A unified model for flux prediction during batch cell ultrafiltration

An analysis of the flux decline encountered during ultrafiltration (UF) in a batch cell is presented by including the combined influence of the osmotic pressure and the gel layer. A predictive model for the flux decline in unstirred and stirred batch cell UF processes is developed by unifying the osmotic pressure and gel layer models. UF experiments were performed in a batch cell with polymeric solutes (PEG, dextran and PVA) and a protein (BSA), ranging widely in molecular weights and physico-chemical properties, under various operating conditions (pressure, solution pH, and stirrer speed). The present unified model predictions match closely with the experimental flux behaviour for all cases, while individual osmotic pressure and gel layer models are found to be inadequate.     

Generalized integral and similarity solutions of the concentration profiles for osmotic pressure controlled ultrafiltration

A mathematical model describing the concentration polarization phenomenon during osmotic pressure controlled ultrafiltration is presented. Generalized integral and similarity solutions of the concentration profile in the mass transfer boundary layer are obtained. The parameters governing the shape of the concentration profile vary with time in case of a batch cell and axial distance in a cross flow cell. The model is used to predict the permeate flux and the solute rejection simultaneously during unstirred batch cell and cross flow UF. The results obtained by integral and similarity solutions are compared with the results of detailed numerical solution of the governing equations for both the systems. The predictions of permeate flux from the generalized integral method are also compared with some approximate solutions in order to assess the limitations of the various approximations. UF experiments were performed with Dextran (T-20) in cross flow system and with PEG-6000 and Dextran (T-40 and T-20) in unstirred batch cell. Predictions of the model are in remarkably good agreement with detailed simulation as well as experimental results. Moreover, the integral solution can also account for the variation of diffusivity with solute concentration. Comparisons show that (a) while the generalized integral method is much simpler than the detailed numerical solutions, it is much more general and accurate than other analytical and semi-analytical solutions, and, (b) the proposed solution predicts the osmotic pressure controlled flux decline accurately over a wide range of operating conditions. The expression for gel layer governed UF (constant membrane surface concentration) is found to be an asymptotic case of the present solution.     

Free-solvent model shows osmotic pressure is the dominant factor in limiting flux during protein ultrafiltration

In protein ultrafiltration (UF), the limiting flux phenomenon has been generally considered a consequence of the presence of membrane fouling or the perceived formation of a cake/gel layer that develops at high operating pressures. Subsequently, numerous theoretical models on gel/cake physics have been made to address how these factors can result in limiting flux. In a paradigm shift, the present article reestablishes the significance of osmotic pressure by examining its contribution to limiting flux in the framework of the recently developed free solvent osmotic pressure model. The resulting free-solvent-based flux model (FSB) uses the Kedem–Katchalsky model, film theory and the free solvent representation for osmotic pressure in its development. Single protein tangential-flow diafiltration experiments (30 kDa MWCO CRC membranes) were also conducted using ovalbumin (OVA, 45 kDa), bovine serum albumin (BSA, 69 kDa), and immuno-gamma globulin (IgG, 155 kDa) in moderate NaCl buffered solutions at pH 4.5, 5.4, 7 and 7.4. The membrane was preconditioned to minimize membrane fouling development during the experimental procedure. The pressure was randomly selected and flux and sieving were determined. The experimental results clearly demonstrated that the limiting flux phenomenon is not dominated by membrane fouling and the FSB model theoretically illustrates that osmotic pressure is the primary factor in limiting flux during UF. The FSB model provides excellent agreement with the experimental results while producing realistic protein wall concentrations. In addition, the pH dependence of the limiting flux is shown to correlate to the pH dependency of the specific protein diffusion coefficient.     

