Concentration Polarization Model Research Articles

Electroosmotic pump performance is affected by concentration polarizations of both electrodes and pump

Current methods of optimizing electroosmotic (EO) pump performance include reducing pore diameter and reducing ionic strength of the pumped electrolyte. However, these approaches each increase the fraction of total ionic current carried by diffuse electric double layer (EDL) counterions. When this fraction becomes significant, concentration polarization (CP) effects become important, and traditional EO pump models are no longer valid. We here report on the first simultaneous concentration field measurements, pH visualizations, flow rate, and voltage measurements on such systems. Together, these measurements elucidate key parameters affecting EO pump performance in the CP dominated regime. Concentration field visualizations show propagating CP enrichment and depletion fronts sourced by our pump substrate and traveling at order mm/min velocities through millimeter-scale channels connected serially to our pump. The observed propagation in millimeter-scale channels is not explained by current propagating CP models. Additionally, visualizations show that CP fronts are sourced by and propagate from the electrodes of our system, and then interact with the EO pump-generated CP zones. With pH visualizations, we directly detect that electrolyte properties vary sharply across the anode enrichment front interface. Our observations lead us to hypothesize possible mechanisms for the propagation of both pump- and electrode-sourced CP zones. Lastly, our experiments show the dynamics associated with the interaction of electrode and membrane CP fronts, and we describe the effect of these phenomena on EO pump flow rates and applied voltages under galvanostatic conditions.

A novel approach based on distinction of actual and pseudo resistances in membrane fouling: “ Pseudo resistance” concept and its implementation in nanofiltration of single solutions

This study proposes an integrated modeling approach based on distinction of actual and pseudo resistances to elucidate the relationships between flux decline and actual fouling in nanoscale membrane processes. The approach was based mainly upon joint solution of gel-modified concentration polarization and gel-concentration polarization-modified osmotic pressure models proposed herein. Both models were developed by a novel mass transport model in accordance with simultaneous transport of mass along sequential layers comprising concentration polarization, gel and membrane. Actual resistances of the fouling in each layer and the membrane itself could be estimated by taking into account viscosity differences of bulk solution and pure water in the pores compared to the feed solution. The implementation of the approach was carried out for nanofiltration of single solutions containing anionic dye (tartrazine), monovalent salt (NaCl) and anionic surfactant (linear alkyl benzene sulfonate, LABS). The surface properties and layer thicknesses of the membranes studied were investigated by scanning electron microscope, atomic force microscope and contact angle measurements. It was determined that flux decline increased with increasing of gel thickness regardless of solution type as directly dependent on the decrease in solvent amount penetrating from membrane–gel interface toward the membrane. External fouling accounted for the most of all actual membrane fouling with a ratio between 90.0 and 97.7% in which the gel resistance performed dominant effect with a ratio between 81.0 and 92.5%. As flux decline increased in an order of dye, NaCl and LABS, portion of actual fouling in all fouling increased by a decrease in proportional total pseudo resistance as a function of decreasing of proportional pseudo intrinsic membrane resistance. Proportional total pseudo resistances were calculated as much as 25.6, 37.3 and 60.9% for LABS, NaCl and dye solutions, respectively. These levels of total pseudo resistances put forward that the pseudo resistance approach needs to be included in mass transport domains through nanoporous membrane structures in order to eliminate both erroneous predictions of resistances in series and false interpretations of process dynamics on membrane fouling and flux decline.

Experimental studies and modeling on concentration polarization in forward osmosis

Concentration polarization (CP) is an important issue in forward osmosis (FO) processes and it is believed that the coupled effect of dilutive internal CP (DICP) and concentrative external CP (CECP) limits FO flux. The objective of this study was to distinguish individual contribution of different types of DICP and CECP via modeling and to validate it by pilot studies. The influence of DICP/CECP on FO flux has been investigated in this study. The CP model presented in this work was derived from a previous study and evaluated by bench-scale FO experiments. Experiments were conducted with drinking water as the feed and NaCl/MgSO(4) as draw solutions at different concentrations and velocities. Modeling results indicated that DICP contributed to a flux reduction by 99.9% for 0.5 M NaCl as a draw solution although the flow pattern of both feed and draw solutions was turbulent. DICP could be improved via selection of the draw solution. The modeling results were well fit with the experimental data. It was concluded that the model could be used for selection of the draw solution and prediction of water flux under similar situation. A draw solution with greater diffusion coefficient or a thinner substrate of an asymmetric FO membrane resulted in a higher flux.

