Theory Of Concentration Polarization Research Articles

An Operational Study and Modeling of a Reverse Osmosis Desalination System

The desalination of brackish water is one of the common issues in the world and spiral wound membrane is mostly used in desalination systems in home and industrial level, in this study a spiral wound brackish water membrane element were used to study the reverse osmosis system practically with the effect of multiple operational parameters and by creating Matlab Simulink modeling to analyze the RO system performance depending on concentration polarization theory then compare both results. The parameters that studied were flow rate range (0.6, 1, 1.3, 1.6, and 2 cm3/s), concentration (100, 200, 300, 400 and 500 ppm), and temperature (15, 25 and 35 °C), of the feed and mass transfer coefficient for the permeate water, the salts that used (CaCl2 and KCl) and by the concentration polarization (a phenomenon of accumulation of solute) the salts will tangle up at the surface of the membrane and affect membrane efficiency. The results indicated that the membrane operation is response sensitively to variations in feed temperature. The modeling results indicated that the major effect on the membrane parameters is the feed temperature and concentration of the salt.

Steel-concrete interface influence on chloride threshold for corrosion – Empirical reinforcement to theory

Reinforcement corrosion is a common cause for reinforced concrete structure deterioration. One of the main causes for reinforcement corrosion is chloride ingress to the concrete. Published work hint at a relationship between susceptibility to chloride induced corrosion and the interface between the concrete and the rebar, known as the steel–concrete interface (SCI). This paper presents an investigation of the relationship between the chloride threshold for chloride-induced corrosion and the properties of the SCI around embedded rebar. The relationship was investigated using 16 different concrete mixes. SCI properties were extracted using automated image analysis. The chloride threshold was found to decrease with the distance between the rebar surface and the concrete solids. In the case of horizontal rebar, the chloride threshold decreased with SCI thickness as well. These results agree with the theory of concentration polarization in localized corrosion and may explain the variety of chloride threshold values reported in the literature.

Steel-Concrete Interface Influence on Chloride Threshold for Corrosion – Empirical Reinforcement to Theory

Abstract Reinforcement corrosion is a common cause for reinforced concrete structure deterioration. One of the main causes for reinforcement corrosion is chloride ingress to the concrete. Published work hint at a relationship between susceptibility to chloride induced corrosion and the interface between the concrete and the rebar, known as the steel–concrete interface (SCI). This paper presents an investigation of the relationship between the chloride threshold for chloride-induced corrosion and the properties of the SCI around embedded rebar. The relationship was investigated using 16 different concrete mixes. SCI properties were extracted using automated image analysis. The chloride threshold was found to decrease with the distance between the rebar surface and the concrete solids. In the case of horizontal rebar, the chloride threshold decreased with SCI thickness as well. These results agree with the theory of concentration polarization in localized corrosion and may explain the variety of chloride threshold values reported in the literature.

Rapid Prediction of the Open-Circuit-Voltage of Lithium Ion Batteries Based on an Effective Voltage Relaxation Model

The open circuit voltage of lithium ion batteries in equilibrium state, as a vital thermodynamic characteristic parameter, is extensively studied for battery state estimation and management. However, the time-consuming relaxation process, usually for several hours or more, seriously hinders the widespread application of open circuit voltage. In this paper, a novel voltage relaxation model is proposed to predict the final open circuit voltage when the lithium ion batteries are in equilibrium state with a small amount of sample data in the first few minutes, based on the concentration polarization theory. The Nernst equation is introduced to describe the evolution of relaxation voltage. The accuracy and effectiveness of the model are verified using experimental data on lithium ion batteries with different kinds of electrodes (LiCoO2/mesocarbon-microbead and LiFePO4/graphite) under different working conditions. The validation results show that the presented model can fit the experimental results very well and the predicted values are quite accurate by taking only 5 min or less. The satisfying results suggest that the introduction of concentration polarization theory might provide researchers an alternative model form to establish voltage relaxation models.

