Transport concentration polarization

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. 

The huge literature on the electronic conductivity of dry conducting polymer samples will not be considered here because it has limited relevance to their electrochemistry. On the other hand, in situ methods, in which the polymer is immersed in an electrolyte solution under potential control, provide valuable insights into electron transport during electrochemical processes. It should be noted that in situ and dry conductivities of conducting polymers are not directly comparable, since concentration polarization can reduce the conductivity of electrolyte-wetted films considerably.139 Thus in situ conductivities reported for polypyrrole,140,141 poly thiophene,37 and poly aniline37 are orders of magnitude lower than dry conductivities.15... 

For isolating the overpotential of the working electrode, it is common practice to admit hydrogen to the counter-electrode (the anode in a PEMFC the cathode in a direct methanol fuel cell, DMFC) and create a so-called dynamic reference electrode. Furthermore, the overpotential comprises losses associated with sluggish electrochemical kinetics, as well as a concentration polarization related to hindered mass transport ... 

Polarization is produced by the slow rate of at least one of the partial processes in the overall electrode process. If this rate-controlling step is a transport process, then concentration polarization is involved if it is the charge transfer reaction, then it is termed charge transfer polarization, etc. Electrode processes are often classified on this basis. 

Concentration Polarization As a reactant is consumed at the electrode by electrochemical reaction, there is a loss of potential due to the inability of the surrounding material to maintain the initial concentration of the bulk fluid. That is, a concentration gradient is formed. Several processes may contribute to concentration polarization slow diffusion in the gas phase in the electrode pores, solution/dissolution of reactants/products into/out of the electrolyte, or diffusion of reactants/products through the electrolyte to/from the electrochemical reaction site. At practical current densities, slow transport of reactants/products to/from the electrochemical reaction site is a major contributor to concentration polarization ... 

Concentration Polarization The rate of mass transport to an electrode surface in many cases can be described by Pick s first law of diffusion ... 

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. 

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). 

As the redox reactions proceed, the availability of the active species at the electrode/electrolyte interface changes. Concentration polarization arises from limited mass transport capabilities, for example, limited diffusion of active species to and from the electrode surface to replace the reacted material to sustain the reaction. Diffusion limitations are relatively slow, and the buildup and decay take >10 s to appear. For limited diffusion the electrolyte solution, the concentration polarization, can be expressed as... 

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. 

Here we are concerned with applying the same model and optical methods to analyze (1) the influence of applied pressure on intrinsic compaction, and (2) aqueous solution effects on Intrinsic transport parameters and concentration polarization. 

Assuming that the concentration polarization, pressure drop and back mixing are negligible, module model can be expressed simply in terms of the transport equation and the material balance of each component. 

When the voltage is critical, regime b), there is no concentration polarization because the electrophoretic transport is equal to the convective transport. Any build up of species on the membrane will be dissipated due to diffusion driven by the concentration difference. In this regime, increasing the tangential velocity is expected to have no influence on the flux because fluid shear can only improve the transport of particles down a concentration gradient. In this case, there is no concentration gradient. 

In Figure 50, the lower curve for E=3.9 v/cm shows a transition in slope. The flux decreases with decreasing Reynolds numbers until a point is reached where the convective transport of particles toward the membrane is just equal to the electrophoretic migration away from the membrane-i.e. the voltage is now the critical voltage. Further decreases in the Reynolds number will not decrease the flux as there is now no concentration polarization. 

Different versions of the above calculations, carried out for particular ionic contexts, form the basis of numerous studies of the ion-selective membrane transport, starting with classical papers by Teorell [7], and Meyer and Sievers [8]. Without attempting to give a full or merely fair account of all these studies, we shall mention here just a typical few Schlogl [5] (arbitrary number of ions in a monopolar membrane), Spiegler [9] (am-bipolar ionic transport in a unipolar membrane and solution layers adjacent to it — concentration polarization), Oren and Litan [10], Brady and Turner [11], Rubinstein [12] (multipolar transport in a unipolar membrane and the adjacent solution layers—effects of concentration polarization upon... 

The lithium polymer battery (LPB), shown schematically in Fig. 7.21, is an all-solid-state system which in its most common form combines a lithium ion conducting polymer separator with two lithium-reversible electrodes. The key component of these LPBs is the polymer electrolyte and extensive work has been devoted to its development. A polymer electrolyte should have (1) a high ionic conductivity (2) a lithium ion transport number approaching unity (to avoid concentration polarization) (3) negligible electronic conductivity (4) high chemical and electrochemical stability with respect to the electrode materials (5) good mechanical stability (6) low cost and (7) a benign chemical composition. 

In deriving eqn. (80), limitations due to mass transport at the interface were not considered. Strictly speaking, this is not realistic and as the reaction rate increases with overpotential in each direction a variation of the concentrations of reactant and product at the surface operates and concentration polarization becomes more important. Each exponential expression in eqn. (80) must be multiplied by the ratio of surface to bulk concentrations, ci s/ci b. The effect of mass transfer in electrode kinetics has been discussed in Sect. 2.4. 

Two approaches have been used to describe the effect of concentration polarization. One has its origins in the dimensional analysis used to solve heat transfer problems. In this approach the resistance to permeation across the membrane and the resistance in the fluid layers adjacent to the membrane are treated as resistances in series. Nothing is assumed about the thickness of the various layers or the transport mechanisms taking place. 

Figure 4.2 Fluid flow velocity through the channel of a membrane module is nonuniform, being fastest in the middle and essentially zero adjacent to the membrane. In the film model of concentration polarization, concentration gradients formed due to transport through the membrane are assumed to be confined to the laminar boundary layer...

In Equation (4.9) the balance between convective transport and diffusive transport in the membrane boundary layer is characterized by the term JvS/Di. This dimensionless number represents the ratio of the convective transport Jv and diffusive transport Dj/8 and is commonly called the Peclet number. When the Peclet number is large (./ 5>> D,/S), the convective flux through the membrane cannot easily be balanced by diffusion in the boundary layer, and the concentration polarization modulus is large. When the Peclet number is small (Jv <5C D,/8), convection is easily balanced by diffusion in the boundary layer, and the concentration polarization modulus is close to unity. 

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. 

The book starts with a series of general chapters on membrane preparation, transport theory, and concentration polarization. Thereafter, each major membrane application is treated in a single 20-to-40-page chapter. In a book of this size it is impossible to describe every membrane process in detail, but the major processes are covered. However, medical applications have been short-changed somewhat and some applications—fuel cell and battery separators and membrane sensors, for example—are not covered at all. 

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. 

Figure 9.10 Hydrogen pressure drop due to depletion, concentration polarization, surface effects, transport in the palladium membrane and porous support, compared to the total hydrogen partial pressure drop, (a) H2 N2 = 50 50 (b) H2 N2 C02 = 50 25 25 ...

This effect, usually known as feed-side concentration polarization, may become particularly relevant for solutes with a high sorption affinity towards the membrane, which may lead to its depletion near the membrane interface if external mass-transfer conditions are not sufficiently good to guarantee their fast transport from the bulk feed to the interface [32, 36] (see Figure 11.3). As a consequence of their depletion near the interface the driving force for transport, and the resulting partial fluxes, become lower. 

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