Rotating disk electrode convective-diffusion equation, solution

Example 2.2 Convective Diffusion Equation The material balance equation near a rotating disk electrode in an electrolyte solution where the migration can be neglected can be written as... 

The classification of models for convective diffusion to a rotating disk electrode may be imderstood in the context of the solution to the steady-state equation (11.3). 

The three-term convective-diffusion model provides the most accurate solution to the one-dimensional convective-diffusion equation for a rotating disk electrode. The one-dimensional convective-diffusion equation applies strictly, however, to the mass-transfer-limited plateau where the concentration of the mass-transfer-limiting species at the surface can be assumed to be both uniform and equal to zero. As described elsewhere, the concentration of reacting species is not uniform along the disk surface for currents below the mass-transfer-limited current, and the resulting nonuniform convective transport to the disk influences the impedance response. ... 

This could be, for example, the RRDE illustrated in Figure 9.4.1 with the disk electrode at open circuit. When this electrode is rotated at an angular velocity, co, the solution flow velocity profile is that discussed in Section 9.3.1. The steady-state convective-diffusion equation that must be solved is... 

The RDE consists of a disk electrode embedded in an insulating rod material as shown in Fig. 14 (44). The composite electrode can be rotated about its axis, which causes electrolyte to be drawn up against, and forced outwards across, the face of the metal disk electrode, as shown in Fig. 15 (45). The convection and diffusion equations that describe solution flow in this situation have been rigorously established making this experimental approach a powerful one for the study of the effects of forced convection of electrochemical reactions. 

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