A Concentration Polarization Model for the Filtrate Flux in Cross-Flow Microfiltration of Particulate Suspensions

Cross-flow filtration with microporous membranes is increasingly used in the separation and concentration of particulate suspensions. Existing models for the filtrate flux are inadequate for correlating experimental observations and are based on contradictory physical mechanisms. We propose that the flux is limited by the formation of a dynamic concentration polarization boundary layer consisting of a high concentration of retained particles. A simple model is developed incorporating a shear-enhanced diffusivity of the large particles which arises from mutually induced velocity fields in the shear flow of the concentrated suspension. Predictions of the model agree well with experimental data for a variety of particulate suspensions. The model provides both a fundamental understanding of the physical phenomena governing flux and a rational basis for design of improved cross-flow filters.