Concentration polarization factor

Beta, sometimes called the "concentration polarization factor," is the ratio of the concentration of a species at the membrane surface to that in the bulk solution. Hence, Beta is a way of quantifying concentration polarization. 

Bani-Melhem, K. Using concentration polarization factors to determine the mass transfer resistance in vacuum membrane distillation. 

A quantitative estimate of the importance of concentration polarization can be derived by defining the concentration polarization factor, T, as... 

So, Equation (21.16) and Equation (21.17) can be used to calculate the mass transfer coefficient, k. The concentration polarization factor is calculated from Equation (21.15). The pressure drops in the... 

In a manner similar to nltrafiltration systems, concentration polarization effects need to be accommodated in designing RO systems. The maximum allowable value of the concentration polarization factor is 1.13—1.2as recommended by different RO membrane suppliers. The concentration polarization factor can be defined as the ratio of salt concentration at the membrane surface to the bulk concentration. 

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. 

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). 

The selectivity here is directly proportional to complex formation constants and can be estimated, once the latter are known. Several methods are now available for determination of the complex formation constants and stoichiometry factors in solvent polymeric membranes, and probably the most elegant one is the so-called sandwich membrane method [31], Two membrane segments of different known compositions are placed into contact, which leads to a concentration polarized sensing membrane, which is measured by means of potentiometry. The power of this method is not limited to complex formation studies, but also allows one to quantify ion pairing, diffusion, and coextraction processes as well as estimation of ionic membrane impurity concentrations. 

Schmidt, R. L., Butler, R. S., Goldstein, J. H. The Role of Polar Factors in Collision Complex Models for the Solvent and Concentration Dependence of Nuclear Magnetic Resonance Parameters. J. Phys. Chem. 73, 1117 (1969). 

Summarizing it can be stated that the separation by gas phase transport (Knudsen diffusion) has a limited selectivity, depending on the molecular masses of the gases. The theoretical separation factor is decreased by effects like concentration-polarization and backdiffusion. However, fluxes through the membrane are high and this separation mechanism can be applied in harsh chemical and thermal environments with currently available membranes (Uhlhorn 1990, Bhave, Gillot and Liu 1989). 

A lithium ion transference number significantly less than 1 is certainly an undesired property, because the resultant overwhelming anion movement and enrichment near electrode surfaces would cause concentration polarization during battery operation, especially when the local viscosity is high (such as in polymer electrolytes), and extra impedance to the ion transport would occur as a consequence at the interfaces. Fortunately, in liquid electrolytes, this polarization factor is not seriously pronounced. 

The individual polarization curves for the metals are often modified as a result of interactions resulting from codeposition. If the alloy deposition occurs at low polarization, the nobler metal will be deposited preferentially (Cu in Example 11.1). All factors, however, that increase polarization during electrodeposition, such as high current density, low temperature, and quiescent solution—factors that increase concentration polarization—will favor the deposition of the less noble metal (Zn in Example 11.1). 

The discussion of concentration polarization so far has centred on the depletion of electroactive material on the electrolyte side of the interface. If the metal deposition and dissolution processes involve metastable active surface atoms, then the rate of formation or disappearance of these may be the critical factor in the overall electrode kinetics. Equation (2.69) can be rewritten for crystallization overvoltage as... 

Kinetic factors may induce a variation of electrode potential with current the difference between this potential and the thermodynamic equilibrium potential is known as the overvoltage and the electrode is said to be polarized. In a plating bath this change of potential can be attributed to the reduced concentration of depositing ions in the double layer which reduces the rate of transfer to the electrode, but the dissolution rate from the metal increases. Since the balance of these rates determines the electrode potential, a negative shift in the value occurs the concentration polarization Olconc)- Anodic effects are similar but in the opposite direction. 

Two other major factors determining module selection are concentration polarization control and resistance to fouling. Concentration polarization control is a particularly important issue in liquid separations such as reverse osmosis and ultrafiltration. In gas separation applications, concentration polarization is more easily controlled but is still a problem with high-flux, highly selective membranes. Hollow fine fiber modules are notoriously prone to fouling and concentration polarization and can be used in reverse osmosis applications only when extensive, costly feed solution pretreatment removes all particulates. These fibers cannot be used in ultrafiltration applications at all. 