Flux decline during nanofiltration of naturally-occurring dissolved organic matter: effects of osmotic pressure,membrane permeability,and cake formation

Nanofiltration of naturally-occurring dissolved organic matter (NOM) by an aromatic polyamide membrane was measured in a crossflow bench-scale test cell and modeled using a semi-empirical osmotic pressure/cake formation model. Our objective was to examine flux decline due to NOM fouling while explicitly accounting for flux decline due to osmotic effects and changes in membrane permeability. This approach allowed quantification of the effect of ionic composition on specific NOM cake resistance, and yielded insight into flux decline due to enhanced NaCl rejection by the NOM deposit. In the absence of NOM, increasing NaCl concentration reduced salt rejection and decreased membrane permeability. Flux decline was modeled by accounting for changes in osmotic pressure with time, and by employing an effective permeability. The addition of calcium significantly reduced rejection of sodium and feed conductivity, and thus mitigated flux decline. Increasing pH from 4 (near membrane pI) to 10 increased the effective permeability but also increased NaCl rejection, which resulted in greater flux decline. The presence of NOM caused greater flux decline resulting from a combination of NOM cake resistance and increased rejection of NaCl by negatively charged NOM functional groups. Increasing NaCl concentration had little effect on the mass of NOM deposited, but significantly increased the specific resistance of the NOM cake. The effect of ionic strength on specific resistance correlated with a reduction in NOM size, estimated by separate UF permeation experiments and size exclusion chromatography analysis of UF permeate. Therefore, increased specific cake resistance is consistent with a more compact, less porous cake. Flux decline by NOM solutions showed a maximum at pH 7, where salt rejection was also a maximum. Binding of calcium reduced the ability of NOM to enhance NaCl rejection, and likely increased NOM cake resistance. Flux decline caused by NOM fouling in the presence of calcium was only significantly different than that caused by NOM in a solution of NaCl at the same ionic strength when the calcium concentration corresponded to saturation of NOM binding sites.     

Tubular ultrafiltration flux prediction for oil-in-water emulsions: analysis of series resistances

Using the resistance-in-series (RIS) approach to permeate flux modeling, a general relationship between permeate flux, transmembrane pressure, cross-flow velocity, and feed kinematic viscosity was developed for the tubular ultrafiltration (UF) of synthetic oil-in-water emulsions. The fouling layer resistance, R_f, was 63% of the total membrane resistance, R_m′; however, concentration polarization was the predominant factor controlling resistance in the tubular UF system. An explicit form of the resistance index, Φ, was postulated based on the observed interactions between Φ, cross-flow velocity and feed kinematic viscosity and the RIS model was modified to further describe the interactions between permeate flux and operational parameters. The modified model adequately predicted flux–pressure data over the range of experimental variables examined in this study. Additionally, a set point operating pressure was determined as a function of cross-flow velocity and feed viscosity to achieve a balance between polarization and total membrane resistance.     

Effect of colloids on salt transport in crossflow nanofiltration

The role of colloid deposition on the performance of a salt-rejecting NF membrane was evaluated by modeling salt transport using a two-layer transport model, which quantified the relative contributions of advection and diffusion in the cake and the membrane layers, and the effects of flux on the membrane sieving coefficient. The model was able to accurately describe how the measured permeate concentration, rejection, osmotic pressure, and flux decline varied with time. The two-layer model confirmed that the Peclet number in the cake layer was about an order of magnitude higher than that in the membrane layer, leading to significant concentration polarization at the membrane surface, as shown by others. However, the cake layer also increased overall resistance, which resulted in flux decline during constant pressure operation. Flux decline caused an increase in the actual sieving coefficient, leading to higher solute flux, lower observed rejection, and thus lower the bulk concentration. These coupled phenomena tended to mitigate the increase in concentration polarization caused by the cake. Therefore, as predicted by the model and verified by experiment, the osmotic pressure does not increase monotonically as the cake grows, and in fact can decrease when the cake layer is thick and the flux decline is significant. In our experimental system, the pressure drop across the cake layer, which was proportional to the cake thickness, was significant under the conditions studied. The effects of cake-enhanced osmotic pressure analyzed here are lower than those observed in previous studies, possibly because the transport model employed explicitly accounts for the effect of flux decline due to cake growth on the membrane sieving coefficient, and possibly because we used a somewhat different methodology to estimate cake porosity.     