Contribution of fouling and gel polarization during ultrafiltration of raw apple juice at industrial scale

The flux behavior during the industrial cross-flow ultrafiltration of apple juice in a batch process was modeled using a combination of the fouling and concentration polarization models. It was observed that the major flux reduction was at the beginning and at the end of operation due to fouling and increasing solute concentration in the feed tank, respectively. The fouling phenomenon was analyzed by classical and empirical models and it was shown that the empirical one has the best correlation within less than 0.3% error for each experiment. The most significant advantage of this model is its ability to predict a steady flux, while other models predict zero flux at infinite time, which is contrary to the observation. With continued permeation, the solute concentration in the feed becomes important in which the back diffusion of solute from the membrane surface to the bulk or concentration polarization becomes controlling. Consequently about 4:53 h after starting the operation, corresponding to increase of solute concentration to about 151% of its initial value, the dominant mechanism changes from fouling to concentration polarization. It was confirmed that at every moment of ultrafiltration actual experimental flux follows that model (fouling or concentration polarization) which predicts lower flux.

Water permeability in polymeric membranes, Part II

This study is a combination of experimental and theoretical works in an attempt to produce a new useful empirical model for the mass transfer in pressure-driven membrane separation processes. Following on from our previous work in Part I, this part II paper introduces three new permeability models when using aqueous solutions as feed. The Solution-Diffusion Pore-Flow Concentration-Polarization (SDPFCP) model, which is a combination between the Solution-Diffusion Pore-Flow (SDPF) model [1] and the Concentration Polarization (CP) model, is presented. The SDPFCP model examines the CP model to represent the transfer phenomena outside the membrane by merging its effect within the water permeability coefficient. A further development for this model, the SDPFCP+, is obtained by adding an additional resistance to the system in series with the membrane resistance and the CP. The second model shows fair representation of the experimental results. The Solution-Diffusion Pore-Flow Fluid-Resistance (SDPFFR) model is then proposed to provide better representation for the system. The feed solution resistance to water flux, the Fluid Resistance (FR), is suggested to replace the CP and the additional resistance. The latter model shows excellent fitting to the experimental results; it may be useful for development and design applications, when based on experimental data.

Crossflow Ultrafiltration Properties of Monodisperse Nanoparticle Suspensions in Laminar Flow

The crossflow filtration properties of monodisperse nanoparticle suspensions were investigated systematically by using flat ultrafiltration (UF) membranes for average nanoparticle diameters of 10, 45, and 80 nm. The relationships between (1) permeate flux and filtration time, (2) steady-state flux and applied pressure, and (3) limiting flux and feed concentration were studied under various experimental conditions. These relationships were found to be similar to those observed for the UF of aqueous macromolecular solutions, although the particle size of our target material was much larger than that of such macromolecules. In addition, the experimental data were analyzed by using the concentration polarization model, which is based on the mass balance beneath the membrane. As in the case of aqueous macromolecular solutions, the gel-layer concentration or limiting flux at low feed concentrations could not be explained well by the abovementioned model. Nevertheless, we demonstrated that UF membrane separation has the potential to be an effective processing technique for nanoparticle suspensions.

Steady state modeling of concentration polarization including adsorption during nanofiltration of dye solution

Steady state modeling of nanofiltration of a dye (eosin as model dye) solution was carried out. The model was based on simultaneous solution of solution-diffusion model, film theory and osmotic pressure model. The osmotic pressure model was modified by incorporating adsorption of dyes onto the membrane surface. The model parameters were estimated by comparing the calculated and experimental data of permeate flux and permeate concentration. It was observed that although membrane hydraulic resistance was the dominant one, adsorption resistance becomes more significant with increase in feed dye concentration and transmembrane pressure drop and decrease in crossflow velocity. For example, for eosin feed concentration of 0.2 kg/m 3 and crossflow velocity of 0.46 m/s and transmembrane pressure of 828 kPa, the resistance offered by adsorbed solutes was found to be as high as 21% of the total resistance. The combined model successfully simulates the system performance in terms of permeate flux and permeate concentration.

