Current density local

In all cases of localized corrosion, tlie ratio of the catliodic to tlie anodic area plays a major role in tlie localized dissolution rate. A large catliodic area provides high catliodic currents and, due to electroneutrality requirements, tlie small anodic area must provide a high anodic current. Hence, tlie local current density, i.e., local corrosion rate, becomes higher witli a larger catliode/anode-ratio. 

Without coke backfill, the anode reactions proceed according to Eqs. (7-1) and (7-2) with the subsequent reactions (7-3) and (7-4) exclusively at the cable anode. As a result, the graphite is consumed in the course of time and the cable anode resistance becomes high at these points. The process is dependent on the local current density and therefore on the soil resistivity. The life of the cable anode is determined, not by its mechanical stability, but by its electrical effectiveness. 

Failures due to delamination of the gunite coating have been reported in the USA, but have not been observed to any significant extent in F.urope although some early failures of the anode system have been associated with high local current densities in areas of low concrete cover and high moisture or salt contentThe major application of this anode system is therefore on structures that are relatively dry with a uniform current requirement. 

Figure 37. Transform of electrochemical information. J, total current a>, mean current density je local current density A, surface area.

Where contact is made, the local current density is high. The local temperature is also high the carbon will be more highly fluorinated and the resistance to current passage will increase even more (in a positive feedback fashion). 

Porous electrodes are systems with distributed parameters, and any loss of efficiency is dne to the fact that different points within the electrode are not equally accessible to the electrode reaction. Concentration gradients and ohmic potential drops are possible in the electrolyte present in the pores. Hence, the local current density, i (referred to the unit of true surface area), is different at different depths x of the porous electrode. It is largest close to the outer surface (x = 0) and falls with increasing depth inside the electrode. 

For a solution of Eq. (18.12), we must also know the dependence of current density on polarization. First we consider the simpler case of low values of polarization when the linear function (6.6) with p as the kinetic parameter is valid. Solving the dilferential eqnation for these conditions, we arrive at the following expression for the distribntion of local current densities in the electrode in a direction normal to the surface ... 

Curves showing the cnrrent densities as functions of x are presented for two val-nes of electrode thickness in Fig. 18.5. The parameter L has the dimensions of length it is called the characteristic length of the ohmic process. It corresponds approximately to the depth x at which the local current density has fallen by a factor of e (approximately 2.72). Therefore, this parameter can be nsed as a convenient characteristic of attenuation of the process inside the electrode. 

The origin of the ohmic potential difference was described in Section 2.5.2. The ohmic potential gradient is given by the ratio of the local current density and the conductivity (see Eq. 2.5.28). If an external electrical potential difference AV is imposed on the system, so that the current I flows through it, then the electrical potential difference between the electrodes will be... 

Equation (23) implies that the current density is uniformly distributed at all times. In reality, when the entire electrode has reached the limiting condition, the distribution of current is not uniform this distribution will be determined by the relative thickness of the developing concentration boundary layer along the electrode. To apply the superposition theorem to mass transfer at electrodes with a nonuniform limiting-current distribution, the local current density throughout the approach to the limiting current should be known. 

Let us assume that the total surface of an electrode is in an active state, which supports dissolution, prior to anodization. The application of a constant anodic current density may now lead to formation of a passive film at certain spots of the surface. This increases the local current density across the remaining unpassivated regions. If a certain value of current density or bias exists at which dissolution occurs continuously without passivation the passivated regions will grow until this value is reached at the unpassivated spots. These remaining spots now become pore tips. This is a hypothetical scenario that illustrates how the initial, homogeneously unpassivated electrode develops pore nucleation sites. Passive film formation is crucial for pore nucleation and pore growth in metal electrodes like aluminum [Wi3, He7], but it is not relevant for the formation of PS. 

The steady-state condition (/ap=Jps) at the pore tip determines not only the pore diameter but also the pore growth rate. The rate rp of macropore growth can be calculated if the local current density at the pore tip is divided by the dissolution valence nv (number of charge carriers per dissolved silicon atom), the elementary charge e (1.602 xlO-19 C) and the atomic density of silicon Nsi (5xl022 cm-3) ... 

Generally in a nail penetration test, an instantaneous internal short would result the moment the nail is tucked into the battery. Enormous heat is produced from current flow (double layer discharge and electrochemical reactions) in the circuit by the metal nail and electrodes. Contact area varies according to depth of penetration. The shallower the depth, the smaller the contact area and therefore the greater the local current density and heat pro-... 

