Modeling of flux decline during crossflow ultrafiltration of colloidal suspensions

Mass transfer during crossflow ultrafiltration is mathematically expressed using the two-dimensional convective–diffusion equation. Numerical simulations showed that mass transfer in crossflow filtration quickly reaches a steady-state for constant boundary conditions. Hence, the unsteady nature of the permeate flux decline must be caused by changes in the hydraulic boundary condition at the membrane surface due to cake formation during filtration. A step-wise pseudo steady-state model was developed to predict the flux decline due to concentration polarization during crossflow ultrafiltration. An iterative algorithm was employed to predict the amount of flux decline for each finite time interval until the true steady-state permeate flux is established. For model verification, crossflow filtration of monodisperse polystyrene latex suspensions ranging from 0.064 to 2.16 μm in diameter was studied under constant transmembrane pressure mode. Besides the crossflow filtration tests, dead-end filtration tests were also carried out to independently determine a model parameter, the specific cake resistance. Another model parameter, the effective diffusion coefficient, is defined as the sum of molecular and shear-induced hydrodynamic diffusion coefficients. The step-wise pseudo steady-state model predictions are in good agreement with experimental results of flux decline during crossflow ultrafiltration of colloidal suspensions. Experimental variations in particle size, feed concentration, and crossflow velocity were also effectively modeled.     

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 ethanol on ultrafiltration of bovine albumin solutions with organic membranes

This paper investigates the ultrafiltration of albumin-ethanol solutions on polysulfone hollow fiber membranes with 30 kDa cut-off. The aim is to identify the mechanisms responsible for the observed permeate flux reduction in presence of ethanol. The variations of permeate flux with transmembrane pressure and wall shear rate fit the usual pattern of flux limitation by concentration polarization. Thus, although ethanol significantly increases the permeate viscosity, the data show that the flux decrease is not a direct consequence of the viscosity increase but rather due to reduced albumin diffusivity which decreases the back transport to the bulk solution. The specific resistance of the albumin layer on the membrane was found to be unaffected by the presence of ethanol. However the fouling potential of our solutions was found to be significantly increased by the addition of ethanol. Thus the observed flux reduction due to ethanol seems to be explained by a combination of a thicker polarization layer caused by reduced back transport and increased membrane fouling. A 10% increase in filtrated volume can be obtained by imposing periodic retrofiltrations which decrease fouling.     

Rotating reverse osmosis: a dynamic model for flux and rejection.

Reverse osmosis (RO) is a compact process for the removal of ionic and organic pollutants from contaminated water. However, flux decline and rejection deterioration due to concentration polarization and membrane fouling hinders the application of RO technology. In this study, a rotating cylindrical RO membrane is theoretically investigated as a novel method to reduce polarization and fouling. A dynamic model based on RO membrane transport incorporating concentration polarization is used to predict the performance of rotating RO system. Operating parameters such as rotational speed and transmembrane pressure play an important role in determining the flux and rejection in rotating RO. For a given geometry, a rotational speed sufficient to generate Taylor vortices in the annulus is essential to maintain high flux as well as high rejection. The flux and rejection were calculated for wide range of operating pressures and rotational speeds.     

A critical flux to avoid biofouling of spiral wound nanofiltration and reverse osmosis membranes: Fact or fiction?

The relation between biofouling and membrane flux in spiral wound nanofiltration and reverse osmosis membranes in drinking water stations with extensive pretreatment such as ultrafiltration has been studied. The flux – water volume flowing through the membrane per unit area and time – is not influencing the development of membrane biofouling. Irrespective whether a flux was applied or not, the feed spacer channel pressure drop and biofilm concentration increased in reverse osmosis and nanofiltration membranes in a monitor, test rigs, a pilot scale and a full-scale installation. Identical behavior with respect to biofouling and feed channel pressure drop development was observed in membrane elements in the same position in a nanofiltration installation operated with and without flux. Calculation of the ratio of diffusive and convective flux showed that the diffusive flux is considerably larger than the convective flux, supporting the observations that the convective flux due to permeate production is playing an insignificant role in biofouling. Since fouling occurred irrespective of the actual flux, the critical flux concept stating that “below a critical flux no fouling occurs” is not a suitable approach to control biofouling of spiral wound reverse osmosis and nanofiltration membranes.     

Membrane performance with a pulp mill effluent: Relative contributions of fouling mechanisms

Severe flux decline was observed during ultrafiltration of a pulp mill effluent. Membrane fouling was the result of varying combinations of adsorption, pore plugging and concentration polarization or gel layer formation. A wide range of membrane materials and pore sizes were evaluated, showing the relationship between the membrane material, pore size and the relative contribution of the different fouling mechanisms. Individual resistances were evaluated for adsorption, R_a, pore plugging, R_pp, and concentration polarization, R_cp, using a series resistance model. These were based on the pure water flux for (1) the new membrane, J_i, (2) after static adsorption with the mill effluent, J_a, (3) the product rate when ultrafiltering the effluent, J_v, and (4) the pure water permeability with the fouled membrane, J_f. These resistances were shown to be misleading in terms of the observed flux loss for cases with significant adsorptive fouling. Adsorptive fouling was underestimated and concentration polarization overestimated. An alternative method, which we shall call flux loss ratios, is proposed, which is based on the flux decline due to a particular mechanisms as a fraction of the overall flux decline. These new measures more accurately reflect the flux decline attributable to each fouling mechanism.     

