Modeling of Fouling of Crossflow Microfiltration Membranes

Steady-state and transient models are reviewed for predicting flux decline for crossflow microfiltration under conditions in which both external cake buildup and internal membrane fouling are contributing factors. Experimental work is not covered in the scope of this review, although reference is made to a few recent studies which have compared experimental measurements with theory. The steady-state cake thickness and permeate flux are governed by the concentration polarization layer adjacent to the cake of rejected particles which forms on the membrane surface. Depending on the characteristic particle size and the tangential shear rate, Brownian diffusion, shear-induced diffusion, or inertial lift is considered to be the dominant mechanism for particle back-transport in the polarization layer. For typical shear rates, Brownian diffusion is important for submicron particles, inertial lift is important for particles larger than approximately ten microns, and shear-induced diffusion is dominant for intermediate-sized particles. For short times, it is shown that the transient flux decline due to cake buildup is closely approximated by deadend batch filtration theory, independent of the tangential shear rate. For long times, however, the steady or quasi-steady flux increases with shear rate, because the tangential flow sweeps particles toward the filter exit and reduces cake buildup.