Types of current distributions

Introducing some mathematical notations (fig. 1.14 ) the potential model and its boundary conditions can be summarized as follows  

This problem is a linear elliptic partial differential equation with, in general, non-linear boundary conditions. 

We know that the current and the potential distribution depend on  

It is clear that in many applications not all of these factors are to be taken into account. This results in a classification of current distributions. 

Mainly, primary, secondary and tertiary distributions can be distinguished. 

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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. 

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). 

The primary current distribution represents the distribution resulting solely from resistance to current flow in the electrolyte. Since temperature and concentration variations as well as overpotential are neglected, this type of current distribution is usually easy to calculate. 

Type of current distribution Nature of the overpotential Important parameters ... 

It is possible conceptually to distinguish three types of current distribution, depending upon the nature of the overpotential (Table 2.4). 

Figure 9.9 illustrates a typical plot of current density distribution across the GDE width for various types of nickel net structures. With a current supply to the back of the electrode structure there is no limitation, in principle, placed on the electrode size, at least from the point of view of current distribution. However, size limitations still... 

Vonnegut and Neubauer (24E), using liquids of low conductivity, have produced two types of droplet distributions by means of high voltage 5000 volts direct current produces a uniform stream of droplets of 100 micron diameter at the rate of about 100 per second. A cloud of fine particles which are so uniform in size that Tyndall spectra are apparent, is also produced. 

On the other hand, the selectivity of the electrochemical deposition of the metal on the substrate must be 100% of the current efficiency, with no interference from the other metal deposition processes. Therefore, the potential distribution needs to be presented for any serious electrochemical reactor study and the electrocatalyst selection problem. The major problem of current distribution depends on the type of the process that controls the entire reaction rate, such as charge transfer, ohmic contributions, or mass transport to or from the electrode. Many parameters have to be evaluated in the course of an electrochemical process to obtain the desired uniform potential and current distributions. One of the conditions that has to be fulfilled is the continuity equation for the current density vector, j ... 

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. 

The phenomenon uneven distribution of current within the same conductor due to the inductive effect is known as the skin effect and results in an increased effective resistance of the conductor. The ratio of a.c. to d.c. resistance, R JR. is the measure of the skin effect and is known as the skin effect ratio . Figure 28.13(a) illustrates the skin elTect for various types and sizes of aluminium in flat sections. For easy reference, the skin effects in isolated round (solid or hollow) and channel conductors (in box form) are also shown in Figures 28.13(b) and (c) respectively. 

Factors that are important for the limitation of protected areas are the pipe network structure, degree of mesh, number of service pipes, type of pipe connections, quality of the pipe coating and availability of protection current as well as stray current effects. A protected area in a distribution network is shown in Fig. 10-11 with separate parts of the network (NT I to NT IV). Previous experience has shown that protected areas of 1 to 2 km with lengths of pipeline from 10 to 20 km are advantageous [30],... 

Electrical power distribution within an industrial installation is most often at a voltage up to and including 33 kV. This section describes the types of cable suitable for power circuits for use up to 33 kV and considers the factors, which will influence the current-carrying capacity of such cables. 

Impressed-current systems for power stations are somewhat more sophisticated than those required for pipelines or marine structures inasmuch that a large number of items of plant, with a wide range of current requirements, are protected by one transformer-rectifier. Each section of every water box in order to provide even current distribution requires one or more anodes. In the case of a large circulating water pump as many as 30 anodes may be required to provide the current distribution necessary. Three types of system should be considered as follows ... 

Impressed current systems are normally based upon anodes of silicon iron, platinised titanium or platinised niobium. The method of anode installation is usually by suspension. The anode configuration and number must be such as to ensure uniform current distribution. Considerable use is made of wire-type platinised-titanium, and niobium anodes which offer minimal weight and relative ease of mounting/suspension. 

If an electric current flows through a wire, ihe heat generated internally will result in a temperature distribution between the central axis and the surface of the wire. This type of problem will also arise in chemical or nuclear reactors where heat is generated internally. It is necessary to determine the temperature distribution in such a system and the maximum temperature which will occur. 

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