Polarisation concentration

Membrane processes are used to accomplish a separation since the membrane has the ability to transport one component more readily than another. For convenience, let us consider a solution consisdng of a solvent and a solute as commonly found in pressure-driven membrane processes such as roiciofiltraiion, ultrafUtration and reverse osmosis. When a driving force acts on the feed solution, the solute is (partly) retained by the. membrane whereas the solvent permeates through the membrane. Thus, the membrane has a certain retentivity for the solute while the solvent can permeate more or less freely. This implies that the concentration of the solute in the penneate(Cp) is lower than the concemrarion in the bulk (c, ). which is in fact the basic concept of membrane separations. This is shou n in figure Vn - 3. 

The retained solutes can accumulate at the membrane surface where their concentration wiir gradually increase. Such a concentration build-up will generate a diffusive flow back to the bulk of the feed, but after a given period of time steady-state conditions will be established. The convective solute flow to the membrane surface will be balanced b the solute flux through the membrane plus the diffusive flow from the membrane surface to the bulk (it should be remembered that only concentration polarisation phenomena are considered here with fouling being, excluded). A concentration profile has now been established in the boundary layer (see figure VII - 4). 

se that the flow conditions in the feed are such that at a distance 5 from the membrane surface complete mixing still occurs (concentration Cj,). However, near the membrane surface a boundary layer is formed where the concentration increases and 

The radoof the diffusion coefficient D and the thickness of the boundary layer 5 is called 

The ratio c ,/ci, is called the concentration polarisation modulus. This ratio increases (i.e. the concentration c at the membrane surface increases) with increasing flux J, with increasing retention Ri , and with decreasing mass transfer coefficient k. 

For simplicity, the following discussion is confined to pure hydrogen as the fuel. Thus, equation (6) reduces to 

Transport of gaseous species usually occurs by binary diffusion, where the effective binary diffusivity is a function of the fundamental binary difiiisivity -HaO. and microstructural parameters of the anode [3, 4]. In electrode microstructures with very small pore sizes, the possible effects of Knudsen diffusion, adsorption/desorption and surface diffusion may also be present. The physical resistance to the transport of gaseous species through the anode at a given current density is reflected as an electrical voltage loss . This polarisation loss is known as concentration polarisation, and is a function of several parameters, given as 

In terms of physically measurable parameters, analytical expressions for anodic concentration polarisation have been derived which allow its explicit determination as a function of a number of parameters. One of the important parameters is the anode-limiting current density, which is the current density at which the partial pressure of the fuel, e.g. Ha, at the anode/electrolyte interface, is near zero such that the cell is starved of fuel. If this condition is realised during operation, the voltage precipitously drops to near zero. This anode-limiting current density, ias, has the following form [6] 

Note that as the current density approaches the anode limiting current density, that is when i — the first term approaches infinity. The maximum value of is limited by the OCV. Thus, the maximum achievable current density will always be less than i s. The dependence of the anodic concentration polarisation given by equation (10) on various parameters can be qualitatively described as follows From the standpoint of physical dimensions, and microstructural parameters, the lower the volume fraction porosity, the higher the tortuosity factor, and the greater the anode thickness, the higher is From the standpoint of fuel gas composition, the lower the partial pressure of hydrogen, the higher is the The temperature dependence is 

As stated earlier, the process of gaseous transport through porous electrodes is not describable by first order kinetics nevertheless a characteristic time constant can be approximated by  

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Zembura has made specific use of the rotating disc for investigation of the effect of flow on corrosion reactions. This work has shown that it is possible to determine the type of control (activation or concentration polarisation) of zinc dissolving in 0.1 N Na2S04 (de-aerated), which followed closely the predicted increase in hydrogen ion reduction as the flow rate increased, and proved that in this example... 

Dissolved oxygen reduction process Corrosion processes governed by this cathode reaction might be expected to be wholly controlled by concentration polarisation because of the low solubility of oxygen, especially in concentrated salt solution. The effect of temperature increase is complex in that the diffusivity of oxygen molecules increases, but solubility decreases. Data are scarce for these effects but the net mass transport of oxygen should increase with temperature until a maximum is reached (estimated at about 80°C) when the concentration falls as the boiling point is approached. Thus the corrosion rate should attain a maximum at 80°C and then decrease with further increase in temperature. 

