Edge currents

A secondary current distribution in the case of the parallel-plate electrodes brings the edge current density to a finite value. The edge current is still greater than that in the center of the electrode, unless the reactions are slow. The secondary current distribution can be estimated by using the dimensionless Wagner number (15)... 

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An alternative approach is to assume that the radiation from a finite array is associated entirely with the edge currents. While Maxwell s equations do not state specifically that radiation or scattering takes place from neither edges or element tips, it is nevertheless an observation that has proven valuable in classical electromagnetic theory. It is a convenient way to handle scattering properties from perfectly conducting half-planes, strips, wedges, and more, even when made of dielectric. 

The field in the forward sector can basically be obtained approximately by integration of the incident field over the aperture width as discussed in Section 2.9.2. Note, however, that the entire pattern in Fig. 8.1 was obtained from the SPLAT program and therefore is as exact as the method of moments. In other words, the effect of edge currents is rigorously observed. See also Section 8.5. 

When discussing scattering from a parabolic antenna the question is often asked, Did you incorporate the edge currents Our answer is, Certainly ... 

This consideration of the very edge current density can be elaborated mathematically in the following way [5] assuming the total ohmic control, the voltage drop in the solution between the electrodes inside the homogeneous field is given by... 

When Eq. (3.16) is integrated from the inter-electrode distance I to the maximum length of the current line, I, the maximum contribution to the edge current density due to current line propagation between the electrode edges and the side walls of the cell, is obtained as... 

In this way, a part of the ohmic potential drop in a homogeneous field transforms into electrochemical overpotential for points at the plane electrode edges, meaning the edge current density is larger than in the homogeneous field. In this way, it is... 

Assuming that maximum edge current density is given by Eq. (3.38), the substitution of q in Eq. (3.39) instead of 4 and further rearranging produce... 

A secondary current distribution in the case of the parallel-plate electrodes brings the edge current density to a finite value. 

Membrane covered amperometric sensors are also suitable for determining gases. If a disc-shaped working electrode radius is less than about 90 membrane thicknesses, then the edge current causes more than 1% exhibition of the one-dimensional (1-D, planar) component of the current, which is proportional to the electrode area [122]. The 1-D mass flux, JiD, can be calculated from ... 

However, independently of any related technological problems, the radius of an electrode cannot be decreased indefinitely if one wants that the contribution of edge currents remains minimal.Indeed, observation of an undistorted cyclic voltammogram requires that diffusion remains planar, which happens only when the diffusion layer is extremely small as compared to the electrode radius. The diffusion layer thickness being about b = (ttDRT/Fv), for a scan rate v, this imposes that the electrode radius must be larger than this limit rQ (7tDRT/Fv) . ... 

In summary, Fig. 5.19 shows that electrodes with exposed front and rear faces will exhibit significant maldistribution of current. With the small-scale electrolyzers commonly encountered in laboratory studies the effect may be significant and have considerable influence on scale-up. If we look at a typical current distribution on one electrode of an identical pair (Fig. 5.20), this distribution, in what is essentially a poor reactor design, exhibits a virtually constant current over about two-thirds of the front face, but at the edges currents rise to over three times that value. At the rear of the electrode, apart from the edges, there is only a small amount of current flowing. A limiting case of this analysis is when the electrodes are embedded into the rear wall, i.e., S = d. 

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