A dynamic film model for ultrafiltration

Abstract

A dynamic film model for ultrafiltration that describes the variation in solvent flux with solute diffusivity, solution viscosity and tangential velocity has been developed. This model uses Pohlhausen's approximate solution [1] to the equations of continuity and the momentum balance equation over a boundary layer. Unlike the stagnant film model, which assumes that the mass transfer coefficient is independent of solute concentration and filtration rate, the dynamic film approach provides a means of explicitly predicting how the mass transfer coefficient of a device is affected by changes in the feed stock and operating parameters. The predictions of the dynamic film model were systematically compared to experimental data for the filtration of a monoclonal antibody. The effects of solute concentration were evaluated by measuring the variation in flux with transmembrane pressure for MAb solutions with bulk concentrations ranging from 4 to 14 g l −1. The filtration studies were then repeated at several feed flow rates to investigate the effect of tangential velocity. In all of these cases, the predicted and experimental mass transfer coefficients differed by less than 11% on an average. In contrast, the fitted values obtained with the stagnant film model differed by as much as 79% from the experimental mass transfer coefficients. Thus the dynamic film model provides a significantly enhanced description of ultrafiltration processes.