Application of a convection–diffusion–electrophoretic migration model to ultrafiltration of lysozyme at different pH values and ionic strengths

In order to account for the role of electrostatic interactions during ultrafiltration of a charged protein, electrokinetic characterisation of the protein-membrane-electrolyte system was performed. The zeta-potential (ψz) of the protein-fouled (membrane) material and the electrophoretic mobility (μi) of the free protein depend on the pH, the ionic strength and the electrolyte chemical nature (indifferent or specifically adsorbed) used in the UF experiments. The free protein and the protein-fouled membrane were always carrying a charge close to each other. The electric field generated by the fouled membrane was found to be significant up to few nanometers from the membrane surface, depending on the ionic strength. Repulsive electrostatic interactions between the fouled membrane and the free protein in this sub-layer, were accounted for by a convection–diffusion–electrophoretic migration approach in the polarisation layer (CDE model). A peculiarity of the CDE model is to predict a depleted sub-layer in the close vicinity of highly charged membranes. Consequently, a new electrostatic partition coefficient φe, accounting for the repulsive effect outside the charged membrane, can be introduced. A new dimensionless number μiψz/Jd (analogous to a Peclet number) is defined. The electrophoretic mobility appears as a significant UF parameter, when this ratio is higher than 0.1.