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.     

Critical flux measurement for model colloids

The conventional operating membrane of a laboratory membrane filtration process is to apply controlled transmembrane pressures to the retentate side of the membrane, with the permeate side open ended. Often the minimum transmembrane pressure available is sufficient to cause membrane fouling in a given system. A membrane rig has been built which monitors transmembrane pressure in increments of 0.001 bar and by pumping permeate at a specified rate controls the flux to be constant. The technique used allows sensitive detection of trace fouling. Under a variety of low flux conditions fouling was not observed and it was found to be useful to produce an experimentally related definition of two types of critical flux. In the first definition a `strong form' of critical flux exists if the flux of a suspension is identical to the flux of clean water at the same transmembrane pressure. In the second definition a `weak form' of the critical flux exists if the relationship between transmembrane pressure and flux is linear, but the slope of the line differs from that for clean water. This paper describes how the use of this operating mode led to the successful experimental measurements of critical fluxes for two colloidal silica suspensions, BSA solution and a baker's yeast suspension with a 50k MWCO membrane. These measurements could not be made successfully in constant-pressure mode. The paper also reports experimental evidence in support of a `strong form' of the critical flux for the filtration of X30 silica suspension. Finally, we report the effect of membrane pore size on critical flux measurements for the three types of feed fluids.     

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.     

Ceramic membrane ultrafiltration of anionic and nonionic surfactant solutions

The ultrafiltration of two types of surfactants, sodium dodecyl sulfate (SDS, anionic) and Tergitol NP-9 (nonylphenol polyethylene glycol ether, nonionic), using a 20 nm ZrO₂ tubular membrane was investigated. The influence of crossflow velocity, temperature, pressure, and surfactant concentration on the permeate flux, close to and above the critical micelle concentration (CMC), is reported. Permeate flux and surfactant retention were measured in order to evaluate concentration polarization and fouling phenomena, and also the variation of these parameters due to surfactant/membrane interactions. High surfactant retentions (60–70%) were achieved depending on the feed concentration.     

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.     

Prediction of permeate flux during osmotic pressure-controlled electric field-enhanced cross-flow ultrafiltration

Electric field-enhanced cross-flow ultrafiltration has been carried out to separate protein, bovine serum albumin, from aqueous solution using a 30,000 molecular weight cutoff membrane. A theoretical model is developed to predict permeate flux under a laminar flow regime including the effects of external d.c. electric field and suction through the membrane for osmotic pressure-controlled ultrafiltration. The governing equations of the concentration profile in the developing mass transfer boundary layer in a rectangular channel are solved using a similarity solution method. The effect of d.c. electric field on the variation of membrane surface concentration and permeate flux along the length of the channel is quantified using this model. The expression of Sherwood number relation for estimation of mass transfer coefficient is derived. The analysis revealed that there is a significant effect of electric field on the mass transfer coefficient. A detailed parametric study has been carried out to observe the effect of feed concentration, electric field, cross-flow velocity, and pressure on the permeate flux. For 1 kg/m3 BSA solution, by applying a d.c. electric field of 1000 V/m, the permeate flux increases from 42 to 98 L/m2 h compared to that with zero electric field. The experimental results are successfully compared with the model predicted results.     

Micellar Enhanced Ultrafiltration of Reactive Black 5 from Aqueous Solution by Cationic Surfactants

Reactive black 5 (RB-5) dye was removed from a water stream using two cationic surfactants, cetyltrimethylammonium bromide (CTAB) and cetylpyridinium chloride (CPC), via micellar enhanced ultrafiltration. Three membranes with different pore size were used for the determination of rejection coefficient and permeate flux of the solution at 1.5 bar trans-membrane pressure (TMP). The two surfactants (CPC and CTAB) played an almost negligible role in rejection efficiency with 5000 and 10,000 molecular weight cut-off membrane (MWCO), respectively. In this case, high rejection and low permeate flux was the result of a larger molecular size of RB-5 DYE being retained by comparatively smaller sized pores of membrane via ultrafiltration. However, CPC and CTAB surfactants showed 83% and 98% rejection coefficient, respectively, at a concentration greater than their CMC values against 30,000 MWCO. Permeate flux remained low and constant in presence of 5000 and 10,000 MWCO with a small variation against 30,000 MWCO for the two surfactants, thereby no appreciable effect on both surfactant concentrations on concentration polarization was estimated. Thus, RB-5 dye alone was determined to be responsible for membrane plugging or concentration polarization and ultimately for low permeate flux. The effect of trans-membrane pressure was also investigated during this study.     