Modeling, control, and dynamic performance analysis of a reverse osmosis desalination plant integrated within hybrid energy systems

An RO (reverse osmosis) desalination plant is proposed as an effective, FLR (flexible load resource) to be integrated into HES (hybrid energy systems) to support various types of ancillary services to the electric grid, under variable operating conditions. To study the dynamic analysis of such system, special attention is given here to the detailed dynamic modeling and control design of RO desalination process that employs a spiral-wound membrane module. In particular, the solution-diffusion model modified with the concentration polarization theory is applied to predict RO performance over a large range of operating conditions. Simulation results involving several case studies suggest that an RO desalination plant can provide operational flexibility to participate in energy management at the utility scale by dynamically optimizing the use of excess electrical energy. The incorporation of additional commodity (fresh water) produced from a FLR allows a broader range of HES operations for maximizing overall system performance and profitability.

Enhancement of counter-ion transport through ion-exchange membranes in electrodialytic processes

Ion-exchange membranes (IEMs) are ionic conducting materials. They have various applications such as: fuel cell (PEMFC), electrochemical synthesis (Cl2/NaOH), desalination, purification, separation, and environment. Despite these applications, several aspects are still unknown, such as: the membrane structure, the conduction mechanisms, and concentration polarization. The main obstacle in electro-membrane processes such as electrodialysis is the concentration polarization phenomenon, which remains one of the incomprehensible phenomena in IEM transport. This phenomenon is common to all systems operating a selective ionic transfer through an interface; it arises from the difference in ions mobility in the solution and in the membrane. A better understanding of concentration polarization can help to improve the membrane performance, the process efficiency, and in the reduction the process operation cost. In this research, we studied the effect of the ammonia buffer (NH3/NH4+) on the counter-ion transfer through the anion- and the cation-exchange membranes AMX and CMX, respectively. The results show that the ammonia addition facilitates the counter-ion transfer in both cases and gives a total elimination of the system polarization, but with different behaviors of CMX and AMX membranes. The classical concentration polarization theory remains insufficient to explain the obtained results.

Electrochemical characterization of the CMX cation exchange membrane in buffered solutions: Effect on concentration polarization and counterions transport properties

In the present work, the combination of both properties of buffer and weak electrolyte solutions and their effects on concentration polarization phenomena, particularly on the limiting current density and the ohmic region resistance (Rohm) is investigated. Acetic acid (pKa=4.75) plays the role of weak electrolyte while at the same time buffers the pH of the system with acetate co-ions. In order to better understand the effect of the counterion nature and the pKa of the buffer acid/base pair, different electrolyte solutions are studied. The current–voltage curve characteristic values such as the limiting current density, the ohmic resistance (Rohm) and the polarization plateau resistance (Rpol) are determined and discussed according to the classical concentration polarization theory. However, it remains insufficient to explain the most important result obtained: The addition of acetic acid increases linearly the limiting current density while the ohmic resistance remains constant whatever the acetic acid concentration is.

CFD modeling and simulation of concentration polarization in microfiltration of oil–water emulsions; Application of an Eulerian multiphase model

In this study, a 2D CFD modeling and simulation of concentration polarization (CP) phenomenon in microfiltration of oil–water emulsion in a narrow rectangular membrane module was presented. As the novelty of this research, an Eulerian based multiphase method was investigated for the first time to capture the concentration of emulsified oil droplets in different extents of membrane module. It was shown that this new model is highly compatible with concentration polarization theory and is highly capable for determining CP profile and mass boundary layer behavior in different operating conditions, as well. In this research it was proved that under developed feed cross-flow shows better performance in terms of membrane surface cleaning. Also it was shown that a small portion of oil droplets accumulates at the roof of membrane module feed channel due to gravity. The simulation results proved that for under developed feed cross-flows, lower feed Reynolds number induces a lower CP profile peak despite increasing the oil droplet concentration on membrane surface and at the feed channel roof.

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.

Electrophoresis of solid particles at large Peclet numbers.

