Simulation of liquid-liquid emulsions under the presence of surfactants with CFD and PBM

In this work, liquid-liquid systems composed by water and silicon-oil are simulated using Computational Fluid Dynamics (CFD) and Population Balance Model (PBM). In a stirred tank, small droplets are formed in the high shear regions, created by the rotating impeller. Their final size affects some of the physical properties of the emulsion, such as stability and viscosity. The simulated stirring equipment is represented by a six liters R&D unit, in which a static anchor and an inclined sawtooth impeller are present. Different silicon oils, corresponding to different viscosities and densities, are simulated using a two-fluid model. The Population Balance Equation is solved to predict the behavior of the droplets by using our own implementation of the Quadrature Method of Moments (QMOM) within the Ansys Fluent code. Coalescence between droplets is neglected due to the presence of small amounts of surfactant, while breakage is dominant, hence modeled using different kernels. Results are validated against experimental data, proving the importance of selecting the appropriate kernels in order to better describe the physics of the system.