Ultrafiltration flux theory based on viscosity and osmotic effects: application to diafiltration optimisation

The optimisation of diafiltration is examined using the new theory of ultrafiltration based on osmotic pressure and the viscosity dependence of the mass transfer coefficient. It is shown that, if the permeate flux is maintained at the limiting value at each bulk macrosolute concentration, the diafiltration time always decreases with increasing concentration. However, the transmembrane pressure required to reach the limiting flux increases rapidly with concentration, thus putting a practical limit on the concentrations at which an ultrafiltration system can be operated under limiting flux conditions. In contrast, when the osmotic pressure is a polynomial function of the wall concentration and operation at a fixed transmembrane pressure is considered, a finite optimum concentration is found which minimises the diafiltration time. A methodology for computing this optimum concentration is developed. It is shown that the optimum concentration increases with increasing transmembrane pressure but is only weakly dependent on feed velocity and membrane resistance.