Coupling population balance model and residence time distribution for pilot-scale modelling of β-lactoglobulin aggregation process

• Hybrid modelling approach using Population Balance and Residence Time Distribution.
• Comparison with modelling approach assuming plug flow.
• Plug flow approach fails to describe the continuous process of protein aggregation.
• Aggregates size distribution is well predicted when residence time distribution is integrated.
• The model could be valuable for whey protein aggregation process design and optimisation.

This study presents a hybrid modelling approach for the prediction of the thermally-induced aggregation of whey protein solutions in a continuous process. Modelling a continuous process needs to account the fluid flow phenomena because the different fluid parcels are not subjected to the same time/temperature/shear history. The modelling approach developed combines a residence time distribution (RTD) model and a colloidal aggregation model based on Population Balance Equations (PBE). This combined model has been compared, on one side, to a Population Balance Model assuming plug flow, and on the other side, to experimental data. A 6% β-lactoglobulin solution with different CaCl2 concentrations (5.0, 6.0, 6.4, 6.6 and 7.0 mM) was used for experimental investigations. Experimental heat treatments were carried out at 87 °C with a holding time of 49 s using tubular heat exchanger and holder. The integration of residence time distribution appears to be very important when the product is subject to large transformations (formation of large aggregates > 10 μm). Comparison of predictions obtained from both models to the experimental data shows that the coupled PBE/RTD model is able to predict the characteristics of the suspensions (aggregate size and viscosity) and successfully integrates the impact of calcium upon aggregation process, while the model assuming plug flow is suitable only when aggregation is low (for low calcium concentrations).