Quantitative predictive modelling of ultrafiltration processes: Colloidal science approaches

Membrane ultrafiltration is a separation process of considerable industrial importance. The specification and optimisation of such processes require the development of good predictive methods. This article reviews the development of a range of such methods based on fundamental descriptions of colloidal interactions and hydrodynamics, especially those close to the membrane surface. Particle–particle interactions may be efficiently calculated using a cell-model description of electrostatic interactions coupled with appropriate quantification of London–van der Waals forces and the entropic pressure. The overall interactions may be described in terms of osmotic pressures, which further facilitate calculation of the corresponding gradient diffusion coefficients. Methods for the calculation of the local solution viscosity are also described. Excellent agreement with experimental data is obtained when these calculated properties are incorporated in mathematical models describing either frontal ultrafiltration of cross-flow ultrafiltration. The predictive calculations may be used in a number of different ways, depending on the level of knowledge of the colloidal properties available. For example, at the most fundamental level the pressure dependence of the rate of cross-flow ultrafiltration of a protein may be calculated from a knowledge of the protein sequence.