A theory of concentration polarization of a thin electrical double layer (DL) on a spherical particle is developed for the regime of large Peclet numbers which is realized in strong electric fields. In this regime, the concentration field arising outside DL is estimated under influence of diffusion and convection. According to the theory developed, polarization of DL at large Peclet numbers causes a change in the Stern potential, the formation of a dipole moment and the long-range potential. The diffuse layer deviates strongly from spherical symmetry and electroneutrality, and the screen of the surface charge is provided not only by the diffuse atmosphere but also by the charge induced in the convective-diffusion layer. The effect of electric field on the induced charge gives rise to the additional electroosmotic slip, that was called "secondary electroosmosis". Thus, a nonlinear additional term for the Smoluchowski formula of electrophoretic velocity is based on the changes of zeta-potential and on the secondary electroosmotic slip. The comparison of theory with experimental results revealed considerable fitting.

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.

Characterization of the effect of high molecular weight hyaluronan on trans-synovial flow in rabbit knees.

1. The effect of a rooster comb hyaluronan (3.6-4.0 g l-1) of similar chain length to rabbit synovial fluid hyaluronan, on the trans-synovial escape of fluid from the joint cavity in the steady state ( 8d s) was studied in 29 rabbit knees at controlled intra-articular pressures (Pj). 2. Rooster hyaluronan caused the pressure-flow relation to flatten out as pressure was raised. At 10-20 cmH2O the slope of the quasi-plateau, 0.05 +/- 0.01 microliter min-1 cmH2O-1 (mean +/- s.e.m.), was 1/39th that for Ringer solution (1.94 +/- 0.01 microliter 2O-1 ). 3. Bovine synovial fluid had a similar effect to hyaluronan in Ringer solution. 4. The quasi-plateau was caused by increasing opposition to outflow; the pressure required to drive unit outflow increased 4.4-fold between 5 and 20 cmH2O. The increased opposition to outflow at 20 cmH2O was equivalent to an effective osmotic pressure of 13-17 cmH2O at the interface. Since the infusate's osmotic pressure was only 0.9 cmH2O, this implied concentration polarization to 15-18 g l-1 hyaluronan at the interface. 5. Mechanical perforation of the lining, or enzymatic degradation of the interstitial matrix by chymopapain, abolished the quasi-plateau. Hydrational expansion of the matrix by approximately 2-fold did not. The increased opposition to outflow was reversible by washing out the hyaluronan, or by reducing Pj. It was unaffected by interruption of tissue blood flow or synoviocyte oxidative metabolism. These properties are compatible with a concentration polarization mechanism, i.e. flow-induced concentration of hyaluronan at the synovial interface due to molecular reflection. 6. A concentration polarization theory was developed for a partially reflected solute. Numerical solutions supported the feasibility of this osmotic explanation of the quasi-plateau. Additional mechanisms may also be involved. 7. It is concluded that native-size hyaluronan helps to retain synovial fluid in the joint cavity when pressure is raised and acts, at least in part, by exerting osmotic pressure at the interface between synovial matrix and a concentration polarization layer.

Current–Voltage Curves for Ion-Exchange Membranes: A Method for Determining the Limiting Current Density

The curves (V,I) of different ion-exchange membranes have been determined under different experimental conditions. Taking into account the classical theory of concentration polarization, a method has been developed to adjust the (V,I) data, up to a certain value ofI, which permits us to obtain easily the value of the limiting current density,IL, in every experimental situation. From these values, the dependence of the limiting current density of the membranes used on the concentration and stirring rate of the solutions has been studied. To check the reliability of the method, the values ofILthus obtained have been compared with those obtained by the usual methods; the similitude between both values is high.