The work of Porter et al. has shown that for copper in phosphoric acid the interfacial temperature was the main factor, and furthermore this was the case for positive or negative heat flux. Activation energies were determined for this system they indicated that concentration polarisation was the rate-determining process, and by adjustment of the diffusion coefficient and viscosity for the temperature at the interface and the application of dimensional group analysis it was found that ... 

Oxygen from the atmosphere, dissolved in the electrolyte solution provides the cathode reactant in the corrosion process. Since the electrolyte solution is in the form of thin films or droplets, diffusion of oxygen from the atmosphere/electrolyte solution interface to the solution/metal interface is rapid. Moreover, convection currents within these thin films of solution may play a part in further decreasing concentration polarisation of this cathodic process . Oxygen may also oxidise soluble corrosion products to less soluble ones which form more or less protective barriers to further corrosion, e.g. the oxidation of ferrous species to the less soluble ferric forms in the rusting of iron and steel. 

Gas separation Hollow-fibre for high-volume applications with low-flux, low-selectivity membranes in which concentration polarisation is easily controlled (nitrogen from air) Spiral-wound when fluxes are higher, feed gases more contaminated, and concentration polarisation a problem (natural gas separations, vapour permeation). 

Concentration polarisation fouling control Poor Good Moderate Good Very good... 

Two other major factors determining module selection are concentration polarisation control and resistance to fouling. Concentration polarisation control is a particularly important issue in liquid separations such as reverse osmosis and ultrafiltration. Hollow-fine-fibre modules are notoriously prone to fouling and concentration polarisation and can be used in reverse osmosis applications only when extensive, costly feed solution pretreatment removes all particulates. These fibres cannot be used in ultrafiltration applications at all. 

S. Yao, A. G. Fane, J. M. Pope 1997, (An investigation of the fluidity of concentration polarisation layers in crossflow membrane filtration of an oil-water emulsion using chemical shift selective flow imaging), Mag. Reson. Imag. 15, 235. 

Polarisation Absent Complete concentration polarisation Minimisation/compensation... 

Permeabilities measured for pure gases can serve as a rough guide for selection of membrane materials. For design, data must be obtained on gas mixtures, where selectivities are often found to be much lower than those calculated from pure-component measurements. This effect is often due to plasticisation of the membrane by sorption of the most soluble component of the gas. This allows easier penetration by the less-permeable components. The problem of concentration polarisation, which is often encountered in small-scale flow tests, may also be responsible. Concentration polarisation results when the retention time of the gas in contact with the membrane is long. This allows substantial depletion of the most permeable component on the feed side of the membrane. The membrane-surface concentration of that component, and therefore its flux through the membrane, decreases. 

The membrane selectively rejects oxygen and nitrogen. The field test showed a selectivity for chlorine over nitrogen of about ten. That this is so much lower than that obtained in the laboratory is attributed to concentration polarisation. Increasing the rate of flow through the module can alleviate this. At the same time, chlorine recovery can be maintained by adding modules in series. This is precisely what would be done in a commercial unit, and so one can reasonably expect better results in full-scale operation. 

Levich VG. The theory of concentration polarisation. Acta Phy-sicochim URSS 1942 17(5-6) 257-307. 

The thermodynamic approach does not make explicit the effects of concentration at the membrane. A good deal of the analysis of concentration polarisation given for ultrafiltration also applies to reverse osmosis. The control of the boundary layer is just as important. The main effects of concentration polarisation in this case are, however, a reduced value of solvent permeation rate as a result of an increased osmotic pressure at the membrane surface given in equation 8.37, and a decrease in solute rejection given in equation 8.38. In many applications it is usual to pretreat feeds in order to remove colloidal material before reverse osmosis. The components which must then be retained by reverse osmosis have higher diffusion coefficients than those encountered in ultrafiltration. Hence, the polarisation modulus given in equation 8.14 is lower, and the concentration of solutes at the membrane seldom results in the formation of a gel. For the case of turbulent flow the Dittus-Boelter correlation may be used, as was the case for ultrafiltration giving a polarisation modulus of ... 

Figure 8.18. Schematic representation of concentration polarisation with demineralisation of the central...

