Concentration Polarization Model Research Articles

Concentration polarizations of PEG and silica colloids in ceramic nanofiltration

A large decrease in permeability is often observed during the filtration of nano-sized colloids, while fouling is widely regarded as the main explanation for this phenomenon. The osmotic pressure or concentration polarization (CP) of colloids can also contribute to the flux decline. However, the contribution of CP to flux loss cannot be determined by the traditional CP model. In this study, the effect of fouling and CP/osmotic pressure on flux was distinguished. The CP values of polyethylene glycol (PEG) and silica-colloids were determined by the osmotic pressures near the membrane surface and in the feed. The CP induced by colloids accounted for 43–95% of the flux loss in our experiments. Silica exhibited higher CP values (127–460), compared to 7–71 for PEG. This was attributed to the slower back diffusion caused by the larger colloids, as evidenced by the diffusion coefficients of 4.30 × 10−11 m2/s for silica (10 nm) and 1.45 × 10−10 m2/s for PEG (2.9 nm). Although the CP was mitigated by increasing the cross-flow velocity, CP values of 31 and 250 were observed for PEG and silica at high Reynolds number of 7317, respectively. The experimentally obtained CP values were also compared with those calculated by the film diffusion model.

A modeling and experimental comparative study of a closed-loop forward osmosis-nanofiltration and standalone nanofiltration systems for fouling-prone wastewater treatment

The forward osmosis-nanofiltration (FO-NF) process presents a potential alternative for the treatment of wastewater effluents, compared to pressure-driven systems like reverse osmosis (RO)/nanofiltration (NF). This work bridges the gap in exploring the impact of continuous draw solute regeneration in FO-NF hybrid, and its influence on the performance over standalone NF at module-scale. The Speigler-Kedem model, along with the concentration polarization model, is used to describe the local mass transport in the membrane. Following this, the combined mathematical models for FO and NF are integrated into the hybrid FO-NF system at module-scale. Subsequent process optimization reveals that NF hydraulic pressure and inlet draw concentration control the NF retentate concentration and then simulate the desired operating conditions for the hybrid system when the NF retentate stream is directly used as a draw solution for the FO process. Further results show that in non-fouling feed solution, the FO-NF system is inferior to standalone NF in terms of SEC. In contrast, for fouling-prone feed solution, the standalone-NF performance degrades with time, which gradually mitigates water recovery from 40 to 15.6 % while increasing the SEC from 0.89 to 2.38 kWh/m3. At the same time, the FO-NF hybrid system performs better with Na2SO4 and MgSO4 as draw solutes with nearly constant water recovery of 32.6 % and 28.6 %, and negligible SEC fluctuations of 3.26 kWh/m3 and 4.70 kWh/m3 for the two draw solutes respectively. Despite this, compared with other state-of-the-art desalination technologies, the FO-NF hybrid exhibits comparably lower water cost (average 0.31 USD/m3) and effectively handles fouling-prone wastewater.

Effects of Concentration Polarization and Membrane Orientation on the Treatment of Naproxen by Sulfate Radical-Based Advanced Oxidation Processes within Nanofiltration Membranes with a Catalytic Support

