MEMBRANE SCIENCE ELSEVIER Journal of Membrane Science 125 (1997) 303-310 A mass transfer model for the prediction of rejection and flux during ultrafiltration of PEG-6000 Chiranjib Bhattacharjee, Siddhartha Datta * Department of Chemical Engineering, Jadavpur University, Calcutta 700032, India Received 30 April 1996; revised 5 August 1996; accepted 12 August 1996 Abstract A mass transfer model in case of ultrafiltration is proposed in the present study which is capable of predicting the permeate volumetric flux and rejection at different pressure, concentration and stirrer speed. The model is based on the steady state mass balance over the boundary layer, coupled with the results from irreversible thermodynamics. It first predicts the membrane surface and permeate concentrations -- which are then utilized to calculate rejection. Permeate flux is then predicted using the result obtained from filtration theory. The model utilizes four parameters, namely, solvent permeability, solute permeability, reflection coefficient and specific cake resistance. These parameters along with the known values of the operating conditions and solution properties enable one to predict the flux as a function of time and rejection. The computed results are found to be in good agreement with the previously published data of Bhattacharjee and Bhattacharya during ultrafiltration of PEG-6000 by cellulose acetate membrane. Keywords: Ultrafiltration; Flux; Rejection; Irreversible thermodynamics; Mathematical model 1. Introduction Ultrafiltration (UF) is a pressure driven membrane process generally used for the separation of macroso- lutes from a solvent. Usually its operational pressure varies in the range of 10 to 140 psi. The process has been an area of active research because of its poten- tial application in the field of separation science. The application of ultrafiltration includes the treatment of industrial effluents, oil emulsion waste water, biolog- * Corresponding author. ical macromolecules, colloidal paint suspensions, medical therapeutics, etc. In UF, the solutes generally accumulate on the membrane surface because of its rejection by the membrane. This process continues and ultimately the concentration of solutes on the membrane surface becomes higher than in the bulk solution. This phe- nomenon is called the 'concentration polarization'. This effect at the surface of the membrane is unde- sirable because it causes an inevitable reduction in solvent flux. Extensive study of the transport phe- nomena is therefore necessary for the better under- standing of the separation mechanism during ultrafil- tration process. In fact different theories have been reported in the literature by a number of workers to 0376-7388/97/$17.00 Copyright © 1997 Elsevier Science B.V. All rights reserved. PII S0376-7388(96)00247-5