Porter, M. C. Ind. Eng. Chem. Prod. Res. Develop, 11 (1972) 234. Concentration polarisation with membrane ultrafiltration. 

The reactions marked with an asterisk ) lead to lower effidences. (The conversion of ferrous to ferric, Eq. 6.8, usually takes place because of dissolved oxygen.) In order for the bath composition to remain constant, the rate of dissolution (Eq. 6.7) must equal the rate of deposition (Eq. 6.9). If they do not occur at the same rate this will lead to concentration polarisation which will act as a barrier to the electrode reactions. We have seen previously (Section 6.2) that ultrasound is able to reduce concentration polarisation. 

In ultrafiltration and reverse osmosis, in which solutions are concentrated by allowing the solvent to permeate a semi-permeable membrane, the permeate flux (i.e. the flow of permeate or solvent per unit time, per unit membrane area) declines continuously during operation, although not at a constant rate. Probably the most important contribution to flux decline is the formation of a concentration polarisation layer. As solvent passes through the membrane, the solute molecules which are unable to pass through become concentrated next to the membrane surface. Consequently, the efficiency of separafion decreases as fhis layer of concentrated solution accumulates. The layer is established within the first few seconds of operation and is an inevitable consequence of the separation of solvent and solute. 

The ultrafiltration of the microemulsion is a very useful operation for separating water and oil in these mixtures [117-120]. Because of the limited availability of solvent stable membranes, most of the work pubHshed so far was performed using ceramic membranes, which show a high adsorption of surfactant at the membrane surface and comparably low rejection rates of reverse micelles. Using electro ultrafiltration, where the concentration polarisation phenomenon of the reverse micelles (using the ionic surfactant AOT) at the membrane surface is depressed by asymmetric high voltage electrical fields, the rejection rates can be increased,but not to economical values [121,122]. 

The change of flux velocity with transmembrane pressure can be explained by the concentration polarisation phenomenon. The physical processes at the membrane surface during the filtration procedure may be described by theo-... 

Although less discussed in the technical and scientific literature, permeate-side concentration polarisation may also become a problem when using thin selective films that require macroporous supports for mechanical stability [13]. 

This type of diffusion/reaction mechanism has been treated semi-analyti-cally by Albery et al. [42, 44, 45], under steady-state conditions and its applications to amperometric chemical sensors has been described by Lyons et al. [46]. In both models, only diffusion and reaction within a boundary layer is considered, while the effect of concentration polarisation in the solution is neglected. Thus, to apply the model to an experimental system it is necessary to be able to accurately determine the concentration of substrate at the polymer/solution interface. Assuming that the system is in the steady state, the use of the rotating disc electrode allows simple determination of the substrate concentration at the interface from the bulk concentration and the experimentally determined flux using [47]... 

Case / No concentration polarisation within the polymer layer In case I, the diffusion within the layer is fast, hence, as soon as the product is produced it diffuses out of the film. Thus, there is virtually no product in the layer and the concentration of substrate is uniform throughout the film. This is only valid when the film is thin (e< 1) and... 

To test the validity of our model, it is necessary to determine expressions for the current from equations (2.5)-(2.8) which are applicable across the case boundaries. These expressions are given in Table 2.3. We can then analyse the experimental data using the appropriate expression. Since these equations do not include concentration polarisation in the solution, equations (2.4) and (2.15) are used to determine the concentrations of NADH and NAD+ at the solution/film interface. The case, or cases, that the experimental data span are determined by inspection and using Table 2.2. Non-linear least squares fitting was used to fit the experimental data to the appropriate equations. The resulting best-fit parameters are critically... 

There have been many models, both simple and sophisticated, that describe the operating patterns of ultrafiltration processes [4]. Most of these models describe how the rate of ultrafiltration is controlled by the properties of a region of very high solute concentration, a filter cake or concentration polarised layer, close to the membrane surface. Relatively few of these models have a genuinely predictive capability. Remarkably, only a very few [5-7] of these models consider the most important feature of the solutes being separated by ultrafiltration—that they fall in the colloidal size range. For colloidal materials, the properties of the filter cake or concentration polarised layer will be controlled by the interparticle interactions in such a region. The important interactions which need to be taken into account are [8] ... 

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