Theory of concentration polarization in crossflow filtration

Abstract

A novel theory is developed for concentration polarization of non-interacting particles in crossflow-filtration systems. This theory reveals that the extent of concentration polarization, a s well a s the behaviour of the permeate flux, a r e characterized by an important dimensionless filtration number (N, = 4m:Ai3/3k~). There is a critical value of the filtration number for a given suspension and operational conditions. When the filtration number is smaller than the critical value, a polarization layer exists directly over the membrane surface and the wall particle concentration is determined by the pressure and temperature. At higher filtration numbers, a cake layer of retained particles forms between the polarization layer and the membrane surface. Mathematical models a r e constructed for both c a s e s and analytical solutions for the permeate flux a r e derived. An increase in permeate flux with increasing pressure is predicted for all operational conditions.

A large‐volume microfiltration system for isolating suspended particulate organic matter: fabrication and assessment versus GFF filters in central North Pacific

“…Two independent processes are important: 1) the concentration polarization phenomena (CPP), and 2) irreversible clogging under high particle load conditions (>10% vol particle :vol reten ; Ghaffour 2004). The CPP is a thin particle layer on the membrane surface (Hong et al 1997;Song and Elimelech 1995). CPP formation is reversible, and layers can be removed during cleaning.…”

A unifying model for concentration polarization, gel-layer formation and particle deposition in cross-flow membrane filtration of colloidal suspensions

“…We adopt the assumption already made by Davis & Sherwood (1990) and Song & Elimelech (1995) that there is no variation in bulk concentration in the axial direction of the membrane tube. This assumption is justified by the fact that, in the calculations performed in this paper, the permeate flow rate is always less than one percent of the bulk flow rate Q and the very low diffusivities of colloidal particles imply that concentration variations only appear within the very thin polarisation layer.…”

Fouling of nanofiltration membranes

“…Concentration polarization, that is, the accumulation of suspended macromolecules above the membrane surface or cake layer, can also result in flux decline [47]. The effect of concentration polarization, however, is negligible for such dilute solutions of macromolecules as those used in this investigation.…”

“…In typical crossflow membrane modules, the flow field is composed of a convective flow perpendicular to the membrane (permeate flow) and a shear flow parallel to the membrane surface (crossflow) [47]. NOM is transported to the membrane surface by the permeate flow and swept away from the membrane surface by the crossflow.…”