During protein ultrafiltration (UF), high protein concentration results at the surface of the membrane. The concentrated protein contributes largely to the osmotic pressure of the system, which has direct effects to the ultrafiltration performances such as permeate flux. This osmotic pressure contribution might also be the direct cause of the limiting flux phenomenon, which is an important phenomenon that imposes the performance limitation of ultrafiltration.

The free-solvent model for osmotic pressure recognizes that the protein-solvent interactions, protein hydration and protein-ion binding, to be specific, can have a tremendous impact on the osmotic pressure in concentrated protein solutions. This model well predicts the osmotic pressure of protein with high concentration (on the order of 100g/L), so it is an ideal model for protein ultrafiltration process.

Ultrafiltration parameters, such as permeate flux and protein permeate concentration, are predicted using free-solvent model for both single protein and binary protein ultrafiltrations. The results show reasonably good agreements to the experimental data. More importantly, the limiting flux phenomenon is predicted and characterized using the free-solvent model. It is well demonstrated that the limiting flux phenomenon is the natural consequence of the osmotic pressure contribution from concentrated protein at the membrane surface.