Modeling and simulation of unstirred dead end ultrafiltration of macromolecules

Abstract

A mass transfer model based on unsteady state component balance over the concentration boundary layer has been developed in the present study. The model uses semi-infinite consideration in order to solve the governing partial differential equation by Laplace transform that gives an analytical expression for the concentration profile. During the solution procedure, pseudo steady state assumption has been used, as a consequence of which permeate flux and membrane surface concentration have been taken constant over any small time interval. Once the expression for concentration profile is known, a time evolution loop has been developed to simulate the permeate flux, membrane surface concentration and permeate concentration under specified operating conditions of transmembrane pressure drop and bulk concentration. The prediction of the proposed model was found to be in good agreement with experimental results obtained during unstirred dead end ultrafiltration of polyethylene glycol (of average molecular weight 6000) solution using a cellulose acetate membrane of 5000 Da molecular weight cut-off.