Population balances combined with Computational Fluid Dynamics: A modeling approach for dispersive mixing in a high pressure homogenizer

• The pressure drop and the number of passes were examined in a homogenizer.
• Population balances combined with CFD were used to model the droplet sizes.
• Four compartments were defined around the high speed jet.
• One set of parameters was found covering all hydrodynamic conditions.
• The model predictions have improved by 65% compared to a single compartment model.

High pressure homogenization is at the heart of many emulsification processes in the food, personal care and pharmaceutical industry. The droplet size distribution is an important property for product quality and is aimed to be controlled in the process. Therefore a population balance model was built in order to predict the droplet size distribution subject to various hydrodynamic conditions found in a high pressure homogenizer. The hydrodynamics were simulated using Computational Fluid Dynamics and the turbulence was modeled with a RANS k–ε model. The high energy zone in the high pressure homogenizer was divided into four compartments. The compartments had to be small enough to secure nearly homogeneous turbulent dissipation rates but large enough to hold a population of droplets. A population balance equation describing breakage and coalescence of oil droplets in turbulent flow was solved for every compartment. One set of parameters was found which could describe the development of the droplet size distribution in the high pressure homogenizer with varying pressure drop. An improvement of 65% was found compared to the same model containing just one compartment. The compartment approach may provide an alternative to direct coupling of CFD and population balances.