Limiting current density resistive

Tertiay Current Distribution. The current distribution is again impacted when the overpotential influence is that of concentration. As the limiting current density takes effect, this impact occurs. The result is that the higher current density is distorted toward the entrance of the cell. Because of the nonuniform electrolyte resistance, secondary and tertiary current distribution are further compHcated when there is gas evolution along the cell track. Examples of iavestigations ia this area are available (50—52). 

The dimensionless limiting current density N represents the ratio of ohmic potential drop to the concentration overpotential at the electrode. A large value of N implies that the ohmic resistance tends to be the controlling factor for the current distribution. For small values of N, the concentration overpotential is large and the mass transfer tends to be the rate-limiting step of the overall process. The dimensionless exchange current density J represents the ratio of the ohmic potential drop to the activation overpotential. When both N and J approach infinity, one obtains the geometrically dependent primary current distribution. 

In general, the membrane resistance Rpem should be considered as a function of as indicated in Equation (6.1). Nonuniform distribution of water in PEMs due to improper water balance can lead to nonlinear effects in Ppem()o)- Under extreme conditions, PEM dehydration on the anode side can give rise to a limiting current density in E(/o). The term 7ccl(/o) = = 0) = ri(,... 

The last part of the polarization curve is dominated by mass-transfer limitations (i.e., concentration overpotential). These limitations arise from conditions wherein the necessary reactants (products) cannot reach (leave) the electrocatalytic site. Thus, for fuel cells, these limitations arise either from diffusive resistances that do not allow hydrogen and oxygen to reach the sites or from conductive resistances that do not allow protons or electrons to reach or leave the sites. For general models, a limiting current density can be used to describe the mass-transport limitations. For this review, the limiting current density is defined as the current density at which a reactant concentration becomes zero at the diffusion medium/catalyst layer interface. 

Mass-transport deposition control occurs when the exchange current density P is high and the limiting current density is low. Ohmic resistance can be a cause of nonuniformity if there is an appreciable difference in solution resistance from the bulk of the solution to peaks or to recesses. Distribution of the current density will be such that ip > i. and peaks will receive a larger amount of deposit than will recesses. Distribution of deposit in the triangular groove under conditions of mass transport and ohmic control nonuniform deposition, with ip > is shown in Figure 10.14. 

Throughput of EL3 (see Table I) is limited almost equally by exposure time (current density/resist sensitivity), mechanical stepping and control system speed. Further improvement will require advances in all areas. 

Figure 10.9 Cowan-Brown plots showing how the limiting current density can be determined by measuring the stack resistance or the pH of the dilute solution as a function of current [22]. Redrawn from R. Rautenbach and R. Albrecht, Membrane Processes, Copyright 1989. This material is used by permission of John Wiley Sons, Ltd...

Exceeding the limiting current density in practical applications of electrodialysis can affect the efficiency of the process severely by increasing the electrical resistance of the solution and causing water dissociation, which leads to changes of the pH values ofthe solution causing precipitation of metal hydroxide on the membrane surface. 

We assumed here a solution of medium conductivity, and yet arrived at an ohmic potential drop of less than 1 mV at the very large current density of 0.8 A/cm. Thus, using an ultramicro electrode extends the range of measurable current densities because (a) the limiting current density is inversely proportional to the radius and (b) the resistivity is proportional to the radius. More concisely, we could say that both the diffusion-limited current density and the conductivity are inversely proportional to the radius. 

As usual, a numerical example will help to illustrate the advantage of ultramicro electrodes, from the point of view of solution resistance. In Section 27.2 we obtained a limiting current density of 0.8 A/cm for an electrode having a radius of 0.25 pm, in a 10 mM solution. If we assume a specific resistivity p of 40 Q cm, the solution resistance R, ... 

The cost data of Katz and Volckman were used as a basis for illustrating the approximate effects of membrane polarization, limiting current density, cost, operating life, and resistance of membranes, and temperature on the over-all costs of demineralization of water with electrodialysis. The major objective was to pinpoint the problem areas needing greatest research effort and to show the probable effect of solving these problems upon the cost of demineralization. 

This analysis of individual costs making up the total cost of demineralization by electrodialysis helps to pinpoint the areas needing the greatest research effort. The costs are based on two published cost estimates, revised on a comparable basis for a 2,000,000-gallon-per-day plant. These studies indicate that development of methods to reduce concentration polarization within the compartments offers the best means of reducing the cost of demineralization by electrodialysis, not only because the limiting current density might be increased, but also because of the reduction in resistance that occurs when concentration polarization is eliminated. 

Heteropolyacid-modified silica-Nafion membranes showed suitable properties for operation at 145°C in direct methanol fuel cell. Since the cell resistance is similar to that of Nafion-silica membrane and the main improvement in polarization is observed at high current density, it is thought that the excellent oxygen solubility characteristics at the electrode/PWA interface are responsible for the significantly higher limiting current density. 

Microflora can form an inhibiting film on the membrane surface. This film increases the membrane s surface resistance and decreases the limiting current density. 

The electrolyte resistivity increases with the decrease of the H2SO4 concentra-ti(Mi (Fig. 3.8c). In this way, the ohmic potential drop becomes more significant. The polarization curves lose their S shape and become more straight Unes. The limiting current density plateau is not so weU pronounced, and it becomes shorter as the / values increase. Finally, the plateau of the limiting diffusion current density disappears at very large electrode edge-side waU distances. This is illustrated for / = 50 mm. 

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