Diffusional phenomena in membrane separation processes

Nowadays membrane filtration processes are used industrially as an alternative to conventional separation methods. Membrane separation methods can be divided into classes according to their separation characteristics: (i) separation by sieving action; (ii) separation due to a difference in affinity and diffusivity; (iii) separation due to a difference in charge of molecules; (iv) carrier-facilitated transport, and (v) the process of (time-) controlled released by diffusion. In all these cases diffusion processes play an important role in the transport mechanism of the solutes. Various mechanisms have been distinguished to describe the transport in membranes: transport through bulk material (dense membranes), Knudsen diffusion in narrow pores, viscous flow in 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 mechanisms models have been derived. The characteristics of a membrane, e.g. its crystallinity or its charge, can also have major consequences for the rate of diffusion in the membrane, and hence for the flux obtained. Apart from the diffusion transport processes in membranes mentioned above, other important diffusion processes are related to membrane processes, viz. diffusion in the boundary layer near the membrane (concentration polarization phenomena) and diffusion during membrane formation. The degree of concentration polarization is related to the magnitude of the mass transfer coefficient which, in turn, is influenced by the diffusion coefficient. The effect of concentration polarization can be rather different for the various membrane processes. The phase inversion membrane formation mechanism is 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

Flux decline in ultrafiltration processes

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.\ud \ud 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.\ud \ud The flux decline behaviour of binary mixtures of equally and unequally charged proteins (α-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.\ud \ud 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

The boundary-layer resistance model for unstirred ultrafiltration. A new approach

The 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 obtaine

Concentration polarization phenomena during dead-end ultrafiltration of protein mixtures. The influence of solute-solute interactions

The 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), α-lactalbumin and/or lysozyme. Of special interest were α-lactalbumin and lysozyme because these proteins are physico-chemically identical, except for the sign of their charge at the conditions used (pH = 7.4, I=0.125 N and T=20°C). The ultrafiltration properties were studied using the boundary layer resistance model. Ultrafiltration of single protein solutions of α-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 α-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/α-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

Ultrafiltration of protein solutions; the role of protein association in rejection and osmotic pressure

The monomer-dimer equilibrium of the protein β-lactoglobulin under neutral conditions appears to influence the rejection and the osmotic pressure build-up, both phenomena closely related to ultrafiltration. Rejection measurements indicate different rejections for the β-lactoglobulin monomers and dimers: the membrane rejects the dimer almost completely and the monomer only partially. The osmotic pressure turns out to be highly dependent on the protein concentration. A good agreement, up to high concentrations, is found between experimental data and theoretical osmotic pressures, calculated by taking into account the state of association, the excluded volume and the Donnan effects. The effect of changes in pH on the osmotic pressure has been measured: a minimum was found around pH = 4.5, where according to the literature, maximum protein-protein interaction occurs

Mass transfer coefficients in cross-flow ultrafiltration

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

Conformational behaviour of poly(2,6-dimethyl-1,4-phenylene oxide) in solution - I: Intrinsic viscosity as a function of temperature

Intrinsic viscosities [η] of poly(2,6-dimethyl-1,4-phenylene oxide) (PPO) solutions have been measured as a function of temperature between 60 and 25°C. The solvents were toluene and trichloroethene. In both solvents, the [η]-T curve exhibited a point of inflection in the range 45-35°. This phenomenon is explained as a conformational transition, which is possibly involved in the nucleation process of the solution crystallization of PPO. Assuming constancy of the coil expansion factor αη and the solvent draining over the whole temperature interval, a slight increase of characteristic parameter Cα, with decreasing temperature has been calculated

Conformational behaviour of poly(2,6-dimethyl-1,4-phenylene oxide) in solution - II. Sedimentation coefficients and permeabilities in the semi-dilute region as a function of temperature

Sedimentation and flotation coefficients of poly(2,6-dimethyl-1,4-phenylene oxide) (PPO) solutions have been measured as a function of temperature between 60 and 25°. The solvents were toluene and trichloroethane (TCE). Solvent permeabilities have been calculated from the sedimentation or flotation coefficients. PPO is less permeable to the solvents used than polystyrene of comparable molecular weight is to toluene and cyclohexane. Strong solvation of toluene and TCE by PPO molecules is proposed as an explanation for this finding. The measured permeabilities were used to check an earlier calculation of the change of radius of gyration with temperature from intrinsic viscosity data. A larger decrease in radius of gyration with increasing temperature has been calculated in this way than with the earlier assumption of essentially impermeable polymer coils, i.e. with the assumption of the value 2.5 × 1023 for the universal viscosity paramete

Linearized cloudpoint curve correlation for ternary systems consisting of one polymer, one solvent and one non-solvent

A linear correlation function is found for cloudpoint composition curves of ternary systems consisting of one polymer, one solvent and one non-solvent. The conditions for validity of this correlation function appear to be that the polymer is strongly incompatible with the non-solvent, and that only liquid-liquid demixing occurs. The linearized cloudpoint (LCP) curve is interpreted in terms of the various parameters occurring in the Flory-Huggins theory. The slope of the LCP line appears to be only dependent on the molar volumes of the components. Information about the binary Flory-Huggins interaction parameters and their concentration dependence can be obtained from the intercept of the linearized curve. Cloudpoints induced by crystallization do not follow the correlation. This gives an opportunity to distinguish between crystallization and liquid-liquid demixing without any additional experiments