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.     

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.     

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 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.     

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.     

Flux decline during cross flow membrane filtration of electrolytic solution in presence of charged nano-colloids: a simple electrokinetic model

An electrokinetic transport based approach for quantification of reversible flux decline due to the concentration polarization of an electrolyte solution in presence of charged colloids is presented. The model envisions the electrolyte transport across a charged cake or gel layer as transport of ions through charged cylindrical capillaries. This model is coupled with the standard theory of concentration polarization during cross flow membrane filtration. The analysis is carried out entirely in terms of generalized, non-dimensional variables. A dimensionless group termed as the scaled gel layer resistance evolves from the analysis, which accounts for the electrical properties of the charged nano-colloids and the electrolyte solution. A parametric study is performed to elucidate the coupled influence of mass transfer, membrane resistance, gel resistance, and electrical properties of the gel-electrolyte polarized layer. The effects of these parameters are examined on the filtration performance through the model equations.     

A constant flux based mathematical model for predicting permeate flux decline in constant pressure protein ultrafiltration

This paper discusses a novel approach for predicting permeate flux decline in constant pressure ultrafiltration of protein solutions. A constant pressure process is assumed to be made up of a large number of small, sequential, constant flux ultrafiltration steps: the flux decreasing due to fouling and other related factors at the end of each step. The advantage of this approach is that constant flux ultrafiltration is easier to study, characterize, and model than constant pressure ultrafiltration. Consequently model parameters can be obtained in reliable and reproducible manner. Constant pressure ultrafiltration is dynamic in nature since both the magnitude of osmotic back-pressure and the extent of membrane fouling decrease as the permeate flux decreases with time. The proposed model takes into consideration the interplay between permeate flux, concentration polarization, and membrane fouling. The model demonstrates that the initial rapid flux decline is due to a combination of concentration polarization and membrane fouling while during the remaining part of the process, the effect of concentration polarization becomes negligible. The model also shows that concentration polarization affects the initial flux decline only at higher transmembrane pressures. This model which was validated using experimental data is conceptually simpler than other available models and easy to use. In addition to its value as a predictive tool it would particularly be useful for deciding appropriate start-up conditions in ultrafiltration processes.     

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.     

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.     

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.     

Reverse osmosis filtration for space mission wastewater: membrane properties and operating conditions

Reverse osmosis (RO) is a compact process that has potential for the removal of ionic and organic pollutants for recycling space mission wastewater. Seven candidate RO membranes were compared using a batch stirred cell to determine the membrane flux and the solute rejection for synthetic space mission wastewaters. Even though the urea molecule is larger than ions such as Na+, Cl-, and NH4+, the rejection of urea is lower. This indicates that the chemical interaction between solutes and the membrane is more important than the size exclusion effect. Low pressure reverse osmosis (LPRO) membranes appear to be most desirable because of their high permeate flux and rejection. Solute rejection is dependent on the shear rate, indicating the importance of concentration polarization. A simple transport model based on the solution-diffusion model incorporating concentration polarization is used to interpret the experimental results and predict rejection over a range of operating conditions. Grant numbers: NAG 9-1053.     

Modeling of Fouling of Crossflow Microfiltration Membranes

Abstract

Steady-state and transient models are reviewed for predicting flux decline for crossflow microfiltration under conditions in which both external cake buildup and internal membrane fouling are contributing factors. Experimental work is not covered in the scope of this review, although reference is made to a few recent studies which have compared experimental measurements with theory. The steady-state cake thickness and permeate flux are governed by the concentration polarization layer adjacent to the cake of rejected particles which forms on the membrane surface. Depending on the characteristic particle size and the tangential shear rate, Brownian diffusion, shear-induced diffusion, or inertial lift is considered to be the dominant mechanism for particle back-transport in the polarization layer. For typical shear rates, Brownian diffusion is important for submicron particles, inertial lift is important for particles larger than approximately ten microns, and shear-induced diffusion is dominant for intermediate-sized particles. For short times, it is shown that the transient flux decline due to cake buildup is closely approximated by deadend batch filtration theory, independent of the tangential shear rate. For long times, however, the steady or quasi-steady flux increases with shear rate, because the tangential flow sweeps particles toward the filter exit and reduces cake buildup.     

The osmotic pressure of concentrated protein and lipoprotein solutions and its significance to ultrafiltration

Side-by-side measurements were made of osmotic pressure and ultrafiltration flux from a stirred cell for separate saline solutions of the proteins, bovine serum albumin, bovine fibrinogen, human low density lipoprotein and for polyethylene oxide .in distilled water. Albumin osmotic pressures were large enough to conclude that concentration polarization limits ultrafiltrate flux mostly by decreasing the driving forceΔP -Δπ. For the other large macrosolutes, concentrated-solution osmotic pressures were so small that polarization probably limits flux at the usual levels of applied pressure by adding a hydrodynamic resistance (gel layer) in series with the membrane resistance.     

Resistance to the permeate flux in unstirred ultrafiltration of dissolved macromolecular solutions

The flux decline during the unstirred ultrafiltration of dissolved macromolecular solutions such as polyethylene glycol and dextran solutions was measured at different pressures from I to 4 x 10⁵ Pa and different bulk concentrations from 0.1 to 0.55 kg/m³ with three types of polysulfone membranes. On the basis of the concept that a concentrated solution layer (not a gel layer) is formed on the membrane surface, the hydraulic resistance of the boundary layer was defined with the help of solvent permeability of dissolved macromolecules. The cake filtration theory was employed to analyze the flux decline behaviour. This simple theory worked well and the effective boundary layer concentrations calculated with the boundary layer resistance model developed here were physically quite reasonable. The calculated boundary layer concentrations depend on the applied pressure. The origin of this dependency might be the step concentration profile assumed in the cake filtration theory.     