The structure with a selective nanofiltration (NF) layer on top of a catalytic ultrafiltration (UF) membrane provides the possibility of treating micropollutants (MPs) by both rejection and degradation. However, such a dense selective layer unavoidably induces a formation of a highly concentrated retentate and a low utilization of the oxidant due to its rejection. A different membrane orientation is expected to solve the problems mentioned above since the concentrated MPs can be degraded within the catalytic support, and the rejection of the oxidants can be avoided when the pressure is applied from the porous support side. However, the resulting complex concentration polymerization (CP) effects are not well understood, and the effects of the following concentration changes of the MPs and the oxidants around the catalyst within the porous support membrane are unclear as well. In this work, three polyelectrolyte multilayers with different selectivity were fabricated on PES@CoFe2O4 catalytic UF membranes by sequential dip-coating. Concentration polarization models are utilized to predict the concentrations of naproxen and peroxymonosulfate (PMS) within the porous catalytic support under different membrane orientations. The results of naproxen removal after adding PMS show that a higher naproxen removal can be obtained with a higher concentration ratio of PMS to naproxen (cPMS/cNPX). Moreover, it is shown that the MPs in the feed solution can be degraded in a catalysis-separation sequence, exhibiting the potential of rejecting and simultaneously degrading MPs. However, the coating of a selective polyelectrolyte multilayer on the catalytic UF membranes also causes lower accessibility of PMS and naproxen to the catalysts embedded within the polymeric membranes, resulting in the decline of degradation efficiency. By coating only one side of the membranes, this negative effect caused by the polyelectrolyte coating can be mitigated. Overall, a 97% removal of naproxen on the permeate side and a 12% degradation of naproxen on the feed side were observed with the one-side-coated membranes under a catalysis-separation sequence. This work highlights the key role that concentration polarization can play in the degradation efficiency of naproxen in catalytic NF membranes, providing valuable guidance for the design of further improved catalytic membranes.

Single-Pass Tangential Flow Filtration (SPTFF) of Nanoparticles: Achieving Sustainable Operation with Dilute Colloidal Suspensions for Gene Therapy Applications.

Recent approval of several viral-vector-based therapeutics has led to renewed interest in the development of more efficient bioprocessing strategies for gene therapy products. Single-Pass Tangential Flow Filtration (SPTFF) can potentially provide inline concentration and final formulation of viral vectors with enhanced product quality due. In this study, SPTFF performance was evaluated using a suspension of 100 nm nanoparticles that mimics a typical lentivirus system. Data were obtained with flat-sheet cassettes having 300 kDa nominal molecular weight cutoff, either in full recirculation or single-pass mode. Flux-stepping experiments identified two critical fluxes, one based on boundary-layer particle accumulation (Jbl) and one based on membrane fouling (Jfoul). The critical fluxes were well-described using a modified concentration polarization model that captures the observed dependence on feed flow rate and feed concentration. Long-duration filtration experiments were conducted under stable SPTFF conditions, with the results suggesting that sustainable performance could potentially be achieved for as much as 6 weeks of continuous operation. These results provide important insights into the potential application of SPTFF for the concentration of viral vectors in the downstream processing of gene therapy agents.

Evaluation of casein protein transport through surface functionized membranes using irreversible thermodynamics and concentration polarisation model

ABSTRACT Casein is an important protein in the raw milk and many approaches have been established to separate casein to make cheese. This study mainly deals with the analysis of casein protein (19 kDa, pI 4.6) transport characteristics through ultrafiltration (UF) membranes. Polysulfone (PS) based polymer membranes are used and modified with polyethylene imine (PEI), polydiallyl dimethyl ammonium chloride (PDDA) and polyacrylic acid (PAA). The fabricated membranes are characterized by contact angle and Fourier transforms infrared (FTIR) spectroscopy. The UF process was conducted with a dead-end filtration unit and the volumetric flux and transmission values are recorded and that varies with pressure and pH. The experimental results are explained using the concentration polarization and irreversible thermodynamics model. The characteristics of the transport of casein are determined from the values of the parameters such as the solute concentration near the surface of the membrane [Cm], the solute permeability [Pm], mass transfer coefficient [k], and the reflection coefficient [σ]. From the results, it is concluded that the casein transport through the UF membrane was controlled by convection with decrease in casein rejection. Although, this model predicts the transmission behavior as a function of flux and supports the experimental results for both membranes.

Reverse Osmosis Modeling Study of Lead and Arsenic Removal from Drinking Water in Tarija and La Paz, Bolivia

An investigation of primary water sources in two Bolivian basins identified the presence of heavy metals toxic to health that exceeded the permissible limits for drinking water. Lead deposited in the San Jacinto and Huacata–Tarija reservoirs within the Guadalquivir basin and arsenic in the Milluni–La Paz basin were identified. The work studies reverse osmosis (RO) to remove Pb and As. The main contribution of this research is the development and construction of a mathematical model based on the Spiegler–Kedem concentration polarization model using different concentrations of Pb and As. The model makes it possible to design high conversion facilities (>80%) and optimize the process from the point of view of energy efficiency in future works. The model was developed to also include an Arrhenius temperature adjustment factor that allows for an accurate prediction of the process performance. The experimentation was carried out in two RO pilot plants using polyamide membranes. The model fits correctly with a maximum relative error between the experimental and theoretical flows of 5.4% and 4.4%. Among the benefits of the study, it guarantees the rejection of metals greater than 99%, even at low pressures.