Concentration Polarization of Interacting Solute Particles in Cross-Flow Membrane Filtration

A theoretical approach for predicting the influence of interparticle interactions on concentration polarization and the ensuing permeate flux decline during cross-flow membrane filtration of charged solute particles is presented. The Ornstein-Zernike integral equation is solved using appropriate closures corresponding to hard-spherical and long-range solute-solute interactions to predict the radial distribution function of the solute particles in a concentrated solution (dispersion). Two properties of the solution, namely the osmotic pressure and the diffusion coefficient, are determined on the basis of the radial distribution function at different solute concentrations. Incorporation of the concentration dependence of these two properties in the concentration polarization model comprising the convective-diffusion equation and the osmotic-pressure governed permeate flux equation leads to the coupled prediction of the solute concentration profile and the local permeate flux. The approach leads to a direct quantitative incorporation of solute-solute interactions in the framework of a standard theory of concentration polarization. The developed model is used to study the effects of ionic strength and electrostatic potential on the variations of solute diffusivity and osmotic pressure. Finally, the combined influence of these two properties on the permeate flux decline behavior during cross-flow membrane filtration of charged solute particles is predicted. Copyright 1999 Academic Press.     

Resistance in series model for micellar enhanced ultrafiltration of eosin dye

A study has been performed to quantify the extent of flux decline during micellar enhanced ultrafiltration (MEUF) of an acid dye (eosin red) using hexadecyl (cetyl) pyridinium chloride as the cationic surfactant. Effects of the operating conditions, e.g., transmembrane pressure drop and feed-surfactant-to-dye ratio, on the permeate flux profile and observed retention have been investigated in an unstirred batch ultrafiltration (UF) cell. A simple resistance-in-series model has been used to quantify the flux decline. From the flux decline history, it has been found that the membrane permeability decreases rapidly due to reversible pore blocking and further flux decline is caused by the growth of a gel-type layer over the membrane surface. The different resistances and growth kinetics of the gel layer have been investigated as functions of the operating conditions.     

Removal of natural organic matter by ultrafiltration with TiO2-coated membrane under UV irradiation

This study investigates the performance of ultrafiltration (UF) by membranes coated with titanium dioxide (TiO2) photocatalyst under ultraviolet (UV) illumination in removing natural organic matter (NOM) and possibly in reducing membrane fouling. Experiments were carried out using heat-resistant ceramic disc UF membranes and humic acids as model substances representing naturally occurring organic matter. Membrane sizes of 1, 15, and 50 kDa were used to examine the effects of coating under ultraviolet irradiation. A commercial humic solution was subjected to UF fractionation (batch process); gel filtration chromatography was applied to study the effects of molecular weight distribution of NOM on UF membrane fouling. When compared to naked membranes, UV254 (ultraviolet light of lambda=254 nm) illumination of TiO2-coated membranes exhibits more flux decline with similar effluent quality. Although the UF membrane is able to remove a significant amount of humic materials, the incorporated photocatalysis results in poor performance in terms of permeate flux. The TiO2-coated membrane under UV254 irradiation alters the molecular weight (MW) distribution of humic materials, reducing them to <1 kDa, which is smaller than the smallest (1-kDa) membrane in this study. Thus, TiO2-coated membranes under UV254 irradiation do not perform any better in removing natural organic matter and reducing membrane fouling.     

Degumming and production of soy lecithin, and the cleaning of a ceramic membrane used in the ultrafiltration and diafiltration of crude soybean oil

The optimization of the cleaning process, aiming to recover the permeate flux, and diafiltration as a means to obtain and purify soybean lecithin, were analyzed in this study as a means of delaying the decrease in permeate flux during the ultrafiltration (UF) of vegetable oils and their derivatives. It also aimed to maximize the exploration of the use of this type of technology during the processing steps. Thus the influence of the transmembrane pressure, cross flow velocity, and the opening of the permeate valve during the cleaning process (hexane circulation) of a ceramic membrane with a permeation area of 0.2 m² and a pore diameter of 0.01 mm in a pilot unit with a processing capacity of 40 L, was studied. Four different operational cleaning conditions, associating combinations of pressure (0.5–2.0 bar) and velocity (1.0–5.0 m s⁻¹), as well as the influence of opening the permeate valve, were studied. Also the production and purification of soybean lecithin was carried out by diafiltration of the retentates derived from the UF of the miscella, resulting in a product with about 90% of acetone insoluble matter. The most favorable cleaning condition was associated with a low pressure (0.5 bar) and elevated velocity (5.0 m s⁻¹), with which it was possible to recover the permeate flux in about 85 min.     

