Modeling the performance of a standard single stirred ultrafiltration cell using variable velocity back transport flux

A semi-analytical model based on unsteady state mass transfer has been developed for the prediction of permeate flux, membrane surface concentration and permeate side concentration during ultrafiltration in a standard single stirred cell. Starting from the basic fluid mechanical analysis of the system, stirrer induced back transport flux was evaluated considering the actual non-uniform velocity field and the final expression was incorporated in the fundamental mass balance equation. As a result the obtained partial differential equation (PDE) became associated with variable coefficients. The PDE after taking Laplace transform was reduced to standard confluent hypergeometric equation via a series of appropriate substitutions, which was finally mapped again in the time domain considering only the first four terms of the resulting series solution. Once the analytical form of a concentration field was obtained, permeate flux and the membrane surface concentration were evaluated using polymer solution theory and irreversible thermodynamics. Finally an iterative scheme has been designed to simulate the permeate flux and the membrane surface concentration under specified set of operating parameters. The prediction from this model was found to be in good agreement with experimental data obtained from PEG-6000/water system using cellulose acetate membrane of 5000 Da molecular weight cut-off.