Ultrafiltration system of an MFI-type zeolite-coated membrane in N,N-dimethylformamide solvent

Resistance to polar organic solvents is a desirable characteristic of membranes which needs further development for membrane separation systems. Inorganic membranes are one type of material with the potential to confer the desired resistance. In the present work, an MFI-type zeolite-coated tubular membrane was therefore prepared and evaluated for application to an ultrafiltration system using a polar organic solvent. The membrane was successfully prepared by a secondary growth method on an α-alumina membrane continuously with thickness of ca. 100 µm. The ultrafiltration of gold nanoparticles, as a model solute, in N,N-dimethylformamide (DMF) was achieved by the membrane under investigation, although the pure DMF permeability was 1.56 ( ± 0.41) × 10−7 m3/m2·s·MPa which is lower than conventional polymeric nanofiltration membranes. Real rejection of the gold nanoparticles was calculated based on concentration polarization model and was obtained as 1.00. The MFI-type zeolite-coated membrane maintained a stable effective rejection level over a long-term operation of 80 h, which indicates that the membrane possesses sufficient resistance to polar organic solvents.

Flow Rate Prediction for a Semi-permeable Membrane at Low Reynolds Number in a Circular Pipe

A concise and accurate prediction method is required for membrane permeability in chemical engineering and biological fields. As a preliminary study on this topic, we propose the concentration polarization model (CPM) of the permeate flux and flow rate under dominant effects of viscosity and solute diffusion. In this model, concentration polarization is incorporated for the solution flow through a semi-permeable membrane (i.e., permeable for solvent but not for solute) in a circular pipe. The effect of the concentration polarization on the flow field in a circular pipe under a viscous-dominant condition (i.e., at a low Reynolds number) is discussed by comparing the CPM with the numerical simulation results and infinitesimal Péclet number model (IPM) for the membrane permeability, strength of the osmotic pressure, and Péclet number. The CPM and IPM are confirmed to be a reasonable extension of the model for a pure fluid, which was proposed previously. The application range of the IPM is narrow because the advection of the solute concentration is not considered, whereas the CPM demonstrates superior applicability in a wide range of parameters, including the permeability coefficient, strength of the osmotic pressure, and Péclet number. This suggests the necessity for considering concentration polarization. Although the mathematical expression of the CPM is more complex than that of the IPM, the CPM exhibits a potential to accurately predict the permeability parameters for a condition in which a large permeate flux and osmotic pressure occur.

Single Pass Tangential Flow Filtration (SPTFF) of monoclonal antibodies: Experimental studies and theoretical analysis

Single Pass Tangential Flow Filtration (SPTFF) enables continuous ultrafiltration and diafiltration for inline concentration and buffer exchange in downstream bioprocessing of monoclonal antibody (mAb) products. However, the high conversion in SPTFF modules leads to large variations in local flow rate, protein concentration, and transmembrane pressure drop, significantly complicating the design of effective SPTFF modules/processes. In this study, a recent concentration polarization model for the filtrate flux in protein ultrafiltration that accounts for protein-protein interactions has been extended to the analysis of SPTFF, specifically including the effects of the mAb and membrane properties as well as the long path-length. Model calculations are in good agreement with experimental data for the filtrate flux and pressure drop in two commercial SPTFF systems with very different module geometries. The model was then used to analyze the design of SPTFF processes for inline mAb concentration, providing additional insights into the underlying physical phenomena governing the performance and optimization of SPTFF modules for bioprocessing.

