Concentration polarization 6.32

Concentration polarization may be illustrated by considering copper cathode in copper sulfate solution as an example. Using the Nernst equation we have for the oxidation potential. 

Upon current flow, copper is deposited, thereby reducing the amount of cupric ions to a new value (Cu2+)s, when, 

As the current flow increases, the smaller is the (Cu)s value and the larger is the polarization this is known as concentration polarization. When [Cu]s approaches zero, the current density is known as the limiting current density. 

When the limiting current density is /L for the cathodic reaction, as i approaches l an expression is obtained of the form, 

It is to be noted that the Helmholtz double layer plays a significant role in concentration polarization since the concentration of the ions on the electrode surface, and the diffusion of ions from the bulk of the solution into the Helmholtz plane are contributing factors to the limiting current density. This situation may be visualized as shown below  

Concentration polarization is the polarization component caused by concentration changes in the environment adjacent to the surface as illustrated in Fig. 5.4. When a chemical species participating in a corrosion process is in short supply, the mass transport of that species to the corroding surface can become rate controlling. A frequent case of concentration polarization occurs when the cathodic processes depend on the reduction of dissolved oxygen since it is usually in low concentration, that is, in parts per million (ppm) as shown in Table 5.2 [1]. 

As illustrated in Fig. 5.5, mass transport to a surface is governed by three forces, that is, diffusion, migration, and convection. In the absence of an electrical field the migration term is negligible since it only affects charged ionic species while the convection force disappears in stagnant conditions. For purely diffusion controlled 

SCg is the concentration gradient of species O across the interface between the metallic surface and the bulk environment (mol cm ) 

Fioure 5.6 Nernst diffusion layer for a limiting current situation. 

This is represented by the horizontal line where C = C. There is also a region where the concentration drops, falling to zero at the electrode surface. The Nernst diffusion layer associated with this drop has a specific thickness (S) that depends upon the nature of the solution into which it extends. For stirred aqueous solutions the thickness of the diffusion layer varies between 0.01 and 0.001 mm. 

Feed-side concentration polarization When feed components sorb in the membrane, a local concentration gradient develops in the feed phase adjacent to the membrane upstream face. Owing to this gradient, transport of components from the bulk into the bulk-membrane interface occurs, thus replenishing the components that were absorbed by the membrane. The transport of a solute across the phase adjacent to the membrane can be either convective or diffusive, depending on the solute concentration as well as the fluid dynamic conditions over the membrane surface. 

In pervaporation, as the feed fluid is a liquid, a thin, stagnant boundary layer always exists over the membrane surface in which the solute transport is diffusive (Fig. 3.6-11). The thickness of this boundary layer (stagnant liquid film) can be calculated from well-established boundary layer equations (for critical reviews on the use of the most common correlations see, for example, Gekas and Hallstrom, 1987 and Cussler, 1997). If the flux of a solute i across the concentration boundary layer toward the membrane is lower than the maximum (for the respective solute bulk feed concentration) attainable solute flux across the membrane, then solute i will be depleted in the boundary layer over the membrane upstream surface. As a consequence, the concentration of i in the membrane upstream surface will also be lower (assuming a constant sorption coefficient), the concentration gradient over the membrane will decrease and hence so will the trans-membrane flux. 

This phenomenon is denoted feed-side concentration polarization and, in practice, affects mainly the fluxes of compounds of high sorption coefficient, even under turbulent hydrodynamic conditions over the membrane, as their permeability (and hence flux across the membrane) is high. It should at this point be emphasized that contrary to the non-ideal transport phenomena discussed earlier, feed-side concentration polarization is not a membrane-intrinsic phenomenon, but stems from poor design of the upstream flow conditions in practice it may in fact not be overcome owing to module design limitations (Baker et ah, 1997). 

In vapor permeation, feed-side concentration polarization is much less prone to occur than in pervaporation, owing to the high mass-transfer rate of the solute in the vapor feed phase. In fact, this feature is one of the main factors that distinguish the two processes. 