Bench-scale evaluation of seawater desalination by reverse osmosis

In bench-scale tests of seawater reverse osmosis desalination it is important to carefully consider osmotic pressure effects and determine the extent of concentration polarization so that sources of flux variation—whether from fouling, compaction, or osmotic pressure changes—can be properly assessed. Rigorous modeling of concentration polarization is difficult because of the complex geometries and flow regimes in RO modules; typically, concentration polarization must be measured. However, concentration polarization measurement usually requires knowledge of membrane permeability, which can vary from coupon to coupon. In this study a method is presented to determine both the membrane permeability and the concentration polarization regime in a single test. The key to the test is to allow the salt concentration to vary over time in a predictable way and extract parameters from a model fitted to the flux data. The usefulness of this technique is highlighted by evaluating results from several seawater experiments. It was found that specific flux decline in the experiments was caused by changes in osmotic pressure and membrane compaction. RO fouling by seawater organic-matter was not significant for the several seawater samples tested.

Study of mass transfer characteristics for a hollow fiber reverse osmosis module

The reverse osmosis separation process has become important as an energy saving (no phase change) process for brackish water and seawater desalination. Several analyses on hollow fiber reverse osmosis modules in which permeate water flows from outer side to inner side of hollow fiber bore have been attempted over the past twenty years. An FCP Model (Friction Concentration Polarization Model) was previously presented that showed good fit with a wide range of actual performance data on a hollow fiber reverse osmosis module. However, this analytical model contained the anomaly that the simulated boundary layer thickness is larger than the apparent length of the clearance among hollow fibers. Here, we propose a hollow Fiber Group Model that is consistent with the features of the hollow fiber arrangement of the practical reverse osmosis module. As a result of verifying this model, it was confirmed that the boundary layer thickness on the surface of the fiber group is smaller than the length of clearance between the fiber groups. Consequently the anomaly was broken off by this Fiber Group Model.

Analyses of hydrodynamic resistances and operating parameters in the ultrafiltration of grape must

Grape must destined to the production of white wine was clarified by cross-flow ultrafiltration (UF), on laboratory scale, by using polysulphone hollow fibre membranes with a molecular weight cut-off of 100 kDa. The effects of transmembrane pressure (Δ P), feed flow rate ( Q f) and temperature ( T) on permeation flux and resistances were studied. Results showed that permeate fluxes decreased with time until a steady-state was established. A maximum steady-state permeate flux was reached at a Δ P of about 100 kPa. Steady-state permeate fluxes increased with temperature in the range 15–39 °C. It was also observed that flux increased by increasing bulk flow rates according to the concentration polarization model. The permeate flux decay was analysed through the resistance-in-series model. Analyses of results showed that the membrane resistance ( R m) was constant, while both cake layer resistance ( R c) and fouling resistance ( R f) increased with Δ P and decreased with Q f. An increasing of temperature determined a significant decreasing of the cake layer resistance in the range 15–23 °C, while the fouling resistance showed a little increase in all the range of the investigated temperatures. Observed rejections of the UF membrane towards total soluble solids (TSS) and total phenolics increased by increasing Δ P in the range 20–130 kPa. A decreasing of the color intensity associated to an increasing of the clarity of the clarified must was observed when the pressure is raised. pH and acidity of the clarified must were not affected by the operating pressure.

Assessing the Impact of Concentration-Dependent Fluid Properties on Concentration Polarization in Crossflow Membrane Systems

The effects of concentration-dependent fluid properties (viscosity, diffusivity, and osmotic-pressure coefficient) of sucrose−water solution on the permeate flux, wall concentration, Sherwood numbers, and velocity profiles in three different membrane systems were assessed using a 2D finite element model, which was developed by modifying the fluid property terms to incorporate the concentration dependency in a coupled concentration polarization model that was developed earlier. It was found that wall concentration, permeate velocity, and Sherwood numbers were significantly affected by the variations of the fluid properties. If any of the concentration dependencies of the fluid properties is neglected, wall concentrations would be either significantly overestimated or underestimated, whereas permeate velocity would always be overestimated. In different membrane systems, the relative importance of the effects of the concentration-dependent viscosity, diffusivity, and osmotic-pressure coefficient on wall concentration and permeate velocity may vary. These results suggest that the effects of concentration-dependent properties on concentration polarization would be strongly affected by the system operating conditions, especially the system value of Δp/Δπ0. It was also found that the errors in the solution of Berman for the velocity profile may be considerable when the variations of the fluid properties are considered under the simulation conditions.