Modeling of the permeate flux decline during MF and UF cross-flow filtration of soy sauce lees

Cross-flow ultrafiltration and microfiltration have been used to recover refined soy sauce from soy sauce lees for over 25 years. The precise mechanism which dominated the permeate flux during batch cross-flow filtration has not been clarified. In the present study, we proposed a modified analytical method incorporated with the concept of deadend filtration to determine the initial flux of cross-flow filtration and carried out the permeate recycle and batch cross-flow filtration experiments using soy sauce lees. We used UF and MF flat membrane (0.006 m² polysulfone) module under different transmembrane pressures (TMP) and cross-flow velocities. The modified analysis provided an accurate prediction of permeate flux during the filtration of soy sauce lees, because this model can consider the change in J₀ at initial stage of filtration which was caused by the pore constriction and plugging inside membrane, and these changes may not proceed when the cake was formed on the membrane surface. Mean specific resistance of the cake increased with TMP due to the compaction of the cake and decreased with cross-flow velocity due to the change of deposited particle size, but less depended on the membrane in the present study. These results indicate that the value of J₀ determined by modified method was relevant to exclude the effects of the initial membrane fouling by pore constriction due to protein adsorption and plugging with small particles. The modified analytical method for the cake filtration developed in the present study was considered to be capable of selecting an appropriate operating conditions for many cross-flow filtration systems with UF, MF membranes.     

A novel approach for modeling concentration polarization in crossflow membrane filtration based on the equivalence of osmotic pressure model and filtration theory

A theoretical model for prediction of permeate flux during crossflow membrane filtration of rigid hard spherical solute particles is developed. The model utilizes the equivalence of the hydrodynamic and thermodynamic principles governing the equilibrium in a concentration polarization layer. A combination of the two approaches yields an analytical expression for the permeate flux. The model predicts the local variation of permeate flux in a filtration channel, as well as provides a simple expression for the channel-averaged flux. A criterion for the formation of a filter cake is presented and is used to predict the downstream position in the filtration channel where cake layer build-up initiates. The predictions of permeate flux using the model compare remarkably well with a detailed numerical solution of the convective diffusion equation coupled with the osmotic pressure model. Based on the model, a novel graphical technique for prediction of the local permeate flux in a crossflow filtration channel has also been presented.     

The dynamics of polarisation in unstirred and stirred ultrafiltration

Polarisation of a retentive UF membrane has been studied for three types of solute, a colloid (silica sol), a protein (albumin) and a branched chain polymer (Dextran), with and without stirring. For unstirred conditions the data have been analysed by modified constantpressure filtration theory, which gives specific resistances, a, of the solutes consistent with their sizes and conformation. The simple Carman—Kozeny relationship approximates a for the colloid and the protein. For all three solutes a increased with pressure and concentration. Times to steady-state flux for stirred conditions ranged from 10 to 50 seconds, with longest times for the lowest concentrations and the largest solute. The amount of solute in the polarised layer was estimated from the measured cake (gel) resistances and the known specific resistances. Layer thicknesses ranged up to to ? 5 μm for the protein, ? 6μm for the Dextran and ? 20 μm for the silica sol. Slight deviations of flux—time profiles from the filtration model are explained by membrane—solute interactions, such as irreversible pore plugging and reversible pore obstruction.     

Fouling of reverse osmosis membranes by biopolymers in wastewater secondary effluent: Role of membrane surface properties and initial permeate flux

Reverse osmosis (RO) is being increasingly used in treatment of domestic wastewater secondary effluent for potable and non-potable reuse. Among other solutes, dissolved biopolymers, i.e., proteins and polysaccharides, can lead to severe fouling of RO membranes. In this study, the roles of RO membrane surface properties in membrane fouling by two model biopolymers, bovine serum albumin (BSA) and sodium alginate, were investigated. Three commercial RO membranes with different surface properties were tested in a laboratory-scale cross-flow RO system. Membrane surface properties considered include surface roughness, zeta potential, and hydrophobicity. Experimental results revealed that membrane surface roughness had the greatest effect on fouling by the biopolymers tested. Accordingly, modified membranes with smoother surfaces showed significantly lower fouling rates. When Ca²⁺ was present, alginate fouled RO membranes much faster than BSA. Considerable synergistic effect was observed when both BSA and alginate were present. The larger foulant particle sizes measured in the co-existence of BSA and alginate indicate formation of BSA-alginate aggregates, which resulted in greater fouling rates. Faster initial flux decline was observed at higher initial permeate flux even when the flux was measured against accumulative permeate volume, indicating a negative impact of higher operating pressure.     