An illustrative example for permeate-side concentration polarization is the per-vaporation of vanillin, a high-boiling aroma compound. The boiling point of vanillin is about 558 K and its saturation vapor pressure correspondingly low (0.29 Pa at 

See reference 1 for a more complete discussion about concentration polarization. 

The transfer of reactants from the bulk solution to the electrode interface and in the reverse direction is an ordinary feature of all electrode reactions. As the oxidation-reduction reactions advance, the accessibility of the reactant species at the electrode/electrolyte interface changes. This is because of the concentration polarization effect, that is, r c, which arises due to the limited mass transport capabilities of the reactant species toward and from the electrode surface, to substitute the reacted material to sustain the reaction [6,8,10,66,124], This overpotential is usually established by the velocity of reactants flowing toward the electrolyte through the electrodes and the velocity of products flowing away from the electrolyte. The concentration overpotential, r c, due to mass transport restrictions, can be expressed as 

C is the concentration at the electrode surface C0 is the concentration in the bulk of the solution 

The slower the velocity of water through the pipe, the thicker the boundary layer becomes. 

Concentration polarization has a negative effect on the performance of an RO membrane. It acts to reduce the throughput of the membrane in three important ways. First, it acts as a hydraulic resistance to water flow through the membrane. Second, the build up of solutes increases 

The situation is often encountered where, upon the passage of current through an electrochemical cell, only one of the mobile species is discharged at the electrodes. Examples are (a) the use of a liquid or polymeric electrolyte, where both ions are mobile, and yet where only one is able to participate in the electrode reaction and (b) a mixed conducting solid in which current is passed by electrons, but in which cations also have a significant transport number. 

Consider a system consisting of a binary, unsupported electrolyte between electrodes which are reversible only to the cation. The cell is initially at equilibrium (no net currents are passing). At very short times after the imposition of a potential difference, the concentrations of all species in the bulk of the electrolyte are uniform and the ions move in response to the applied field. The current is determined by the uniform electrolyte conductivity. 

At long times, on the other hand, the flux of the blocked anion falls to zero, and a constant flux of cations passes through the system. In order to maintain electroneutrality there must also be a gradient in anion concentration and hence in electric potential, which just balances the gradient in anion chanical potential. 

there is effectively a gradient in the concentration of neutral species across the cell, and therefore we must include in the total potential difference a Nemstian term which is equal to the potential difference that would exist immediately after the interruption of current flow but before the reestablishment of uniform concentration profiles. The other contribution to the potential difference, that which is due to the flow of current itself, is a term arising from the gradient in conductivity due to the variations in concentration. This of conrse arises from differences in the mobility of the two species. It must be distinguished from the ohmic term present at very short times (high frequencies) due to the initially uniform conductivity of the electrolyte. The concentration polarization is therefore the additional polarization which is present due to concentration gradients caused by the current flow this is compared to the ohmic polarization that would be present if the current flow (and distribution) were the same bnt the concentration gradients were absent Substitution of the condition (144) into the flux equation for cations 

The ohmic potential difference may then be found by integration of Eq. (144) across the cell using this flux equation. Since the current is constant the concentration profile must also be uniform. The Nemstian term may be included as the potential of a concentration ceU with the same concentration profile. It is possible to show that the ratio of the steady-state resistance to the high-frequency resistance depends on the transference numbers of the ions. 

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Fig. 23. Two types of hollow-fiber modules used for gas separation, reverse osmosis, and ultrafiltration applications, (a) Shell-side feed modules are generally used for high pressure appHcations up to - 7 MPa (1000 psig). Fouling on the feed side of the membrane can be a problem with this design, and pretreatment of the feed stream to remove particulates is required, (b) Bore-side feed modules are generally used for medium pressure feed streams up to - 1 MPa (150 psig), where good flow control to minimise fouling and concentration polarization on the feed side of the membrane is desired.