Characterization and retention of NF membranes using PEG, HS and polyelectrolytes

Nanofiltration (NF) membranes retention depends on charge repulsion and size exclusion, combining the properties of ultrafiltration and reverse osmosis membranes. The molecular weight cut-off of two NF membranes was determined using cross-flow filtration of different molecular weights of non-ionized polyethylene glycol (PEG). Their retention of humic acid (HA), fulvic acid (FA), diallyldimethylammonium chloride and copolymer of dimethyl aminoethyl acrylate was also determined. NF270 membrane's pure water flux was higher than NF90. NF270 also produced lower retention compared to NF90. Observed retention of PEG using NF270 was lower than NF90, but real retention of PEG was higher for NF270 than NF90. This unexpected result is due to the inconsistency of the concentration polarization model. According to the concentration polarization model, real retention determination is dependent on permeate flux (Jv) instead of taking account of membrane flux reduction. The two membranes are supposed to operate at similar flux to overcome this inconsistency. Incomplete retention of poly diallyldimethylammonium chloride (PDADMAC) and copolymer of dimethyl aminoethyl acrylate (CoAA) is due to the presence of their monomers. HA retention is higher than FA because of its higher molecular weight range. NF270 membrane retention of HA and FA is lower than NF90 because of its higher pore size and porosity. Solute retention is constant with increasing pressure due to the competition between concentration polarization and dilution effects at the studied range of trans-membrane pressure (TMP).

Limiting Partition Coefficient in a Tubular Ice System for Progressive Freeze-concentration

A tubular ice system is effective for the scale-up of progressive freeze-concentration. The effective partition coefficient, K, as an index for the effectiveness of progressive freeze-concentration, is defined by the ratio of solute in ice and liquid phase. K is dependent both on the ice crystal growth rate and the mass transfer coefficient at the ice-liquid interface, as described by the concentration polarization model. The limiting partition coefficient, K0, corresponds to K at the infinitesimal ice crystal growth rate and/or infinite mass transfer at the interface. K0 is an important process parameter for progressive freeze-concentration. A method is proposed for determining K0 experimentally for a tubular ice system. K0 increased with increase in the concentration of solute, which suggests that K0 is not determined by the equilibrium process but by the nonequilibrium process at the ice-liquid interface.

Estimation of Ultrafilter Performance Based on Characterization Data

AbstractBecause of limited availability of test data with actual Hanford tank waste samples, a method was developed to estimate expected filtration performance based on physical characterization data for the Hanford Waste Treatment and Immobilization Plant in Richland, Washington. A test with simulated waste was analyzed to demonstrate that filtration of this class of waste is consistent with a concentration polarization model. Subsequently, filtration data from actual waste samples were analyzed to demonstrate that centrifuged solids concentrations provide a reasonable estimate of the limiting concentration for filtration.

Mathematical modeling of multiple solutes system for reverse osmosis process in palm oil mill effluent (POME) treatment

Abstract A membrane transport model suitable for the multiple solutes system in reverse osmosis is developed for unsteady-state simulation and prediction of membrane filtration dynamics in terms of permeate flux and concentration of each solute. This model is based on coupling the concentration polarization model using unsteady-state differential material balance and extended Spiegler-Kedem model. This model is characterized by the parameters solute diffusivity in the concentration polarization layer (Dbi), reflection coefficient (σi), osmotic constant (ai), hydraulic permeability constant (Lp), mass transfer coefficient (ki) and solute permeability coefficient (Pii). These parameters are estimated by using the Levenberg–Marquardt method coupled with the Gauss–Newton algorithm using the experimental data. The experimental data were obtained from the treatment of pretreated palm oil mill effluent (POME) as a feed in the pilot plant scale reverse osmosis system. The pretreated POME composed of a ternary system with the solutes of carbohydrate constituents, protein and ammoniacal nitrogen. The simulation results show a good agreement with the experimental data. The proposed model is suitable for predicting the performance of multiple solutes in a reverse osmosis process. The concentration of each solute present is correlated with the COD of the permeate stream.

