Cross‐flow ultrafiltration of micellar surfactant solutions

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Abstract
A Steady‐state fouling‐resistance and osmotic‐pressure model is used to predict flux in the laminar, Cross‐flow ultrafiltration of micellar cetyl ( =hexadecyl)pyridinium chloride (CPC) solutions at 0.01‐M NaCl background electrolyte. The model assumes a constant overall hydraulic resistance including the effect of surfactant fouling and native membrane resistance. Measurements of osmotic pressures of CPC solutions at 0.01‐M NaCl as a function of surfactant concentration describe the effect of concentration polarization on permeate flux. Two types of asymmetric polythersulfone membranes are used : 5,000 molecular weight cutoff (MWCO) membranes that allow partial monomer permeation, but quantitatively reject all micelles; 50,000 MWCO membranes that allow some micelle permeation. For the former, the intrinsic refection coefifient for monomer, measured separately, is sufficient to describe surfactant rejection, without adjustable parameters. Predictions of the volumetric flux of the permeate, including the value of the limiting flux, agree well with the experimental results over the entire range of pressure drop, axial velocity, and bulk surfactant concentration. For the 50,000 MWCO membrances, the data are described using a best‐fit value of the overall surfactant rejection coefficient. For the first time, unusual behavior is observed experimentally in which the flux levels off with increasing pressure drop. Both effects are in accord with the proposed model. No gel layer need be postrulated to explain the flux behavior of either membrane type.