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.     

On the behavior of the electrostatic colloidal interaction in the membrane filtration of latex suspensions

In order to investigate effects of the colloidal interaction in the membrane filtrations, the dead-end ultrafiltration of latex colloids was conducted with fully retentive membranes. Experimental results concerning the permeate flux during the filtration indicate that the void fraction of cake layer increased with the decrease of the ionic strength, due to the expanded Debye double layer thickness around the particles. The concentration dependence of the gradient diffusion coefficient of colloidal particles has been examined as a function of solution ionic strength. The NVT Monte Carlo simulation was applied on the bulk suspension so as to determine the thermodynamic coefficient, and the hydrodynamic coefficient was evaluated from the previously developed relation for an ordered system. The long-range electrostatic interactions between the particles are determined by using a singularity method, which provides accurate solutions to the linearized electrostatic field. The predictions on the variation of concentration polarization layer have been presented, from which we found that both the permeate flux and the particle diffusion are related to determine the concentration distribution above the cake layer.     

Modeling of concentration polarization and depolarization with high-frequency backpulsing

Rapid backpulsing to reduce membrane fouling during crossflow microfiltration and ultrafiltration is studied by solving the convection-diffusion equation for concentration polarization and depolarization during cyclic operation with transmembrane pressure reversal. For a fixed duration of reverse filtration, there is a critical duration of forward filtration which must not be exceeded if the formation of a cake or gel layer on the membrane surface is to be avoided. The theory also predicts an optimum duration of forward filtration which maximizes the net flux, since backpulsing at too high of frequency does not allow for adequate permeate collection during forward filtration relative to that lost during reverse filtration, whereas backpulsing at too low of frequency results in significant flux decline due to cake or gel buildup during each period of forward filtration. In general, short backpulse durations, low feed concentrations, high shear rates, and high forward transmembrane pressures give the highest net fluxes, whereas the magnitude of the reverse transmembrane pressure has a relatively small effect.Rapid backpulsing experiments with yeast suspended in deionized water performed with a flat-sheet crossflow microfiltration module and cellulose acetate membranes with 0.07 μm average pore diameter. The optimum forward filtration times were found to be 1.5, 3, and 5 s, respectively, for backpulse durations of 0.1, 0.2, and 0.3 s. Both theory and experiment gave net fluxes with backpulsing of about 85% of the clean membrane flux (0.022 cm/s = 790 l/m² h), whereas the long-term flux in the absence of backpulsing is an order-of-magnitude lower (0.0026 cm/s = 94 l/m² h).     

Ideal limiting fluxes in ultrafiltration: comparison of various theoretical relationships

The ultrafiltration of macromolecules is characterised by a limiting flux at high transmembrane pressures. There is also some evidence that at high pressures and low crossflow velocities the flux decreases slightly with increasing pressure. It is confirmed from a theoretical viewpoint that this can only be caused by a decrease in the average mass-transfer coefficient due to concentration increases in the boundary layer. At the practical level, we propose an expression which, for a given system, enables the ideal flux to be estimated a priori as a function of the transmembrane pressure. The ideal flux is defined as that flux which would occur in the absence of fouling and gelation. The model includes the influence of both osmotic pressure and the variation in viscosity due to concentration polarisation. Thus for predictive purposes knowledge of osmotic pressure and viscosity as a function of concentration is required. The only membrane parameter that has to be experimentally determined is the membrane permeability. In the absence of adsorption (which is the ideal case) this is the permeability to the pure solvent. The model has been tested against Jonsson's data for the ultrafiltration of dextran solutions. The results are most encouraging.     

Temperature and concentration polarization in membrane distillation of aqueous salt solutions

In this paper we have studied water transport in membrane distillation using a flat PTFE membrane. Experiments have been carried out with water and aqueous solutions of NaCl as feed. The effects of temperature and concentration polarization on the reduction of vapour pressure differences across the membrane with regard to the vapour pressure differences corresponding to the bulk phases which are separated by the membrane, are evaluated. A coefficient which measures this reduction has been introduced. This coefficient and the temperature polarization coefficient coincide when water is used as feed, but they are more and more different when the salt concentration of feed increases.The measured flux results and the calculated polarization results are discussed for different temperatures, recirculation rates and solution concentrations.     

In situ characterization by SAXS of concentration polarization layers during cross-flow ultrafiltration of Laponite dispersions

The structural organization inside the concentration polarization layer during cross-flow membrane separation process of Laponite colloidal dispersions has been characterized for the first time by in situ time-resolved small-angle X-ray scattering (SAXS). Thanks to the development of new "SAXS cross-flow filtration cells", concentration profiles have been measured as a function of the distance z from the membrane surface with 50 μm accuracy and linked to the permeation flux, cross-flow, and transmembrane pressure registered simultaneously. Different rheological behaviors (thixotropic gel with a yield stress or shear thinning sol) have been explored by controlling the mutual interactions between the particles as a result on the addition of peptizer. The structural reversibility of the concentration polarization layer has been demonstrated being in agreement with permeation flux measurements. These observations were related to structure of the dispersions under flow and their osmotic pressure.