The relationship between membrane surface pore characteristics and flux for ultrafiltration membranes

Surface porosities of Amicon XM100A and XM300 membranes have been measured by electron microscopy and found to be less than 1 per cent. From the measured pore size distributions it is deduced that 50 per cent of the solvent flow is through 20 to 25 per cent of the pores.The conventional model for concentration polarisation in ultrafiltration (UF), which assumes a homogeneously permeable membrane surface, has been modified to account for regions of differing permeability. An effective free area correction factor (≤ 1.0) has been introduced to allow for the effect of membrane surface properties on gel-polarised UF flux.Ultrafiltration experiments with protein solutions and membranes with a range of water fluxes confirm that gel-polarised UF flux is dependent on membrane permeability and surface properties. Effective free area correction factors vary from about 0.4 to 1.0 with values < 1.0 obtained for membranes with water fluxes typically < 150 1/m² hr at 100 kPaSupport for the effective free area concept in UF is provided by an analogy between a gel-polarised UF membrane and a composite reverse osmosis membrane. In both cases the magnitude of the upper ‘controlling’ resistance may be influenced by the pore size and spacing of the lower supporting structure.     

Selection of appropriate training and validation set chemicals for modelling dermal permeability by U-optimal design

Quantitative structure-activity relationship (QSAR) models are being used increasingly in skin permeation studies. The main idea of QSAR modelling is to quantify the relationship between biological activities and chemical properties, and thus to predict the activity of chemical solutes. As a key step, the selection of a representative and structurally diverse training set is critical to the prediction power of a QSAR model. Early QSAR models selected training sets in a subjective way and solutes in the training set were relatively homogenous. More recently, statistical methods such as D-optimal design or space-filling design have been applied but such methods are not always ideal. This paper describes a comprehensive procedure to select training sets from a large candidate set of 4534 solutes. A newly proposed ‘Baynes’ rule’, which is a modification of Lipinski's ‘rule of five’, was used to screen out solutes that were not qualified for the study. U-optimality was used as the selection criterion. A principal component analysis showed that the selected training set was representative of the chemical space. Gas chromatograph amenability was verified. A model built using the training set was shown to have greater predictive power than a model built using a previous dataset [1].     

Hydrodynamic resistance of concentration polarization boundary layers in ultrafiltration

The influence of concentration polarization on the permeate flux in the ultrafiltration of aqueous Dextran T70 solutions can be described by (i) the osmotic pressure model and (ii) the boundary layer resistance model. In the latter model the hydrodynamic resistance of the non-gelled boundary layer is computed using permeability data of the Dextran molecules obtained by sedimentation experiments. It is shown both in theory and experiment that the two models are equivalent.     

The role of bentonite addition in UF flux enhancement mechanisms for oil/water emulsion

The main problem in treating oil/water emulsion from car wash waste-water by ultrafiltration (UF) is fouling caused by oil adsorption on the membrane surface and internal pore walls. This study demonstrates that the addition of bentonite clay can reduce the adsorption layer on cellulose acetate UF membrane, resulting in a reduction of total membrane resistance (R_t). Experiments were conducted to identify and describe three possible mechanisms: (i) bulk oil emulsion concentration reduction; (ii) particle aggregation and (iii) detachment of the adsorbed gel layer by shear force. Adsorption of oil emulsion by bentonite can lead to a significant reduction of bulk oil emulsion concentration, one of the major causes of flux enhancement. Results show that contact of oil emulsion with bentonite forms larger particles resulting in flux increment. An optimum particle size of 37 μm, corresponds with a bentonite concentration of 300 mg/l and provided the highest flux. Beyond this limiting concentration, flux improvement gradually declined, possibly due to the formation of packed cake of particles on the membrane surface. The presence of bentonite in the oil emulsion promotes high shear stress which acts against the gel layer. This high shear stress, caused by bentonite particles and cross-flow velocity, reverses the adsorbed gel layer to the bulk of the liquid phase.