Separation of metal oxides from supercritical water by crossflow microfiltration

Low-shear crossflow microfilters rated for 34.5 MPa and 455°C were evaluated for their ability to remove α-alumina particles from supercritical water. The crossflow microfilters were tested in conjunction with a 2.5 L/h bench-scale apparatus and a 150 L/h pilot plant. The filter elements were made of sintered Stainless Steel 316L tubes with a nominal pore size of 0.5 μm. Process variables included volumetric feed concentration, feed flow rate, temperature, and fluid density and viscosity. The mean particle diameter was about 1.6 μm. Filtration characteristics were similar at supercritical water conditions to those at ambient conditions: Increased shear rates and decreased fluid viscosity resulted in increased filtrate fluxes. Filtrate flow deterioration over time and the required transfilter pressure drop were about 40% less at supercritical water conditions as compared to the performance obtainable at ambient conditions. Higher shear rates delayed the establishment of steady state operating conditions. Filtrate flux could be augmented by pressure swings or periodic increases in the shear rate. Particle separation efficiencies typically exceeded 99.9%. A modified concentration polarization model for turbulent flow yielded steady state filtrate fluxes that were within a factor of two of the experimental results. Back diffusion was modeled as a process-in-series of molecular diffusion and eddy diffusion. The proposed model was consistent with findings of numerical diffusion studies and the theory of concentration polarization as recently presented in the literature. To save on energy costs it might be possible to achieve the benefits of filtration at supercritical conditions at near-critical subcritical conditions: viscosity and mass diffusion coefficients are similar but the density of subcritical water is 3 to 4 times higher than supercritical water thus increasing the filtrate mass flow rate by a factor of 3 to 4 for a given filter.

Theory of concentration polarization in crossflow filtration

A novel theory is developed for concentration polarization of non-interacting particles in crossflow-filtration systems. This theory reveals that the extent of concentration polarization, as well as the behaviour of the permeate flux, are characterized by an important dimensionless filtration number (NF= 4πa3pΔP/3kT). There is a critical value of the filtration number for a given suspension and operational conditions. When the filtration number is smaller than the critical value, a polarization layer exists directly over the membrane surface and the wall particle concentration is determined by the pressure and temperature. At higher filtration numbers, a cake layer of retained particles forms between the polarization layer and the membrane surface. Mathematical models are constructed for both cases and analytical solutions for the permeate flux are derived. An increase in permeate flux with increasing pressure is predicted for all operational conditions.

Theory of concentration polarization in cross-flow ultrafiltration: gel-layer model and osmotic-pressure model

A mathematically rigorous theory of concentration polarization in a steady-state cross-flow ultrafiltration is developed. The theory proceeds from the results of the analysis of laminar flow of a solution and convective diffusion of the low-mobile solute in porous channels with non-uniform wall suction. Two physical models of concentration polarization which are typically used in the literature are analyzed in detail, namely, the gel-layer model and the osmotic-pressure model. For either model, an equation describing the pressure/flux curve is derived. In the case of the gel-layer model, the theory leads to a simple analytical formula for the limiting flux. The flux turns out to be proportional to the cube root of the ratio of the gel concentration to the feed solution concentration, rather than to the logarithm of this ratio, as the simplified Michaels-Blatt theory predicts. On the other hand, in the case of the osmotic-pressure model, the rigorous theory allows the conclusion that at high applied transmembrane pressure, the permeate flux increases as a cube root of the pressure, so that the limiting flux is never reached. This suggests a simple criterion for the choice between the two models when interpreting experimental pressure/flux curves.

Study of protein transmission through ultrafiltration membranes

This paper presents a study of protein transmission through ultrafiltration membranes in a vortex flow filtration unit. Pure dilute solutions of one peptide, the antibiotic bacitracin (1.4 kDa), and three proteins, viz. cytochrome c (12.3 kDa), lysozyme (14.3 kDa) and myoglobin (17.8 kDa), in the appropriate buffers were ultrafiltered through Membrex Ultrafilic TM membranes with a molecular weight cut-off of 10 and 100 kDa. The variation in protein transmission with the applied pressure for the 10 kDa membrane follows a trend which can be explained by a combined concentration polarization-irreversible thermodynamics approach. However, ultrafiltration with 100 kDa membranes surprisingly exhibits up to 120% protein transmission for cytochrome c and lysozyme. The enrichment of protein in the permeate can be explained either by a modified concentration polarization theory or a reasoning similar to Sourirajan's preferential sorption-capillary flow mechanism for reverse osmosis.

