MODELING OF TRANSIENT PERMEATE FLUX IN CROSS-FLOW MEMBRANE FILTRATIONINCORPORATING MULTIPLE PARTICLE-TRANSPORT MECHANISMS

Dominant mechanisms of particle transport in cross-flow membrane filtr ation are unified to obtain a generalized model for time-dependent per meate 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 c ontaminant sizes encompassing macromolecules, colloidal and fine parti cles, and large particles. The combined theory predicts an unfavorable particle size, of the order of 10(-1) mu m, where the net back-transp ort away from the membrane attains a minimum, leading to maximum cake growth. For the system simulated in this work, this implies minimum pe rmeate fluxes in the size range of 0.01-0.1 mu m, depending on the ope rating time. Inside-out hollow-fiber geometry is predicted to be favor able for feed suspensions with small particles and/or low concentratio ns which form thin resistive cakes. However, larger particles, which f orm thick cakes, may result in reduced surface area available for filt ration due to curvature effects in inside-out membranes, making the sl it or outside-in geometry more favorable for these particles. Fine par ticles (< 0.1 mu m) are predicted to demonstrate mass-transport limite d behavior. For larger particles, different combinations of fiber radi us and cross-flow velocity, resulting in the same shear rate, demonstr ate different permeate fluxes.