As a result of these improvements in membrane performance, the major factors determining system performance have become concentration polarization and membrane fouling. All membrane processes are affected by these problems, so... 

Equation (4.9) shows the factors that determine the magnitude of concentration polarization, namely the boundary layer thickness S, the membrane enrichment E0, the volume flux through the membrane. / , and the diffusion coefficient of the solute in the boundary layer fluid >, The effect of changes in each of these parameters on the concentration gradients formed in the membrane boundary layer are illustrated graphically in Figure 4.5 and discussed briefly below. 

The final parameter in Equation (4.9) that determines the value of the concentration polarization modulus is the diffusion coefficient A of the solute away from the membrane surface. The size of the solute diffusion coefficient explains why concentration polarization is a greater factor in ultrafiltration than in reverse osmosis. Ultrafiltration membrane fluxes are usually higher than reverse osmosis fluxes, but the difference between the values of the diffusion coefficients of the retained solutes is more important. In reverse osmosis the solutes are dissolved salts, whereas in ultrafiltration the solutes are colloids and macromolecules. The diffusion coefficients of these high-molecular-weight components are about 100 times smaller than those of salts. 

Figure 4.7 Concentration polarization modulus ciolcih as a function of the Peclet number Jv8/Di for a range of values of the intrinsic enrichment factor E . Lines calculated through Equation (4.9). This figure shows that components that are enriched by the membrane (E0 > 1) are affected more by concentration polarization than components that are rejected by the membrane (E0 < 1) [13]...

Table 4.1 shows typical enrichments and calculated Peclet numbers for membrane processes with liquid feeds. In this table it is important to recognize the difference between enrichment and separation factor. The enrichments shown are calculated for the minor component. For example, in the dehydration of ethanol, a typical feed solution of 96 % ethanol and 4 % water yields a permeate containing about 80 % water the enrichment, that is, the ratio of the permeate to feed concentration, is about 20. In Figure 4.11, the calculated Peclet numbers and enrichments shown in Table 4.1 are plotted on the Wijmans graph to show the relative importance of concentration polarization for the processes listed. 

In the case of pervaporation of dissolved volatile organic compounds (VOCs) from water, the magnitude of the concentration polarization effect is a function of the enrichment factor. The selectivity of pervaporation membranes to different VOCs varies widely, so the intrinsic enrichment and the magnitude of concentration polarization effects depend strongly on the solute. Table 4.2 shows experimentally measured enrichment values for a series of dilute VOC solutions treated with silicone rubber membranes in spiral-wound modules [15], When these values are superimposed on the Wijmans plot as shown in Figure 4.12, the concentration polarization modulus varies from 1.0, that is, no concentration polarization, for isopropanol, to 0.1 for trichloroethane, which has an enrichment of 5700. 

Figure 9.6 Comparative separation factors for toluene and trichloroethylene from water with various rubbery membranes [28]. These experiments were performed with thick films in laboratory test cells. In practice, separation factors obtained with membrane modules are far less because of concentration polarization effects. Reprinted from Nijhuis et al. [28], p. 248 with permission of Bakish Materials Corporation, Englewood, NJ...

Figure 9.6 shows the separation factors measured by Nijhuis et al. [28] for various membranes with dilute toluene and trichloroethylene solutions. The separation factor of silicone rubber is in the 4000-5000 range, but other materials have separation factors as high as 40000. However, in practice, an increase in membrane separation factor beyond about 1000 provides very little additional benefit. Once a separation factor of this magnitude is obtained, other factors, such as ease of manufacture, mechanical strength, chemical stability, and control of concentration polarization become more important. This is why silicone rubber remains prevalent, even though polymers with higher selectivities are known. 

Concentration polarization plays a dominant role in the selection of membrane materials, operating conditions, and system design in the pervaporation of VOCs from water. Selection of the appropriate membrane thickness and permeate pressure is discussed in detail elsewhere [50], In general, concentration polarization effects are not a major problem for VOCs with separation factors less than 100-200. With solutions containing such VOCs, very high feed velocities through... 

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