Nitrate removal studies on polyurea membrane using nanofiltration system – membrane characterization and model development

Abstract Desalination of nitrates from brackish water is prominent in the coastal areas due to excessive disposal of pesticides by agricultural industries. Nowadays, membrane processes are growing tremendously for the desalination of brackish water. In this context, polyurea (PU) could be a useful membrane material for the treatment of brackish water. The present work deals with the removal of nitrates from synthetic water using PU membranes by nanofiltration (NF) process. Polyurea thin film composite (PU-TFC) membranes were prepared by interfacial polymerization followed by thermal crosslinking and characterized using Fourier transformed infrared spectral (FTIR), X-ray diffraction (XRD), scanning electron microscopy– energy dispersion X-ray spectroscopy (SEM–EDS), Atomic force microscopy (AFM), thermogravimetric (TGA), and universal testing machine (UTM) for structural analysis, crystallinity, morphological, compositional, thermal and mechanical properties, respectively. Experimental studies were conducted on an NF pilot plant by varying operating pressure from 2 to 10 bar and feed nitrate concentration from 60 to 200 mg/L for evaluating PU membrane performance. Experimental observations revealed a maximum water flux of 30.6 L/m2 h and nitrate rejection of 97.2% at a pressure of 10 bar for feed containing 140 mg/L of nitrate. A mass transfer model was developed on the basis of solution–diffusion mechanism for a semi-batch NF process by considering cake enhanced concentration polarization model, for laminar flow with feed recycle, using a plate and frame membrane module. A generic semi-batch NF process model was integrated taking into account concentration polarization and fouling layer resistance. The integrated model was successfully compared with existing data in literature and could be used for process scale-up. Due to the merits of hydrophilicity, negative charge, high thermal and mechanical resistance, the PU membrane can be termed as a low cost, commercially viable and ecofriendly barrier for separation of nitrates.

Facultative hybrid RO-PRO concept to improve economic performance of PRO: Feasibility and maximizing efficiency

A facultative hybrid reverse osmosis (RO) – pressure retarded osmosis (PRO) system can switch its operation between i) RO mode, where high quality water is produced from waste-water treatment plant effluent and ii) PRO mode, where the salinity difference between seawater desalination brine and wastewater is converted to energy. This system takes advantage of fluctuating energy pricing, by consuming low cost energy to produce water and producing high value energy.The system was modeled by a local concentration polarization and solution diffusion model, considering several geometries. The system was optimized and for different ratios of the economic value of electricity vs water, to find process settings and switch points. A necessary condition for the feasibility of the facultative hybrid RO-PRO concept is that the permeate value satisfies: i) low enough, to justify electricity production and ii) high enough, to justify water production. With a maximum energy price of 0.25 USD/kWh, the first condition translates into <0.10–0.17 USD/m3 (ALFS) or <0.20–0.28 USD/m3 (ALDS). The facultative hybrid RO-PRO concept is only feasible as improvement to a PRO system, where there is a limited demand for purified WWTP-effluent. It is expected that it is usually preferred to produce purified WWTP-effluent.

Reduced‐order modeling of flow and concentration polarization in membrane systems with permeation

AbstractModeling of concentration polarization (CP) is important to ensure a successful membrane system design. Although computational fluid dynamics (CFD) remains a common approach to study CP, it usually requires a long computational time to investigate a short simulated time in membrane systems. In this work, we proposed a reduced‐order model to predict CP in membrane systems with permeation. We modify Berman's velocity profile and incorporated it to the reduced‐order model of the mass‐transfer equation. The proposed model shows excellent agreement with CFD results, while offering a reduction of two orders of magnitude in computational time. We also validate the model with published experimental data and demonstrate that the model can predict permeate flux in close proximity under various operating conditions. The proposed model offers an attractive alternative to solving the full Navier–Stokes and mass‐transfer equations, and opens the possibility to further investigate various approaches to reduce concentration polarization.

