Modeling concentration polarization and fouling layers in cross-flow ultrafiltration

We present a boundary layer approximation (BLA) method for calculating the concentration-polarization (CP) layer and dispersion flow in crossflow ultrafiltration with a cylindrical membrane [1]. Results are discussed for various feed dispersions of colloidal particles, namely hard spheres, charge-stabilized particles [2], solvent-permeable non-ionic microgels [3, 4], and deswelling ionic microgels [5]. State-of-the-art methods are used for the gradient diffusion coefficient and viscosity entering the calculation of filtration profiles [3, 5]. We show that the BLA profiles are in quantitative agreement with predictions by a finite-element method [1]. The BLA results are compared with predictions by a similarity solution [4]. The BLA method is extended to conditions where a filter cake is formed at the membrane, with permeate flux results presented for a hard-sphere system [6].