determine the DSD of a turbulently agitated liquid-liquid dispersion. Large parallel computations were performed in a three-dimensional, fully-periodic domain using a free energy lattice Boltzmann equation model. The utilized numerical method is a diffuse interface method. No interface treatments or reconstructions are required. The interface evolves naturally due to thermodynamic mechanism employed. This issue allows to simulate systems with hundreds of drops during a reasonable time and affordable computational efforts. However, diffuse interface methods suffer from dissolution of small droplets. Our previous studies outlined that in order to mitigate the drop dissolution effect it is necessary to have the final size of the drops in the dispersed systems of 20-30 lattice units [lu]. Then the rate of dissolution significantly slows down, which is demonstrated in the present simulations.

Two liquids of equal viscosity μ=10^-3; Pa·s and density ρ=1000 kg/m³ were considered. The dispersed phase volume fraction varied from 0.005 to 0.1. The simulations were carried out as follows: first, one-phase homogeneous isotropic turbulence was generated throughout the domain by means of linear forcing. Then the second phase was instantaneously injected. The energy input into the system varied to obtain Kolmogorov length scales of η_k=1, 5 and 10 lattice units [lu] in a fixed simulation domain of 500³ size. The entire process of dispersion formation was visualized revealing the drop/eddy interactions on different scales. When equilibrium between drop breakup and coalescence was achieved the DSD was determined. As an example, the dispersed phase field at a Kolmogorov length scale of one lattice unit and the dispersed phase volume fraction of 0.07 is shown in Fig.1.

Fig.1. The dispersed phase field and the velocity magnitude in a cross-section at η_k=1 [lu] and the dispersed phase volume fraction of 0.07.