Current-distribution

The distribution of impedance eilong the surface of an electrode greatly complicates the interpretation of the resulting spectra. Such an impedance distribution may result from a variation of surface properties caused, for example, by differences of grain orientation in a polycrystalline material, residual stresses associated with fabrication, or nonuniform distributions of surface films. A distribution of impedance may also be attributed to the current and potential distributions associated with the electrode geometry. 

The uncertainty associated with the interpretation of the impedance response can be reduced by using an electrode for which the current and potential distribution is uniform. There are two types of distributions that can be used to guide electrode design. As described in Section 5.6.1, the primary distribution accounts for the influence of Ohmic resistance and mass-transfer-limited distributions account for the role of convective diffusion. The secondary distributions account for the role of kinetic resistance which tends to reduce the nonuniformity seen for a primary distribution. Thus, if the primary distribution is uniform, the secondary 

Remember 8.2 Impedance measurements are sensitive to nonuniform surface reactivity, which may he caused by surface heterogeneities, nonuniform mass transfer, or geometry-induced current and potential distributions. 

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Simulations about Eddy Current Distributions and Crack Detection Algorithms for a SQUID Based NDE System. 

In contrast to a direct injection of dc or ac currents in the sample to be tested, the induction of eddy currents by an external excitation coil generates a locally limited current distribution. Since no electrical connection to the sample is required, eddy current NDE is easier to use from a practical point of view, however, the choice of the optimum measurement parameters, like e.g. the excitation frequency, is more critical. Furthermore, the calculation of the current flow in the sample from the measured field distribution tends to be more difficult than in case of a direct current injection. A homogenous field distribution produced by e.g. direct current injection or a sheet inducer [1] allows one to estimate more easily the defect geometry. However, for the detection of technically relevant cracks, these methods do not seem to be easily applicable and sensitive enough, especially in the case of deep lying and small cracks. 

In this paper we present simulations and measurements of several types of excitation coils, which match the special requirements for a SQUID based eddy current NDE system. We note however that all calculations presented here on penetration depths, current distributions and crack-detecting algorithms are also useful for conventional eddy current testing systems. 

We have perfomied some simulations of the eddy current distribution in a test object for a spiral coil and a circular one (see Fig. 4.1). Both coils had 9 turns and the excitation current was 6 mA. Figs. 4.1 show the cross section of the sample at the location of the crack and the amplitude of the eddy current density. One observes a 1.5 higher current density at the sides of the crack for the case of the circular coil. 

JW. Enquire, WE. Deeds, and CV. Dodd. Alternating current distribution between planar conductors. Journal of Applied Physics, 41(10) 3983-3991, September 1970. C. De Mol M. Bertero and E.R. Pike. Linear inverse problems with discrete data. li. stability and regularization. Inverse Problems, 4 pp. 573-594, 1987. 

Albery W J 1985 The current distribution on a wall-]et electrode J. Electroanal. Chem. 191 1... 

For practical applicability, several aspects have to be considered such as tire anode material (sacrificial (e.g. zinc) or inert (e.g. Pt/Ti or graphite)), tlie conductivity of tlie medium and tlie current distribution. Catliodic protection is typically used for buried constmctions (e.g. pipelines), off-shore stmctures or ship hulls. 

Fig. 2. Induction heating cod and load showing (a), current distribution in load, and (b), reference depth.

When a battery produces current, the sites of current production are not uniformly distributed on the electrodes (45). The nonuniform current distribution lowers the expected performance from a battery system, and causes excessive heat evolution and low utilization of active materials. Two types of current distribution, primary and secondary, can be distinguished. The primary distribution is related to the current production based on the geometric surface area of the battery constmction. Secondary current distribution is related to current production sites inside the porous electrode itself. Most practical battery constmctions have nonuniform current distribution across the surface of the electrodes. This primary current distribution is governed by geometric factors such as height (or length) of the electrodes, the distance between the electrodes, the resistance of the anode and cathode stmctures by the resistance of the electrolyte and by the polarization resistance or hinderance of the electrode reaction processes. 

Cell geometry, such as tab/terminal positioning and battery configuration, strongly influence primary current distribution. The monopolar constmction is most common. Several electrodes of the same polarity may be connected in parallel to increase capacity. The current production concentrates near the tab connections unless special care is exercised in designing the current collector. Bipolar constmction, wherein the terminal or collector of one cell serves as the anode and cathode of the next cell in pile formation, leads to gready improved uniformity of current distribution. Several representations are available to calculate the current distribution across the geometric electrode surface (46—50). 

