Concentration polarization determination

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. 

Chronopotentiometry has been widely used to determine diffusion coefficients in molten salts. Chronopotentiometry is an experimental procedure in which the potential of an electrode is observed as a function of time during the passage of a constant current sufficiently large to produce concentration polarization with respect to the species undergoing electrochemical reaction. 

Electrode reactions are heterogeneous since they occur at interfaces between dissimilar phases. During current flow the surface concentrations Cg j of the substances involved in the reaction change relative to the initial (bulk) concentrations Cy p Hence, the value of the equilibrium potential is defined by the Nemst equation changes, and a special type of polarization arises where the shift of electrode potential is due to a change in equilibrium potential of the electrode. The surface concentrations that are established are determined by the balance between electrode reaction rates and the supply or elimination of each substance by diffusion [Eq. (4.9)]. Hence, this type of polarization, is called diffusional concentration polarization or simply concentration polarization. (Here we must take into account that another type of concentration polarization exists which is not tied to diffusion processes see Section 13.5.)... 

Transient measnrements (relaxation measurements) are made before transitory processes have ended, hence the current in the system consists of faradaic and non-faradaic components. Such measurements are made to determine the kinetic parameters of fast electrochemical reactions (by measuring the kinetic currents under conditions when the contribution of concentration polarization still is small) and also to determine the properties of electrode surfaces, in particular the EDL capacitance (by measuring the nonfaradaic current). In 1940, A. N. Frumkin, B. V. Ershler, and P. I. Dolin were the first to use a relaxation method for the study of fast kinetics when they used impedance measurements to study the kinetics of the hydrogen discharge on a platinum electrode. 

Consider the case when the equilibrium concentration of substance Red, and hence its limiting CD due to diffusion from the bulk solution, is low. In this case the reactant species Red can be supplied to the reaction zone only as a result of the chemical step. When the electrochemical step is sufficiently fast and activation polarization is low, the overall behavior of the reaction will be determined precisely by the special features of the chemical step concentration polarization will be observed for the reaction at the electrode, not because of slow diffusion of the substance but because of a slow chemical step. We shall assume that the concentrations of substance A and of the reaction components are high enough so that they will remain practically unchanged when the chemical reaction proceeds. We shall assume, moreover, that reaction (13.37) follows first-order kinetics with respect to Red and A. We shall write Cg for the equilibrium (bulk) concentration of substance Red, and we shall write Cg and c for the surface concentration and the instantaneous concentration (to simplify the equations, we shall not use the subscript red ). 

When more complex polarization functions are involved, particularly when concentration polarization is superimposed, the values of E and 4 are preferably determined by graphical rather than analytical means. 

In an electrochemical system, gas supersaturation of the solution layer next to the electrode will produce a shift of equilibrium potential (as in diffusional concentration polarization). In the cathodic evolution of hydrogen, the shift is in the negative direction, in the anodic evolution of chlorine it is in the positive direction. When this step is rate determining and other causes of polarization do not exist, the value of electrode polarization will be related to solution supersaturation by... 

The choice of solvent directly influences the retention of the analyte on the sorbent and its subsequent elution, whereas the solvent polarity determines the solvent strength (or ability to elute the analyte from the sorbent in a smaller volume than a weaker solvent). Dean [272] gave solvent strengths for normal- and reversed-phase sorbents. The elution solvent should be one in which the analytes are soluble and should ideally be compatible with the final analysis technique. For example, for HPLC analysis, a solvent similar to the mobile phase is a good choice of elution solvent. For the elution step it is also important to consider the volume of the solvent. A minimum volume of elution solvent (typically 250 xL per 100 mg of sorbent) allows maximum concentration of the analytes. 

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. 

To determine actual cell performance, three losses must be deducted from the Nernst potential activation polarization, ohmic polarization, and concentration polarization. Definition of the ohmic polarization is simply the product of cell current and cell resistance. Both activation polarization and concentration polarization required additional description for basic understanding. 

