The effect of shear-induced migration on crossflow filtration of colloids

Membrane crossflow filtration is widely used for the enrichment and purification of colloidal and protein dispersions. In this pressure-driven process, a feed dispersion is steadily pumped through a channel consisting of solvent-permeable membrane walls. The applied transmembrane pressure (TMP) causes advection of the dispersion toward the membrane, and formation of a particle-enriched diffuse layer near its surface. This so-called concentration polarization (CP) layer increases the osmotic particle pressure counteracting the TMP. When the particle concentration reaches a solidification limit, an immobilized particulate layer, termed cake layer, is formed next to the membrane surface. The cake layer adds to the hydraulic membrane resistance and lowers thus the filtration efficiency. A key problem is to understand quantitatively how cake formation is related to filtration operating conditions, and to dispersion and membrane properties. In this study, we theoretically analyze how permeate flux and cake layer formation are influenced by the size, charge and feed concentration of dispersed particles [1]. We consider dispersions of neutral and charge-stabilized colloidal particles. Under conditions where shear-induced migration matters, empirical expressions for shear-rate dependent transport properties are used. Our results for concentration and flow profiles under filtration are obtained using a recently developed modified boundary layer approximation (mBLA) method [2, 3]. The mBLA is a numerically efficient and accurate method for predicting filtration properties. A thorough dicussion of the so-called critical permeate flux related to the onset of cake layer formation is presented. Moreover, an analytic expression for the critical flux is derived and compared with standard predictions by film theory and mass transfer coefficient calculations. References[1] G. W. Park, J. K. G. Dhont, and G. Nägele, manuscript in preparation.[2] G. W. Park and G. Nägele, Journal of Chemical Physics, 2020, 153, 204110[3] G. W. Park and G. Nägele, Membranes, 2021, 11, 960