Characterization and theoretical analysis of protein fouling of cellulose acetate membrane during constant flux dead-end microfiltration

A rapid characterization method was used to study protein fouling of cellulose acetate membrane during dead-end, in-line, constant flux microfiltration. Based on pressure-permeate volume profiles, two fouling phases could be identified and compared at different permeate fluxes. Using protein staining dyes, the model foulant (bovine serum albumin) was found to deposit on the upstream side of the membrane as a loose cake at its isoelectric point. The effects of solution pH on both the nature and extent of membrane fouling, and membrane cleaning were examined. To further understand and quantitatively analyze the fouling behavior, a combined mathematical model which took into account pore blocking, cake formation and pore constriction was developed based on existing fouling models. The data obtained by modeling was in good agreement with experimental fouling data. Theoretical analysis of data clearly indicated that cake formation was the main fouling mechanism. Using methods such as dynamic light scattering, the significant role of large protein aggregates in membrane fouling was confirmed. The dimer composition of protein did not change significantly during the fouling experiments, clearly indicating that smaller aggregates played less important role in membrane fouling.     

The effect of imposed flux on biofouling in reverse osmosis: Role of concentration polarisation and biofilm enhanced osmotic pressure phenomena

This paper describes a systematic study of biofouling in reverse osmosis process using model bacteria of Pseudomonas fluorescens and employing a sodium chloride tracer response technique for fouling characterization. It was found that the growth of biofilm at constant flux following initial bacteria colonization of the membrane surface increased with imposed flux. The rationale was that biofilm growth was nutrient dependent, where the nutrient availability at the membrane wall was controlled by the magnitude of concentration polarization, which is driven by flux. The salt tracer response showed that the biofouling comprised a hydraulic resistance and induced an enhanced osmotic pressure phenomenon; known as the biofilm enhanced osmotic pressure (BEOP) effect [M. Herzberg, M. Elimelech, Biofouling of reverse osmosis membranes: role of biofilm-enhanced osmotic pressure, Journal of Membrane Science 295 (2007) 11–20], due to hindered back diffusion of solutes through the tortuous path of the heterogeneous structure of the biofilm. For the conditions studied, the contribution of BEOP to transmembrane pressure increase was greater than the hydraulic resistance.     

A mass transfer model for the prediction of rejection and flux during ultrafiltration of PEG-6000

A mass transfer model in case of ultrafiltration is proposed in the present study which is capable of predicting the permeate volumetric flux and rejection at different pressure, concentration and stirrer speed. The model is based on the steady state mass balance over the boundary layer, coupled with the results from irreversible thermodynamics. It first predicts the membrane surface and permeate concentrations — which are then utilized to calculate rejection. Permeate flux is then predicted using the result obtained from filtration theory. The model utilizes four parameters, namely, solvent permeability, solute permeability, reflection coefficient and specific cake resistance. These parameters along with the known values of the operating conditions and solution properties enable one to predict the flux as a function of time and rejection. The computed results are found to be in good agreement with the previously published data of Bhattacharjee and Bhattacharya during ultrafiltration of PEG-6000 by cellulose acetate membrane.     

How slug flow can enhance the ultrafiltration flux in mineral tubular membranes

The study deals with the use of a gas-liquid two-phase flow to reduce tubular mineral membrane fouling by injecting air directly into the feed stream. The injected air is supposed to create complex hydrodynamic conditions inside the ultrafiltration module which destabilize the concentration layer over the membrane surface. The experimental study was carried out by filtering suspensions (bentonite and yeast) through an ultrafiltration tubular mineral membrane. A range of transmembrane pressures and various liquid and gas flow-rates were tested. Results related to the permeate flux showed an enhancement by a factor of 3, with a slug flow-structure for the two kinds of suspension (200% of flux increase). Furthermore, the applicability of such an unsteady technique was examined with a view to reduce energy consumption.     

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.     

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.     

Modeling of the Permeate Flux during Microfiltration of BSA-Adsorbed Microspheres in a Stirred Cell

A study on the variation of the permeate flux was performed in a stirred cell charged with microspheres, to investigate the effects of the stirrer speeds (300, 400, and 600 rpm) and the BSA concentration (0.1, 0.2, 0.4, and 0.8 g/L) under constant pressure. The permeate flux increased over time before the saturation point, but it began to decrease after that point. An increase of the BSA concentration and the stirrer speed resulted in the rapid increase of the permeate flux. This is contrary to the observation of the conventional filtration experiments using a stirred cell. A resistance-in-series model was employed for the modeling of the permeate flux. The cake resistance (R(c), induced by the concentration polarization of microspheres) and the fouling resistance (R(f), induced by the adsorption of BSA inside the membrane pore) must be considered simultaneously for the modeling. These modeling results were in good agreement with the experimental data. These can be applied to the special system considering both R(c) and R(f) as well as the general filtration systems using a stirred cell. Copyright 2000 Academic Press.