Dielectric theory of concentration polarization. Relaxation of capacitance and conductance for electrolyte solutions with locally varying conductivity

For a dielectric medium with a locally conductivity used as some simulation of a concentration polarization phase, a complex capacitance is formulated to represent the dielectric relaxation behavior. The frequency dependence of capacitance and conductance was calculated numerically for a combined system of the concentration polarization phase and an aqueous phase with homogeneous concentration. Marked dielectric relaxations were found only in systems where the decrease in concentration is formed inside the concentration polarization phase. The theoritical formulas of dielectric relaxation derived are of great help in finding a significant clue to the estimation of the thickness of the polarization layer and the concentration gradient in a system where concentration polarization occurs alongside a membrane which is subjected to bias voltage.

Electrophoresis at large peclet numbers

The theory of concentration polarization of the double layer (DL) of a spherical particle, developed by J.Th.G. Overboek, F. Booth, S. Dukhin, V. Shilov, R.W. O'Brien, R.J. Hunter and others, in a linear approximation with respect to the external electric field, is generalized as applied to the regime of large Peclet numbers which is realized in strong electric fields. In this regime, the concentration field arising outside DL in its polarization is established not only in the process of diffusion but also under the effect of convection. The theory of concentration polarization is developed in terms of the convective diffusion equation. As with the linear treatment, polarization of DL at large Peclet numbers causes a change in the Stern potential, the formation of a dipole moment and the long-range potential whose distribution is described by a harmonic function. The peculiarity of polarization at large Peclet numbers consists of the formation of the distribution within the diffusion layer, which is not described by a harmonic function, and of the respective deviation from the electrical neutrality. As the external electric field grows, the initial diffuse layer deviates strongly from spherical symmetry and electric neutrality, and the screening of the surface charge is provided not only by the diffuse atmosphere but also by the charge originating in the diffusion layer, i.e. a secondary DL forms. The effect of the electric field on the outer plate of the secondary DL gives rise to the additional mechanism of electro-osmotic slip which is considered to be the secondary electro-osmosis. In strong electric fields, a nonlinear additional term appears for the Smoluchowski formula of electrophoretic velocity caused by the variation ofζ-potential over the surface of the particle and by the secondary electro-osmotic slip. The quantitative theory of the weak nonlinear concentration polarization of DL is developed and a correction term for the Smoluchowski formula based on this theory has been derived. The theory has also been developed for the strong concentration polarization of DL at which the deviation from the Smoluchowski formula is substantial. In the theory, it is assumed that the thickness of the diffuse DL which expanded due to the decrease of concentration polarization, is small compared with the thickness of the diffusion layer. It is also assumed to be possible to neglect the tangential component of the polarization field as compared with the external one. The fulfilment of these assumptions is provided by the restrictions imposed on the value of relaxation criterion Rel. With growing criterion Rel, we can expect the initiation of nonlinear effects to begin at a lower value of the electric field, which is most essential. The effect of the growth of the polarization space charge accelerating the electrophoresis can turn out to be more essential than the effect of the tangential polarization field slowing it down. In this case, the thickness of the diffuse layer and that of the diffusion one is closer together and the difficulty in constructing the theory increases sharply.

Modelling of Plasma-Separation through Microporous Membranes

Available mathematical models of ultrafiltration have been used to predict changes in maximum plasma filtration rate with wall shear rate for given filters and blood properties. We have done many plasmapheresis experiments in vitro, using hollow-fiber filters (500-1000 cm2) and fresh bovine blood collected on ACD or heparin. The comparison between predicted and experimentally obtained filtration rates was good for models based on the concentration polarization theory and lift velocity theory. In other experiments with pulsatile inlet flow we found that plasma filtration rate increased by 20 to 50% compared to non-pulsatile conditions. These results are in good agreement with the modified model of ultrafiltration incorporating pulsating flow. This paper presents relationships between plasma filtration velocity (steady and pulsating flow) and hemolysis limit as a function of wall shear rate and filter size.