Integral Method of Analysis for Combined Concentration Polarization and Pore Flow Model for Prediction of the Performance of a Nanofiltration Membrane

A coupled concentration polarization and pore flow model was used to predict the transport characteristics of a monovalent salt through a nanofiltration membrane. The concentration polarization in the flow channel was modeled using an integral method under the framework of boundary layer analysis. The extended Nernst–Planck equation was used to quantify the ion transport through the membrane pores. Ion partitioning across the solution phase and in the membrane pore was modeled using the Donnan exclusion principle including the steric hindrance. The membrane pore charge density was calculated for different membranes. The contributions of convection, diffusion, and electromigration toward the solute flux within the membrane pore were estimated. The calculated permeate flux and the solute concentration in permeate were compared with the experimental data available in the literature and were found to be in good agreement, indicating validation of the developed model.

Numerical modeling of particulate fouling and cake-enhanced concentration polarization in roto-dynamic reverse osmosis filtration systems

The decline in permeate flux due to fouling is attributed to the flow resistance offered by cake layer and enhanced concentration polarization. The adverse effects on permeate flux can be negated by increasing the fluid shear over the membrane. Roto-dynamic filtration systems, where a rotating disk over a membrane generates high strain rates, have been previously implemented in the ultra and microfiltration regimes. The present work provides a detailed mathematical description of colloidal fouling and cake-enhanced concentration polarization in cross-flow reverse osmosis (CFRO) systems. The mathematical model is numerically implemented in a commercial Computational Fluid Dynamics (CFD) package by employing several subroutines. The proposed model is able to predict the spatio-temporal variation of permeate flux and cake layer thickness in a CFRO filtration system for the first time, the primary focus being a high shear roto-dynamic RO filtration system. The effects of feed pressure, Reynolds number and foulant properties on the permeate flux and salt rejection are discussed in detail. Eventually, the temporal variation of the performance of a roto-dynamic RO filtration system is compared with that of a channel CFRO filtration system and hence the advantages of employing a roto-dynamic RO filtration system have been highlighted.

In Situ Visualization of Concentration Polarization during Membrane Ultrafiltration Using Microscopic Laser-Induced Fluorescence.

A novel noninvasive technique-microscopic laser-induced fluorescence (micro-LIF)-has been applied to achieve in situ visualization of concentration polarization (CP) of nanoparticles during cross-flow ultrafiltration at high resolutions. The reversible, highly dynamic nature of CP and its sensitive response to the filtration conditions were investigated and validated by direct visualization of the CP layer and the well depicted concentration profile near the membrane surface. Using micro-LIF, the formation of a CP layer during filtration and its back-diffusion after the filtration ceased can be directly observed. The dynamic variation of the CP layer with the cross-flow velocity and transmembrane pressure (TMP) change has also been demonstrated. The results showed that CP reached the steady state approximately 1 min after the filtration condition change. A higher cross-flow velocity and/or a lower TMP decrease the CP concentration and thickness. Further quantitative analysis of the filtration test results using the film theory model helps to obtain the particle concentration at the membrane surface and the thickness of the CP layer (30-50 μm). Accordingly, the nature of CP dynamics was characterized and the deficiency of the traditional CP model was explored.

Numerical modeling of concentration polarization and inorganic fouling growth in the pressure-driven membrane filtration process

Concentration polarization and surface fouling may be two of the most remarkable features in the pressure-driven membrane filtration process. A new numerical simulation model is proposed in this paper to study the concentration polarization (CP) and the inorganic fouling growth. The numerical study is based on the lattice Boltzmann method (LBM), which allows a simultaneous solution of the Navier–Stokes equations and the convection-diffusion equation. Simulation results are verified by comparisons with published CP and permeate flux data under the same operating conditions. Then the model is extended to predict CP in a spacer filled desalination channel. The prediction result indicates that there is a higher fouling potential near the spacer filaments due to higher CP values in that area. Coupling of the CP prediction model with gypsum growth kinetics provides an approach to study the inorganic fouling growth on the membrane surface at a single crystal level, with respect to a given solution supersaturation near the membrane surface. Predicted equivalent radius and accumulated mass of the growing gypsum crystal, under the effects of growth retardation by bicarbonate, agree with published test data and analytical results. The presented numerical model enables a direct evaluation of the impacts on the surface crystal development in the presence of antiscalants. This numerical model can be applied to identify suitable operating conditions, assist in dose selection of antiscalants when required properties are available, and predict the fouling mitigation effects in the pressure-driven membrane filtration process.