This chapter will only deal with the possible gas transport mechanisms and their relevance for separation of gas mixtures. Beside the transport mechanisms, process parameters also have a marked influence on the separation efficiency. Effects like backdiffusion and concentration polarization are determined by the operating downstream and upstream pressure, the flow regime, etc. This can decrease the separation efficiency considerably. Since these effects are to some extent treated in literature (Hsieh, Bhave and Fleming 1988, Keizer et al. 1988), they will not be considered here, save for one example at the end of Section 6.2.1. It seemed more important to describe the possibilities of inorganic membranes for gas separation than to deal with optimization of the process. Therefore, this chapter will only describe the possibilities of the several transport mechanisms in inorganic membranes for selective gas separation with high permeability at variable temperature and pressure. 

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. 

Typical curves are shown in Fig. 22 a and b for current and potential steps respectively. For the short times (trate determining step is due to a concentration polarization [78], The variation of the transient current versus ]fi is linear, described satisfactorily by the classical Cottrel-type relation (see Fig. 23). After a certain time which depends on the experimental conditions, mainly the oxygen partial pressure in the surrounding atmosphere, a depolarization effect is observed the V (t) curve shows an overshoot while the I(t) curve shows a net enhancement of current. 

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... 

When the fluid layer mass-transfer coefficient (kM) is large, the resistance Vkbe of this layer is small, and the overall resistance is determined only by the membrane. When the fluid layer mass-transfer coefficient is small, the resistance term 1 /kbb is large, and becomes a significant fraction of the total resistance to permeation. The overall mass transfer coefficient (kov) then becomes smaller, and the flux decreases. The boundary layer mass transfer coefficient is thus an arithmetical fix used to correct the membrane permeation rate for the effect of concentration polarization. Nothing is revealed about the causes of concentration polarization. 

Figure 4.1 shows the concentration gradients that form on either side of a dialysis membrane. However, dialysis differs from most membrane processes in that the volume flow across the membrane is usually small. In processes such as reverse osmosis, ultrafiltration, and gas separation, the volume flow through the membrane from the feed to the permeate side is significant. As a result the permeate concentration is typically determined by the ratio of the fluxes of the components that permeate the membrane. In these processes concentration polarization gradients form only on the feed side of the membrane, as shown in Figure 4.3. This simplifies the description of the phenomenon. The few membrane processes in which a fluid is used to sweep the permeate side of the membrane,...

The increase or decrease of the permeate concentration at the membrane surface cio, compared to the bulk solution concentration c,h, determines the extent of concentration polarization. The ratio of the two concentrations, ciolcib is called the... 

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. 

In the discussion of concentration polarization to this point, the assumption is made that the volume flux through the membrane is large, so the concentration on the permeate side of the membrane is determined by the ratio of the component fluxes. This assumption is almost always true for liquid separation processes, such as ultrafiltration or reverse osmosis, but must be modified in a few gas separation and pervaporation processes. In these processes, a lateral flow of gas is sometimes used to change the composition of the gas on the permeate side of the membrane. Figure 4.14 illustrates a laboratory gas permeation experiment using this effect. As the pressurized feed gas mixture is passed over the membrane surface, certain components permeate the membrane. On the permeate side of the membrane, a lateral flow of helium or other inert gas sweeps the permeate from the membrane surface. In the absence of the sweep gas, the composition of the gas mixture on the permeate side of the membrane is determined by the flow of components from the feed. If a large flow of sweep gas is used, the partial... 

In contrast to the evaluation of critical micelle concentrations the determination of the size of micellar aggregates utilizing the fluorescence depolarization is reasonable as long as the solubilization does not affect the (average) degree of association of the particles and their shapes. Use is made of Perrin s relation164 l96) between the volume V of the micelle and the polarization of light emitted by an immobilized dye molecule p0 and that emitted by the dye solubilized in a micelle p, i.e.,... 

The efficiency of electrodialysis is determined to a large extent by the properties of the membranes. But it is also affected by the process and system design that determine the limiting current density, the current utilization, the concentration polarization and the overall efficiency and costs [20, 21]. 

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