Mass transfer coefficients in cross-flow ultrafiltration

Abstract

Usually, in concentration polarization models, the mass transfer coefficient is an unknown parameter. Also, its variation with changing experimental circumstances is in question. In the literature, many relationships can be found to describe the mass transfer coefficient under various conditions, as well as various corrections for deviating behaviour during ultrafiltration. To obtain reliable mass transfer coefficient relations directly from experimental data, two methods were tested: a method using the osmotic pressure difference during an ultrafiltration experiment, and a method based on the variation in observed retention when cross-flow velocities are changed. The osmotic pressure method appeared to be too insensitive for changing experimental circumstances (according to theoretical considerations). The velocity variation method appeared to be much more useful, although the error in the mass transfer coefficients obtained can be rather large owing to experimental and fitting uncertainties. Therefore the traditional mass transfer relations used in ultrafiltration may be as reliable as (and much more easy to use then) the velocity variation method. The velocity variation method can probably still be used in practice, however, when one or more of the parameters needed in the conventional mass transfer coefficient relations is unknown.