Electrode axisymmetric

With an axisymmetric electrode (like a disk or ring) only y and/or Fr are involved in the mass balance equation. Hence, according to Eq. (2-4) or (2-11) only the F variations are useful for mass transfer measurements. 

A uniformly accessible electrode is an electrode where, at the interface, the flux and the concentration of a species produced or consumed on the electrode are independent of the coordinates that define the electrode surface. The mass flux at the interface is obtained by solving the material balance equation. If migration can be neglected, the material balance equation for dilute electrol5 c solutions is reduced to the convective-diffusion equation. For an axisymmetric electrode, the concentration derivatives with respect to the angular coordinate 9 are equal to zero, and the convective-diffusion equation can be expressed in cylindrical coordinates as... 

With its axisymmetric transport and current distribution, the rotating hemispherical electrode complements the rotating disk as a tool for studying electrode processes. Der-Tau Chin provides a valuable overview and summary of the fundamental theory and applications of this interesting device. 

Microcylindrical electrodes are easier to constract and maintain than microdisk electrodes [37]. Mass transport to a stationary cylinder in quiescent solution is governed by axisymmetrical cylindrical diffusion. For square-wave voltammetry the shape and position of the net current response are independent of the extent of cyhn-drical diffusion [38]. The experiments were performed with the ferri-ferrocyanide couple using a small platinum wire (25 pm in diameter and 0.5 -1.0 cm in length) as the working electrode [37]. 

In the conventional EM flowmeter, point electrodes are used in a circular pipe. This flowmeter is normally overly sensitive to flow near the two electrodes it may accurately measure flow rate if the magnetic field is uniform and flow is rectilinear (i.e., parallel to the flowmeter axis) and axisymmetric. For a rectilinear, axisymmetric flow, Eq. 6.2 can be written as... 

A non-linear wall-stabilized non-transferred arc is shown in Fig. 4 8. It consists of a cylindrical hollow cathode and coaxial hollow anode located in a water-cooled chamber and separated by an insulator. Gas flow blows the arc column out of the anode opening to heat a downstream material, which is supposed to be treated. In contrast to transferred arcs, the treated material is not supposed to operate as an anode. Magnetic 7x5 forces cause the arc roots to rotate around electrodes (Fig. 4-48), which provides longer electrode lifetime. The generation of electrons on the cathode is provided in this case by field emission. An axisymmetric version of the non-transferred arc, usually referred to as the plasma torch or the arc jet, is illustrated in Fig. 4-49. The arc is generated in a conical gap in the anode and pushed out of this opening by gas flow. The heated gas flow forms a very-high-temperature arc jet, sometimes at supersonic velocities. 

In general the potential distribution in the electrode is also governed by the Laplace equation. But, in two-dimensional and axisymmetrical problems with thin electrodes (e.g. fig. 1.13)> the Laplace equation can be replaced by... 

More exact theory for sphere-cap tips was developed by using digital simulations [29,30]. Selzer and Mandler solved numerically a time-dependent 2D axisymmetric diffusion problem for a sphere-cap electrode [29a]. They used the same approach to develop comprehensive time-dependent and steady-state SECM theory for a hemispherical tip approaching either a conductive or an insulating substrate [29b]. Daniele and coworkers [30] focused on diffusion-controlled steady-state responses and calculated approach curves for a broad range of H and various RG values. For RG= 10, the... 

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