Simulating the ultrafiltration of whey proteins isolate using a mixture model

Abstract Ultrafiltration (UF) is widely used in the fractionation and concentration of milk proteins. During this process, proteins concentrate at the membrane surface, increasing the resistance of the membrane system, and decreasing permeate flux leaving the process unit. In this study we use Computational Fluid Dynamics (CFD) to examine the UF of whey proteins. Specifically we employ a multiphase mixture model to predict the solid concentration and velocity distributions near the membrane, under both dead-end and crossflow modes. As whey proteins have a fairly compact globular structure we use hard sphere theory to model the suspension permeability and osmotic pressure: Notably these properties depend only on parameters that can be independently measured, such as protein size and concentration. Model predictions are found to be in good agreement with experimental flux data for both flow modes, significantly in the absence of any additional resistance models representing (for example) pore blockage, surface adsorption or gel/cake formation. We find that during dead-end filtration, the extent of flux decline is logically dependent on the concentration film thickness and maximum solids concentration attained at the membrane surface. Under crossflow conditions suspension advection from the bulk towards the membrane increases the permeate flux, particularly along any upstream membrane area edges. Simulating the system using simplified 2D geometries produces qualitative, rather than quantitative agreement with experiment, highlighting the need to capture the system geometry accurately when modelling concentration polarisation (CP) effects. This work shows that industrially relevant whey protein filtration can be predicted via the multiphase modelling of hard sphere suspensions, using as-measured particle sizes, and points to more accurate methods for optimising and designing whey UF systems.