Assessing the Accuracy of Wall Concentration Estimation Based on Averaged Permeate Velocity in Spacer-Filled Reverse Osmosis (RO) Membrane Systems

The accuracy of estimations of wall concentration using the constant (averaged) permeate velocity method was assessed in both empty and spacer-filled reverse osmosis (RO) channels under various operation conditions, based on the simulation results of a two-dimensional (2-D) concentration polarization model. It was determined that, although it always results in substantially larger variations of wall concentrations, the constant permeate velocity method is able to mimic the general variation patterns of wall concentrations in both empty and spacer-filled channels. The constant permeate velocity method can reasonably estimate the averaged wall concentration. The error is usually <10%, under the simulation conditions. It was also determined that the constant permeate velocity method always overestimates the maximum wall concentration. For the membrane that is not in contact with transverse filaments, the error is usually within 20%, and increasing the mesh length or increasing the system value of Δp/Δπ0 woul...

Transmission analysis in ultrafiltration of ternary protein mixture through a hydrophilic membrane

One of the main reasons for the underutilization of ultrafiltration has been the lack of experimental data on transmission of proteins for complex systems and its corresponding theoretical analysis. Of course, the presence of fouling coupled with concentration polarization have had their share in making ultrafiltration operation a difficult one to understand. In the present study, the systematic ultrafiltration of 3-protein mixture, namely lysozyme, myoglobin and ovalbumin, has been carried out using a hydrophilic 30,000 molecular weight cut off membrane. The experimental data of individual protein transmission in ternary mixture showed a very low transmission (as low as 3% for ovalbumin) to a very high transmission (as high as 90% for lysozyme) of proteins for different operating conditions. This behaviour of each protein in the mixture was analyzed using combined concentration polarization and irreversible thermodynamics model. The parameters of the modeled values gave a very good fit with experimental data and the resulting analysis indicated some interesting findings, which are discussed in this paper. The comparison of parameters obtained for single protein solution and the ternary protein solution showed some unusual results that point to the presence of the protein–protein and protein–membrane interactions.

A combination of serial resistances and concentration polarization models along the membrane in ultrafiltration of pectin and albumin solutions

Ultrafiltration of pectin and albumin solutions was carried out on two different membranes. For both solutions, tests were performed at different transmembrane pressures, concentrations and velocities. A model combining the serial resistances and concentration polarization models in the steady state and laminar flow regime was proposed and compared with the experimental results. The model takes into account the mass-transfer and the transmembrane pressure along the membrane to determine a possible transition from pressure- to mass-transfer-controlled regime and to estimate the average permeate flux. For the most part of the tests, the observed behaviour of albumin and pectin ultrafiltration and measured fluxes were in accordance with the model predictions.

A concentration polarization model for the ultrafiltration of nonionic surfactants

A theoretical model has been developed that describes ultrafiltration of nonionic surfactants. The model takes into account the fact that surfactants start to aggregate and form micelles at the critical micelle concentration. The model can be used to predict the performance of the membrane if the transport properties inside and at the membrane surface as well as the surfactant association behavior, are known. Three hydrophilic ultrafiltration membranes, made of regenerated cellulose, were used in the investigation. The cut-offs of the membranes were 10,000, 20,000, and 30,000 Da. The surfactant used in the investigation was the nonionic surfactant Triton X-100. The influence of the concentration of surfactant, transmembrane pressure and pure water flux were studied theoretically and experimentally. From the results presented in this work it can be concluded that the calculated values are in good agreement with experimental data.

Effect of axial dispersion on the concentration polarization level in spiral wound modules

One of the primary requirements in the design of a reverse osmosis desalination process is control of the concentration polarization (CP) level in the spiral wound elements. Though residence time distribution (RTD) studies indicate the presence of a significant axial dispersion effect in the flow through spiral wound modules, this effect is commonly ignored in concentration polarization models. The objective of this paper is to analyze the effect of axial dispersion on concentration polarization and permeate flow.