Fig. 8. Representation of the current distribution in porous electrodes showing the effect of conductivities of the electrolyte and electrodes where for (a)...

Laplace s equation is appHcable to many electrochemical systems, and solutions are widely available (8). The current distribution is obtained from Ohm s law... 

The distribution of current (local rate of reaction) on an electrode surface is important in many appHcations. When surface overpotentials can also be neglected, the resulting current distribution is called primary. Primary current distributions depend on geometry only and are often highly nonuniform. If electrode kinetics is also considered, Laplace s equation stiU appHes but is subject to different boundary conditions. The resulting current distribution is called a secondary current distribution. Here, for linear kinetics the current distribution is characterized by the Wagner number, Wa, a dimensionless ratio of kinetic to ohmic resistance. 

For large Wa, the current distribution is uniform. For example, when electroplating (qv) an object, usually a uniform deposit is desirable. Equation 35 suggests that a larger piece, ie, low Wa, would be more difficult to plate uniformly than a smaller one. 

As the Nemst equation suggests, concentration variations in the electrolyte lead to potential differences between electrodes of the same kind. These potential differences are concentration polarizations or concentration overpotentials. Concentration polarizations can also affect the current distribution. Predicting these is considerably more difficult. If concentration gradients exist, equations 25 and 27 through 29 must generally be solved simultaneously. 

Charge Transport. Side reactions can occur if the current distribution (electrode potential) along an electrode is not uniform. The side reactions can take the form of unwanted by-product formation or localized corrosion of the electrode. The problem of current distribution is addressed by the analysis of charge transport ia cell design. The path of current flow ia a cell is dependent on cell geometry, activation overpotential, concentration overpotential, and conductivity of the electrolyte and electrodes. Three types of current distribution can be described (48) when these factors are analyzed, a nontrivial exercise even for simple geometries (11). 

Seconday Current Distribution. When activation overvoltage alone is superimposed on the primary current distribution, the effect of secondary current distribution occurs. High overpotentials would be required for the primary current distribution to be achieved at the edge of the electrode. Because the electrode is essentially unipotential, this requires a redistribution of electrolyte potential. This, ia turn, redistributes the current. Therefore, the result of the influence of the activation overvoltage is that the primary current distribution tends to be evened out. The activation overpotential is exponential with current density. Thus the overall cell voltages are not ohmic, especially at low currents. 

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). 

Scale- Up of Electrochemical Reactors. The intermediate scale of the pilot plant is frequendy used in the scale-up of an electrochemical reactor or process to full scale. Dimensional analysis (qv) has been used in chemical engineering scale-up to simplify and generalize a multivariant system, and may be appHed to electrochemical systems, but has shown limitations. It is best used in conjunction with mathematical models. Scale-up often involves seeking a few critical parameters. Eor electrochemical cells, these parameters are generally current distribution and cell resistance. The characteristics of electrolytic process scale-up have been described (63—65). 

Electrolytic plating rates ate controUed by the current density at the metal—solution interface. The current distribution on a complex part is never uniform, and this can lead to large differences in plating rate and deposit thickness over the part surface. Uniform plating of blind holes, re-entrant cavities, and long projections is especiaUy difficult. 

A problem that affects the accuracy of the prediction of plating thickness is in estimating the actual current density. Current is not evenly distributed over the surface of the part being plated, rather, it takes the path of least resistance. Current also concentrates on sharper points, corners, and edges even the shape of the plating tank can have an influence on the current distribution. The difference in current and, subsequendy, the plate thickness distribution, is minimal when geometrically conforming anodes are part of the system, but this condition is not often achieved. 

The requirements with respect to current distribution and anode placement vary with the resistivity of soils or the electrolyte involved. 

In a d.c. system the current distribution through the cross-section of a current-canying conductor is uniform as it consists of only the resistance. In an a.c. system the inductive effect caused by the induced-electric field causes skin and proximity effects. These effects play a complex role in determining the current distribution through the cross-section of a conductor. In an a.c. system, the inductance of a conductor varies with the depth of the conductor due to the skin effect. This inductance is further affected by the presence of another current-carrying conductor in the vicinity (the proximity effect). Thus, the impedance and the current distribution (density) through the cross-section of the conductor vaiy. Both these factors on an a.c. system tend to increase the effective... 

If there is more than one current-carrying conductor other than of the same phase, placed adjacent to each other, so that the electric field produced by one can link the other, mutual induction will take place. The magnitude of this will depend upon the amount of current and the spacing between the two. This tends to further distort the selfresistance of the conductor over and above the distortion already caused by the skin effect current distribution... 

Figure 28.18 Current distribution in round conductors, illustrating the effect of proximity...

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