Current Distribution Problems

Current distribution problems are usually classified according to the rate-limiting process ... 

Current distribution problems are often categorized according to the process that limits or determines the current and potential distribution (1,6). 

It would not be unreasonable to include through-holes in printed wiring boards in the scope of feature-scale current distribution problems. In through-hole plating. 

Perhaps the first numerical investigation of lithographically patterned electrodeposition was published by Alkire et al. [46]. In this work, the finite-element method was used to calculate the secondary current distribution at an electrode patterned with negligibly thin insulating stripes. (This is classified as a secondary current distribution problem because surface overpotential effects are included but concentration effects are not.) Growth of the electrodeposit was simulated in a series of pseudosteady time steps, where each node on the electrode boundary was moved at each... 

Consider current-distribution problem discussed in example 6.5. Redo this problem using the methodology described in section 10.1.3. Hint the node spacing in y changes as a function. 

In the majority of the Laplace equation solutions, the electrical potential, subject to appropriate boundary conditions, is determined. These primary or secondary current-distribution problems may appear to be particularly relevant for electrodeposition, where useful deposit properties are obtained at small fractions of the limiting current. However, the fact that industry has paid considerable attention to fluid flow in reactor design suggests that flow effects can be important, even at a relatively small fraction of the limiting current density. ... 

T. Pastore, P. Pedeferri, L. Bertolini, F. Bolzoni, Current distribution problems in the cathodic protection of reinforced-concrete structures , Proc. Int. RILEM Conference Rehabilitation of Concrete Structured, Melbourne, 189-200, 1992. 

The FEM and the FDM are the most used numerical methods to solve current distribution problems. Pioneers are J.A. Klingert et al. [ 6o] and R.N. Fleck et al. [ 4.2], using the finite difference method (19 4) and R. Alkire et al. [ 7] using the finite element method (1978). More recent papers were presented by Clerc and Landolt [ 63] and Martin et al. [ 69]. 

Some Soviet mathematicians (under V.T. Ivanov [ 52]) used the "method of straight lines" to solve several current distribution problems. This method consists in a reduction of the Laplace equation to a system of ordinary differential equations by approximating the differentials in one dimension with finite differences. This method can also be considered as a particular WRM but its applicability is limited. 

Up till now, the potentialities of the boundary element method were little used for current distribution problems. 

This chapter deals only with the particular aspects of the boundary element method used in two-dimensional and axisymmetric current distribution problems. 

Regardless of the method used to discretize the current distribution problem, a non-linear system of equations is obtained that can be written under the form... 

In this work we applied the boundary element method for the solution of many current distribution problems in electrochemical systems, including electrode shape change simulations. 

Moreover, the reduced number of unknowns needed (here max 75) permits the use of smaller computers giving accurate results within an acceptable time. Indeed, all the calculations ran on a HP-1000 21MX/E(196K) minicomputer and with this configuration a current distribution problem takes maximum ten minutes. 

A Survey of Numerical Methods and Solutions for Current Distribution Problems". 

Because of the complex geometries and the nonlinear boundary conditions involved in the current distribution problems, there are few analytical solutions. The primary concurrent distribution profiles for various geometries have been calculated and tabulated in an excellent series of papers by Kojima [8,9] and Klingert et al. [10]. Prentice and Tobias [11] reviewed current distribution problems solved by numerical methods in the literature. The finite difference method and the finite element method are widely used for determining current distribution profiles. 

Of related interest, Ramachandran and coworkers have reported a range of papers on the influence of mass transport [154-156], including diffusion-reaction problems [157]. Further work was reported on a variety of current distribution problems [158-161] in the early 1990s, with a comparison of the FEM and the BEM efficiency reported by Matlosz and coworkers [162]. A two-dimensional study of coplanar auxiliary electrodes was reported by Mehdizadeh and coworkers [163] and was used to assess the influence of the electrode configuration on uniform growth over the cathode electrode. Electroplating and corrosion protection in industrial cell configurations have also been addressed by Druesne and coworkers [164,165]. 

There have been a number of systems developed to detect current distribution problems and a few have been applied across electrowinning and electrorefming operations for a variety of metals. The most eommon methods include infra-red imaging, cell voltage monitoring, and hand held gauss and individual cathode current measurement devices. 

Figure 1. Use of handheld thermal device to scan electrowinning cell contacts for signs of current distribution problems ... 

The real importance of current distribution problems in impedance measurements, however, lies in the fact that the distribution is frequency-dependent. This arises because of the influence of interfacial polarization combined with the geometrical aspects of the arrangement. 

The question of the frequency dependence of the current distribution and its effect on the measured impedance of a solid state electrochanical system has been hardly considered, although it is important in discussing the impedance of, for example, porous gas electrodes on anion conductors, of rough electrodes (discussed below), and also perhaps of polycrystalline materials. In aqueous electrochemical situations the effects has been considered with respect to the rotating disk electrode, where there may be severe current distribution problems. 

It is recognized that porosity or roughness of the electrode surface could be expected to lead to a frequency dispersion of the interfacial impedance even in the absence of detailed considerations of the current distribution problems as outlined above. 

Prentice GA, Tobias CW (1982) A survey of numerical methods and solutions for current distribution problems. J Electrochem Soc 129(l) 72-78... 

Cahan BD, Scherson D (1988) I-BIEM. An iterative boundary integral equation method for computer solutions of current distribution problems with complex boundaries - a new algorithm. I. Theoretical. J Electrochem Soc 135 285-293... 

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