Analytical micro model for size exclusion: pore blocking and permeability reduction

Abstract

A pore scale model, incorporating particle and pore size distributions, and the corresponding averaged equations are discussed and applied to predict pore blocking and permeability reduction during dead-end and cross-flow microfiltration in membranes. The model assumes that size exclusion is the dominant particle retention mechanism and accounts for pore accessibility and flow reduction factors due to particle transport only via larger pores. The exact analytical solutions obtained for injection of single-sized and polydispersed particles into porous media with N different pore radii are in accordance with the experimental data on dead-end and crossflow microfiltration. Therefore, since size exclusion was the dominant particle-capture mechanism in the aforementioned experiments, good agreement between modeling and experimental data validates the proposed model for size exclusion. Furthermore, integration of the pore scale equations leads to averaged equations that significantly differ from the classical deep bed filtration model. The resulting averaged model contains constitutive relations for flux reduction and accessibility factors, which are obtained from the analytical micro scale model.