Modeling of transient permeate flux in cross-flow membrane filtration incorporating multiple particle transport mechanisms
Dominant mechanisms of particle transport in cross-flow membrane filtration are unified to obtain a generalized model for time-dependent permeate flux. The unified model extends an earlier model based on shear-induced diffusion and a concentrated flowing layer to include Brownian diffusion and inertial lift. It is applicable over a broad range of contaminant sizes encompassing macromolecules, colloidal and fine particles, and large particles. The combined theory predicts an unfavorable particle size, of the order of 10-1 μm, where the net back-transport away from the membrane attains a minimum, leading to maximum cake growth. For the system simulated in this work, this implies minimum permeate fluxes in the size range of 0.01-0.1 μm, depending on the operating time. Inside-out hollow-fiber geometry is predicted to be favorable for feed suspensions with small particles and/or low concentrations which form thin resistive cakes. However, larger particles, which form thick cakes, may result in reduced surface area available for filtration due to curvature effects in inside-out membranes, making the slit or outside-in geometry more favorable for these particles. Fine particles (< 0.1 μm) are predicted to demonstrate mass-transport limited behavior. For larger particles, different combinations of fiber radius and cross-flow velocity, resulting in the same shear rate, demonstrate different permeate fluxes.
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