Simulation of continuous stirred ultrafiltration process: an approach based on analytical solution coupled with turbulent back transport

Abstract

A mass transfer model based on unsteady state mass balance over the concentration boundary layer, coupled with back transport resulting from the stirring action, opposing ultrafiltrate flux, has been developed in the present study. This model uses semi-infinite consideration to solve the governing partial differential equation by the Laplace transformation method, which gives the analytical solution of the concentration profile. During the solution procedure, pseudo-steady state assumption has been used, as a consequence of which volumetric flux and turbulent back transport flux have been taken as constants. Once the analytical expression for the concentration profile has been found, an iterative technique has been developed for simulating flux and rejection under any specified operating condition. The prediction from this model is found to be in good agreement with experimental results obtained during continuous stirred ultrafiltration of PEG-6000 solution using a cellulose acetate membrane of 5000 Da molecular weight cut-off. The average absolute deviation in the prediction of permeate flux has been found to be 5.6% and that for the prediction of rejection was 6.4%. Copyright © 2003 Society of Chemical Industry