A key factor determining the performance of ultrafiltration membranes is concentration polarization due to macromolecules retained at the membrane surface. In ultrafiltration, both solvent and macromolecules are carried to the membrane surface by the solution permeating the membrane. Because only the solvent and small solutes permeate the membrane, macromolecular solutes accumulate at the membrane surface. The rate at which the rejected macromolecules can diffuse away from the membrane surface into the bulk solution is relatively low. This means that the concentration of macromolecules at the surface can increase to the point that a gel layer of rejected macromolecules forms on the membrane surface, becoming a secondary barrier to flow through the membrane. In most ultrafiltration appHcations this secondary barrier is the principal resistance to flow through the membrane and dominates the membrane performance. 

The phenomenon of concentration polarization, which is observed frequently in membrane separation processes, can be described in mathematical terms, as shown in Figure 30 (71). The usual model, which is weU founded in fluid hydrodynamics, assumes the bulk solution to be turbulent, but adjacent to the membrane surface there exists a stagnant laminar boundary layer of thickness (5) typically 50—200 p.m, in which there is no turbulent mixing. The concentration of the macromolecules in the bulk solution concentration is c,. and the concentration of macromolecules at the membrane surface is c. 

Reviews of concentration polarization have been reported (14,38,39). Because solute wall concentration may not be experimentally measurable, models relating solute and solvent fluxes to hydrodynamic parameters are needed for system design. The Navier-Stokes diffusion—convection equation has been numerically solved to calculate wall concentration, and thus the water flux and permeate quaUty (40). 

A = 4.05 X lO " cm/(s-kPa)(4.1 X 10 cm/(s-atm)) and = 1.3 x 10 cm/s (4)//= 1 mPa-s(=cP), NaCl diffusivity in water = 1.6 x 10 cm /s, and solution density = 1 g/cm . Figure 4 shows typical results of this type of simulation of salt water permeation through an RO membrane. Increasing the Reynolds number in Figure 4a decreases the effect of concentration polarization. The effect of feed flow rate on NaCl rejection is shown in Figure 4b. Because the intrinsic rejection, R = 1 — Cp / defined in terms of the wall concentration, theoretically R should be independent of the Reynolds... 

Fig. 4. Mathcad simulations (Cp = 5000 mg/L) as a function of Reynolds number for a NaCl solution (a) concentration polarization (CP), and (b) (-...

J. Siler, "Reverse Osmosis Membranes-Concentration Polarization and Surface Fouling Predictive Models and Experimental Verifications," dissertation. University of Kentucky, Lexington, Ky., 1987. 

Dynamic membranes are concentration—polarization layers formed in situ from the ultrafiltration of coUoidal material analogous to a precoat in conventional filter operations. Hydrous zirconia has been thoroughly investigated other materials include bentonite, poly(acryhc acid), and films deposited from the materials to be separated (18). 

Fig. 5. Concentration polarization = concentration at membrane wall, Cj, = bulk concentration, Cj,. = bulk concentration of species i, J = flux, and...

P. Dejmek, "PermeabiHty of the Concentration Polarization Layer in Ultrafiltration of Macro Molecules," Proceedings of the International Symposium, Separation Processes by Membranes, Paris, Mar. 13—14,1975. 

Whereas the above discussion on concentration polarization was developed for electrolyte-side supply of reactants, concentration polarization can also arise... 

Fig. 6. Discharge behavior of a battery where is the open circuit voltage (a) current—potential or power curve showing M activation, ohmic, and M concentration polarization regions where the double headed arrow represents polarization loss and (b) voltage—time profile.

As the Nemst equation suggests, concentration variations in the electrolyte lead to potential differences between electrodes of the same kind. These potential differences are concentration polarizations or concentration overpotentials. Concentration polarizations can also affect the current distribution. Predicting these is considerably more difficult. If concentration gradients exist, equations 25 and 27 through 29 must generally be solved simultaneously. 

