A Maxwell-Stefan approach to modelling the cross-flow ultrafiltration of protein solutions in tubular membranes

A non-parameterised model is developed to predict the crossflow membrane ultrafiltration permeate flux for protein solutions. A relatively simple hydrodynamic model is used to predict the rate of growth of the concentration polarissation boundary layer along the length of a tubular membrane. Protein transport within the boundary layer is evaluated using the Maxwell-Stefan transport equations, accounting for electrostatic interactions created by filtering charged protein molecules. Numeric simulations were performed with and without considering viscous interactions in the concentration polarisation boundary layer. In the main, the model appears to qualitatively describe the ultrafiltration process very well when tested for a range of different operating parameters and solution conditions. However, at high TMPs viscous interactions were exaggerated and the model underpredicted permeate flux. Under such conditions, use of the model without accounting for viscous interactions seemed more appropriate. The model predictions are tested against sample experimental data for the protein BSA and the results were highly encouraging.