Role of organic fouling layer on the rejection of trace organic solutes by nanofiltration: mechanisms and implications

To investigate how the organic fouling layers on nanofiltration (NF) membrane surface and the strong matrix effect (particularly by Ca2+) influence the rejection of trace organic compounds (TOrCs), filtration experiments with two TOrCs, bisphenol A (BPA) and sulfamethazine (SMT), were carried out with virgin and organic-fouled NF membrane. Organic fouling layer on the membrane was induced by sodium alginate (SA) at different concentrations of Ca2+. The results indicated that NF membrane maintained consistently rejection of TOrCs with little influence by membrane fouling at lower Ca2+ concentration. In contrast, organic fouling caused at higher concentration of Ca2+ observably restrained the rejections of both BPA and SMT. Furthermore, based on the cake-enhanced concentration polarization (CECP) model, the rejection of TOrCs was divided to the real rejection and the mass transfer coefficient. Moreover, it was found that the decrease in rejection resulted by organic fouling was due to the real rejection that was restrained by fouling layer with irregular impact on the mass transfer coefficient. Although the mechanism of trace compounds rejection was complex, the controlling factors varied among foulants. Nevertheless, the steric effect of the cake layer played an important role in determining solute rejection by organic-fouled NF membrane.

Key factors affecting water permeate velocity in reverse osmosis based on concentration polarization model

Key factors affecting water permeate velocity in reverse osmosis based on concentration polarization model

Quantitative study of RNA transmission through ultrafiltration membranes

Nucleic acid-based therapies have the potential to treat a wide range of diseases through their ability to silence and/or regulate gene expression. Strategies for the large-scale purification of RNA are still being developed, creating a need for more fundamental understanding of the behavior of RNA in different separation systems. The objective of this work was to evaluate RNA transmission through a series of composite regenerated cellulose and polyethersulfone ultrafiltration membranes with different molecular weight cutoffs. Data were obtained using Torula yeast RNA, with the size distribution evaluated by both dynamic light scattering and agarose gel electrophoresis. Results with dilute RNA solutions were strongly influenced by RNA adsorption to the composite regenerated cellulose membrane; this effect was not seen with the polyethersulfone membranes. Data for the polyethersulfone membranes were analyzed using the concentration polarization model, which describes the affects of bulk mass transfer on RNA transmission, in combination with available hydrodynamic models for membrane transport. The results provide important insights into the factors controlling RNA transmission and the potential for using ultrafiltration for the purification of nucleic acid therapeutics.

Ultrafiltration behavior of an Fc-fusion protein: Filtrate flux data and modeling

Fc-fusion proteins are an important new class of biotherapeutics; however, there is currently little published data on the behavior of these proteins in downstream processing operations. The objective of this study was to evaluate the ultrafiltration behavior of a highly purified Fc-fusion protein in both citrate/phosphate and histidine buffers over a wide range of protein concentrations. Filtrate flux data were obtained using a Pellicon 3 tangential flow filtration cassette. Results were analyzed using a modified version of a recently developed ultrafiltration model that accounts for the effects of intermolecular interactions on protein mass transfer, suitably extended to include the flux in the pressure-dependent regime. The key parameters in this model were evaluated from independent measurements of the solution viscosity and osmotic pressure for protein concentrations up to 200g/L. The filtrate flux and maximum achievable protein concentration in the histidine buffer were both significantly lower than the corresponding values in the citrate/phosphate buffer due primarily to the greater viscosity in the histidine buffer. The modified concentration polarization model was in good agreement with filtrate flux data over the full range of protein concentrations in both the pressure-dependent and pressure-independent regime. These results provide important insights into the factors controlling the ultrafiltration behavior of the Fc-fusion protein.