A theoretical study of transient cross-flow filtration using force balance analysis

Abstract

A model of transient cross-flow filtration in a permeable cylindrical tube based on a force balance analysis is presented. Particle layer (or cake) formation on the tube is simulated. A slip boundary condition for cross-flow is applied at the interface between the flow and the porous surface of the tube, which represents the hydrodynamic effect of the porosity of the tube wall and cake on the cross-flow. For a given particle size distribution in the fluid, the mean radius of particles at different depths in the cake and at different positions along the tube is calculated. It is found that when a slip boundary condition is applied, the critical radius of particles is reduced, resulting in a slower growth of cake on the surface of the tube. In the model, the thickness of the cake can either increase or decrease along the axial direction of the tube depending on the conditions, pressures, permeability of the tube etc. This differs from results of concentration polarization models, which predict a continuously increasing particle layer.