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.

When a membrane filtration process such as ultrafiltration is used a flux-and yield-decline can be observed. The causes are i) concentration polarization (i.e. accumulation of retained solutes, reversibly and immediately occurring) and ii) fouling phenomena such as adsorption, pore-blocking and deposition of solidified solutes, a long-term, and more or less irreversible process. The result of both these phenomena are a decreasing driving force for the filtration or an increasing resistance against transport of the permeating solvent during the filtration. The degree of flux decline depends on many variables, both solution and equipment related.Several models have been developed to describe the polarization phenomena, in general they can be subdivided in (A) resistance models, (B) gel-polarization models and (C) osmotic pressure models. A new boundary layer resistance model for unstirred dead-end ultrafiltration is described more in detail. This model can predict fluxes and related phenomena; the simulations agree very well with the experimental data.The flux decline behaviour of binary mixtures of equally and unequally charged proteins (a-lactalbumin, BSA and lysozyme) was studied. In case the mixture consists of oppositely charged proteins a considerable increase of the resistance of the concentrated layer near the membrane interface can be observed, which depends on the mixing ratio of the proteins. When equally charged proteins are filtered the resistance decreases a little, again depending on the mixing ratio.Several methods exist to improve the flux, they can be generally divided into: (1) adapting the operation conditions in the existing equipment, (2) altering the conditions in the solution, (3) using a different or pretreated membrane, (4) taking additional measures to prevent or decrease the flux decline.OOll-9164/90/$03.50 0 1990 Elsevier Science Publishers B.V.

Nowadays membrane filtration processes are used mdustrlally as an alternative to conventional separation methods Membrane separation methods can be divided into classes according to their separation characterlstlcs (1) separation by sieving action, (11) separation due to a difference m affinity and dlffuslvlty, (111) separation due to a difference m charge of molecules, (m) carrier-fachtated transport, and (v) the process of (time-) controlled release by diffusionIn all these cases dlffuslon processes play an important role m the transport mechanism of the solutes Various mechanisms have been distinguished to describe the transport m membranes transport through bulk material (dense membranes), Knudsen diffusion m narrow pores, viscous flow m wide pores or surface diffusion along pore walls In practice, the transport can be a result of more than only one of these mechanisms For all of these mechamsms models have been derived The characterlstlcs of a membrane, e g its crystalhmty or its charge, can also have major consequences for the rate of diffusion m the membrane, and hence for the flux obtained Apart from the diffusion transport processes zn membranes mentloned above, other important diffusion processes are related to membrane processes, viz diffusion zn the boundary layer near the membrane (concentration polanzatlon phenomena) and diffusion durzng membrane formatzon The degree of concentration polarlzatlon IS related to the magnitude of the mass transfer coefficient which, m turn, 1s influenced by the diffusion coefficientThe effect of concentration polarlzatlon can be rather different for the various membrane processes The phase mverslon membrane formation mechanism 1s determined to a large extent by the kinetic aspects during membrane formation, which are diffusion of solvent and of non-solvent and the kinetics of the phase separation itself

SummaryThe possibility to analyse concentration polarization phenomena during unstirred dead-end ultrafiltration by the boundary layer resistance theory has been shown by Nakao et al. [ 1). Experimental data on the ultrafiltration of BSA at pH 7.4, at various concentrations and pressures, were analysed by this model and by a new version of the model in this paper. Instead of the assumption of the cake filtration theory, the new version of the model uses the unsteady state equation for solute mass transport to predict flux data by computer simulations. This approach requires no assumptions concerning the concentration at the membrane, the concentration profile or the specific resistance of the boundary layer. The computer simulations agree very well with the experimental data. Many agreements with Nakao's analyses are confirmed and some new data on the concentration polarization phenomena are obtained.

SummaryThe flux decline behaviour of some charged proteins and of binary mixtures of charged solutes during unstirred dead-end ultrafiltration has been studied. The mixtures consisted of the proteins bovine serum albumin, (BSA), cy-lactalbumin and/or lysozyme. Of special interest were a-lactalbumin and lysozyme because these proteins are physico-chemically identical, except for the sign of their charge at the conditions used (pH=7.4,1=0.125 N and T=20"C).The ultrafiltration properties were studied using the boundary layer resistance model. Ultrafiltration of single protein solutions of a-lactalbumin and of lysozyme showed identical characteristics. The fouling behaviour during ultrafiltration of binary mixtures of the three components appeared to be dependent on both the charge of the solutes and the (unequal) dimensions of the solutes. A mixture of oppositely charged proteins (i.e., BSA/lysozyme or a-lactalbumin/lysozyme) sometimes showed a considerable increase of the resistance of the concentrated layer near the membrane, depending on the mixing ratio of the two proteins. When equally charged (i.e., BSA/a-lactalbumin) proteins are ultrafiltered, a small decrease of the resistance could be observed, again depending on the mixing ratio of the proteins. The charge of the proteins, especially opposite charges, appeared to influence the flux behaviour more than the slightly denser packing of the solutes (as a result of unequal dimensions) would account for.