Concentration polarization effects

The theoretical approach by Samec based on the ion-free compact layer model established that the true apparent transfer coefficient is obtained after correction for concentration polarization effect [1] [see Eq. (14)]. Subsequent studies by Samec and coworkers on the ferricyanide-Fc system provided values of a smaller than the expected 0.5. Preliminary attempts to rationalize this behavior were based on defining effective interfacial charges and separation distance between reactants [79]. The inconclusive trends reported in these studies were ascribed to complications arising from ion pairing of the ferro/ferricyanide ions. Later analysis of the same system appeared to show that k i is... 

Equation (4) states that the linear deposition rate vj is a diffusion controlled boundary layer effect. The quantity Ac is the difference in foulant concentration between the film and that in the bulk flow and c is an appropriate average concentration across the diffusion layer. The last term approximately characterizes the "concentration polarization" effect for a developing concentration boundary layer in either a laminar or turbulent pipe or channel flow. Here, Vq is the permeate flux through the unfouled membrane, 6 the foulant concentration boundary layer thickness and D the diffusion coefficient. 

Figure 4. The correction for concentration polarization effects. Parent solution was 50 g/L at pH 13.0. Stirrer rates varied from 350 to 510 rpm, transmembrane pressure ranged from 34 to 207 kP0.

I. Rubinstein, Concentration polarization effects upon the counterion selectivity of an ion-exchange membrane with differing counterion distribution coefficients, J. Chem. Soc., Faraday Trans., 86 (1990), pp. 1857-1861. 

In any process, if one component is enriched at the membrane surface, then mass balance dictates that a second component is depleted at the surface. By convention, concentration polarization effects are described by considering the concentration gradient of the minor component. In Figure 4.3(a), concentration polarization in reverse osmosis is represented by the concentration gradient of salt, the minor component rejected by the membrane. In Figure 4.3(b), which illustrates dehydration of aqueous ethanol solutions by pervaporation, concentration polarization is represented by the concentration gradient of water, the minor component that preferentially permeates the membrane. 

In coupled transport and solvent dehydration by pervaporation, concentration polarization effects are generally modest and controllable, with a concentration polarization modulus of 1.5 or less. In reverse osmosis, the Peclet number of 0.3-0.5 was calculated on the basis of typical fluxes of current reverse osmosis membrane modules, which are 30- to 50-gal/ft2 day. Concentration polarization modulus values in this range are between 1.0 and 1.5. 

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. 

Concentration polarization in gas separation processes has not been widely studied, and the effect is often assumed to be small because of the high diffusion coefficients of gases. However, the volume flux of gas through the membrane is also high, so concentration polarization effects are important for several processes. 

Membrane processes offer an alternative approach to natural gas dehydration and are being developed by a number of companies. Membranes with intrinsic selectivities for water from methane of more than 500 are easily obtained, but because of concentration polarization effects, actual selectivities are typically about 200. Two possible process designs are shown in Figure 8.33. In the first... 

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...

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... 

Figure 10.11 Comparison of the theoretical energy consumption and the actual energy consumption of electrodialysis desalination systems. Most of the difference results from concentration polarization effects [24]...

The limiting current density is determined by concentration-polarization effects at the membrane surface in the diluate containing compartment that in turn is determined by the diluate concentration, the compartment design, and the feed-flow velocity. Concentration polarization in electrodialysis is also the result of differences in the transport number of ions in the solution and in the membrane. The transport number of a counterion in an ion-exchange membrane is generally close to 1 and that of the co ion close to 0, while in the solution the transport numbers of anion and cations are not very different. 

Investment costs in electrodialysis with bipolar membranes Investment costs include nondepreciable items such as land and depreciable items such as the electrodialysis stacks, pumps, electrical equipment, and monitoring and control devices. The investment costs are determined mainly by the required membrane area for a certain plant capacity. The required membrane area for a given capacity plant can be calculated from the current density in a stack that is in electrodialysis with a bipolar membrane not limited by concentration-polarization effects. The required membrane area for a given plant capacity is given by ... 

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... 

The positive effect of velocity on the permeate flux is a result of enhanced hydrodynamic effects at the membrane surface, since high velocities lead to high shear and turbulent flow, which results in the formation of vortices and eddies that minimize the concentration polarization effects and the development of a fouling layer. The bigger the thickness of this layer, the higher its flow resistance and the smaller the permeate flux through the membrane becomes. Under turbulent flow conditions, shear effects induce hydrodynamic diffusion of the particles from the boundary layer back into the bulk, with a positive effect on the permeate flux. 

As in the case of all membrane separation processes, the choice of an appropriate module type is based on feed type (viscosity, suspended solids content, and particle size), required membrane packing density (based on flux, total throughput, and available floor space), good flow hydrodynamics (for minimization of concentration polarization, effective cleaning and sanitation), and module cost. The various types of membrane modules and their fabrication have been reviewed by Strathmann.f Hollow fiber modules, which have the highest membrane packing density of all module types, are the most suitable for use in OD because of the inherently low flux of this process. However, the membranes that have provided the best fluxes and volatiles retention because of their relatively large pore diameters and porosities, that is those fabricated from PTFE, have not yet become available in hollow fibers with an acceptably low wall thickness. 

An effect not considered in the above models is the added resistance, caused by fouling, to solute back-diffusion from the boundary layer. Fouling thus increases concentration polarization effects and raises the osmotic pressure of the feed adjacent to the membrane surface, so reducing the driving force for permeation. This factor was explored experimentally by Sheppard and Thomas (31) by covering reverse osmosis membranes with uniform, permeable plastic films. These authors also developed a predictive model to correlate their results. Carter et al. (32) have studied the concentration polarization caused by the build-up of rust fouling layers on reverse osmosis membranes but assumed (and confirmed by experiment) that the rust layer had negligible hydraulic resistance. 

The true measure of the dynami c layer s selectivity, is the intrinsic salt rejection, Rint However, due to concentration polarization effects caused by the large volume flow through the membrane, one actually measures Robs> He apparent salt rejection, given by the relation... 

The effect of osmotic pressure in macromolecular ultraflltra-tlon has not been analyzed in detail although many similarities between this process and reverse osmosis may be drawn. An excellent review of reverse osmosis research has been given by Gill et al. (1971). It is generally found, however, that the simple linear osmotic pressure-concentration relationship used in reverse osmosis studies cannot be applied to ultrafiltration where the concentration dependency of macromolecular solutions is more complex. It is also reasonable to assume that variable viscosity effects may be more pronounced In macromolecular ultra-filtration as opposed to reverse osmosis. Similarly, because of the relatively low diffuslvlty of macromolecules conqiared to typical reverse osmosis solutes (by a factor of 100), concentration polarization effects are more severe in ultrafiltration. 

Almost all cross-flow filtration processes are inherently susceptible to flux decline due to membrane fouling (a time-dependent phenomenon) and concentration polarization effects which reflect concentration buildup on the membrane surface. This means lower flux (i.e., product output) which could drive the capital costs higher due to the requirement of a larger surface area to realize the desired production rate. In some situations, the lower flux could also result in lower selectivity which means reduced recoveries and/or incomplete removal of impurities from the filtrate. For example, removal of inhibitory metabolites such as lactic acid bacterial or separation of cells from broth while maximizing recovery of soluble products. 1 1... 

This behavior has been explained by the so-called tubular pinch effect, which enhances movement of particles away from the boundary layer thus reducing concentration polarization effect (see Sec. 3.3). 

Concentration of Solute or Particle Loading. It is essential to distinguish or separate the effects of membrane fouling from concentration polarization effects. 

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