To expand on the last remark, the simulation results from Fuller and Newman are shown in Figure 17. The curves clearly show a nonuniform current distribution that is mainly due to the change in the gas concentrations and the membrane hydration. In the simulation, the initial decrease in the current density is due to the change in the oxygen concentration. However, once enough water is generated to hydrate the membrane, the increased conductivity yields higher local current densities. What... 

Figure 17. Mole fraction of water vapor, hydrogen, and oxygen in the gas channels at a cell potential of 0.72 V, at a temperature of 80 °C, and in a coflow arrangement. The local current density is shown by the solid line. (Reproduced with permission from ref 15. Copyright 1993 The Electrochemical Society, Inc.)...

Figure 1. Local current density profiles along a straight-channel fuel cell as predicted by the same computer model for two cases differing only in two model parameters. ...

Figure 21. Comparison of local current density distributions in a two-channel serpentine PEFC at Eceii — 0.4...

Figure 22. Local current density profiles along the channel direction for different humidification levels at Ueii = 0.65 V. Anode and cathode stoichiometries are 1.4 at 1.0...

Figure 24. Local current density profiles along the channel direction of single-channel PEFC for different inlet stoichiometric ratios at Keii = 0.65V at the inlet relative humidity 20% cathode and 100% anode at 80...

The effect of inlet stoichiometry on transport characteristics and performance of PEFC was also investigated by Pasaogullari and Wang. In Figure 24 the local current density distributions along the flow direction are displayed at a cell voltage of 0.65 V. As explained earlier, the membrane is hydrated much faster in lower flow rates, and therefore, the performance peak is seen earlier in lower stoichio-... 

To measure the current distribution in a hydrogen PEFC, Brown et al. ° and Cleghorn et al. ° employed the printed circuit board approach using a segmented current collector, anode catalyst, and anode GDL. This approach was further refined by Bender et al. ° to improve ease of use and quality of information measured. Weiser et al. ° developed a technique utilizing a magnetic loop array embedded in the current collector plate and showed that cell compression can drastically affect the local current density. Stumper et al."° demonstrated three methods for the determination of current density distribution of a hydrogen PEFC. First, the partial membrane elec-... 

Detailed validation for low humidity PEFC, where the current distribution is of more interest and likely leads to discovery of optimal water management strategies, was performed most recently. Figure 35 shows a comparison of simulated and measured current density profiles at cell potentials of 0.85, 0.75, and 0.7 V in a 50 cm cell with anode and cathode RH of 75% and 0%. Both experimental data and simulation results display the characteristics of a low humidity cell the local current density increases initially as the dry reactants gain moisture from product water, and then it decreases toward the cathode outlet as oxygen depletion becomes severe. The location of the peak current density is seen to move toward the cathode inlet at the lower cell potential (i.e., 0.7 V) due to higher water production within the cell, as expected. 

In the previous analysis, homogeneous current distribution has been assumed but, on many occasions, corrosion occurs with localized attack, pitting, crevice, stress corrosion cracking, etc., due to heterogeneities at the electrode surface and failure of the passivating films to protect the metal. In these types of corrosion processes with very high local current densities in small areas of attack, anodic and cathodic reactions may occur in different areas of disparate dimensions. 

The most commonly utilized embedded sensor for temperature distribution mapping is the thermocouple. Wilkinson et al.130 developed a simple, in-situ, and noninvasive method of measuring the temperature distribution of a fuel cell with micro-thermocouples. In this study, thermocouples were located in the landing area of the flow field plates (in contact with the GDL of the MEA) of a fuel cell. The temperature data taken at different locations along the flow channel was then used to find each temperature slope, which in turn were related through mathematical equations to the local current density of each location. Thus, the current density distribution in the fuel cell was determined by simple temperature measurements. The results of this approach are discussed in more detail in Section... 

Another method to determine current distribution in a PEM fuel cell was presented by Sun et al.169 in which they designed a current distribution measurement gasket that can be placed anywhere in the fuel cell (usually at the back of the cathode side) and can measure the local current density at various point along the active area of the cell. The advantage of this approach is that it can be used without having to modify any component of the cell. The same technique was also used by Zhang et al.170 to compare the performance of interdigitated and serpentine flow fields. 

As mentioned previously in Section 2.6, Wilkinson et al.130 demonstrated that local temperature measurements at specific experimental conditions correlate well with local current densities determined through other published current density approaches. Then-results suggest that current mapping can be indirectly conducted through local temperature measurements using an array of microthermocouples in the active area. 

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