Polarization. When the appHed current density equals the AX membrane and the apparatus are said to be concentration polarized or simply polarized. At the fluid at the surface of the membrane is essentially depleted of electrolyte and the electrical resistance of the apparatus iacreases... 

Graphical solutions for concentration polarization. Uniform velocity through walls. 

Thin concentration polarization layer. Short tubes, concentration profile not fully developed. Use arithmetic concentration difference. 

Fouling is the term used to describe the loss of throughput of a membrane device as it becomes chemically or physically changed by the process fluid (often by a minor component or a contaminant). A manifestation of fouling in cross-flow UF is that the membrane becomes unresponsive to the hydrodynamic mass transfer which is rate-controlling for most UF. Fouling is different from concentration polarization. Both reduce output, and their resistances are additive. Raising the flow rate in a cross-flow UF will increase flux, as in Eq. 

Concentration polarization is a significant problem only in vapor separation. There, because the partial pressure of the penetrant is normally low and its solubihty in the membrane is high, there can be depletion in the gas phase at the membrane. In other applications it is usually safe to assume bulk gas concentration right up to the membrane. 

Further, as the current density of the fuel cell increases, a point is inevitably reached where the transport of reactants to or products from the surface of the electrode becomes limited by diffusion. A concentration polarization is estabhshed at the elec trode, which diminishes the cell operating potential. The magnitude of this effect depends on many design and operating variables, and its value must be obtained empirically. 

Electrodialysis can be applied to the continuous-flow type of operation needed in industry. Multi-membrane stacks can be built by alternately spacing anionic- and cationic-selective membranes. Among the technical problems associated with the electrodialysis process, concentration polarization is perhaps the most serious (discussed later). Other problems in practical applications include membrane scaling by inorganics in feed solutions as well as membrane fouling by organics. 

You may be surprised, but fouling is not always detrimental. The term dynamic membrane describes deposits that benefit the separation process by reducing the membrane s effective MWCO Molecular Weight cut-off) so that a solute of interest is better retained. Concentration polarization refers to the reversible build-up of solutes near the membrane surface. Concentration polarization can lead to irreversible fouling by altering interactions between the solvent, solutes and membrane. 

Major problems inherent in general applications of RO systems have to do with (1) the presence of particulate and colloidal matter in feed water, (2) precipitation of soluble salts, and (3) physical and chemical makeup of the feed water. All RO membranes can become clogged, some more readily than others. This problem is most severe for spiral-wound and hollow-fiber modules, especially when submicron and colloidal particles enter the unit (larger particulate matter can be easily removed by standard filtration methods). A similar problem is the occurrence of concentration-polarization, previously discussed for ED processes. Concentration-polarization is caused by an accumulation of solute on or near the membrane surface and results in lower flux and reduced salt rejection. 

Polarization can be divided into activation polarization and concentration polarization , Activation polarization is an electrochemical reaction that is controlled by the reaction occurring on the metal-electrolyte interface. Figure 4-418 illustrates the concept of activation polarization where hydrogen is being reduced over a zinc surface. Hydrogen ions are adsorbed on the metal surface they pick up electrons from the metal and are reduced to atoms. The atoms combine to... 

Concentration polarization is an electrochemical process controlled by the diffusion within the electrolyte. 

Figure 4-419 illustrates the concept of corrosion process under concentration polarization control. Considering hydrogen evolution at the cathode, reduction rate of hydrogen ions is dependent on the rate of diffusion of hydrogen ions to the metal surface. Concentration polarization therefore is a controlling factor when reducible species are in low concentrations (e.g., dilute acids). 

Figure 4-419. Concentration polarization during hydrogen reduction. (From Ref. [183].)...

As shown in Fig. 8, three types of polarization exist during the discharge of porous MnOa. The battery active EMD or CMD (chemical manganese dioxide) is highly porous and the concentration polarization due to the pH change, r (ApH), is very important. Kozawa studied the three types of... 

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