Stationary planar electrode

In addition, the Reynold, Schmidt, Rayleigh (iJa), and Grashof (Gr) numbers are empirically defined by 

An electrowinning cell can be treated as an open channel (open top) with an equivalent diameter as the characteristic length, which depends on the geometry of the aoss-sectional area. This diameter is needed for determining the Reynolds Number. In general, this diameter is also known as hydraulic diameter defined as 

For square cross-sectional and rectangular cross-sectional areas, d becomes 

According to Twidwell [2], in most electrowinning cells d = 2x where x is the distance betwem electrodes. In addition, the fluid velocity is defined as 

Recall that Fr is the volume flow rate and it is defined in terms of mass flow rate and density 

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Verbrugge MW, Tobias CW (1985) Triangular current-sweep chronopotentiometry at rotating disk and stationary, planar electrodes. J Electroanal Chem 196 243-259... 

Up until the mid-1940s, most physical electrochemistry was based around the dropping mercury electrode. However, in 1942, Levich showed that rotating a disc-shaped electrode in a liquid renders it uniformly accessible to diffusion, yet the hydrodynamics of the liquid flow are soluble and the kinetic equations relatively simple. In addition, in contrast to the case of a stationary planar electrode, the current at an RDE rapidly attains a steady-state value. 

Electrode Reactions of Dissolved Species on Stationary Planar Electrodes... 

Figure 2.22 shows SWV responses of electrochemically reversible reaction on stationary planar electrodes covered with a thin mercury film ... 

The expressions treated here may be compared with the diffusion layer approximation for the stationary planar electrode mentioned in Sect. 1.2.1. With aQ = Dq2 (ntm) U2 and aR = DR2 (irtm) 1/2 (see Table 1), it follows from eqns. (14) and eqns. (45) and (46) that the approximation is equivalent to the substitution... 

In practice two methods are used for stationary planar electrodes in quiescent solution chronoamperometry and chronopotentiometry. By use of an electroactive species whose concentration, diffusion coefficient, and n value are known, the electrode area can be calculated from the experimental data. In chronoamperometry, the potential is stepped from a value where no reaction takes place to a value that ensures that the concentration of reactant species will be maintained at essentially zero concentration at the electrode surface. Under conditions of linear diffusion to a planar electrode the current is given by the Cottrell equation [Chapter 3, Eq. (3.6)] ... 

Normally, such as at stationary planar electrodes and at uniformly accessible hydrodynamic electrodes, for example the rotating disc, the flux over the electrode surface is constant in this case we have the simple relation... 

Figure 7.1.3 is an illustration of the current-time curves for several drops as predicted by the Ilkovic equation. Immediately apparent is that the current is a monotoni-cally increasing function of time, in direct contrast to the Cottrell decay found at a stationary planar electrode. Thus, the effects of drop expansion (increasing area and stretching of the diffusion layer) more than counteract depletion of the electroactive substance near the electrode. Two important consequences of the increasing current-time function are that the current is greatest and its rate of change is lowest just at the end of the drop s life. As we will see, these aspects are helpful for applications of the DME in sampled-current voltammetric experiments. 

These principles are valid regardless of the electrode employed, as long as semi-infinite linear diffusion can be assumed and renewal of the concentration profile can be accomplished in each cycle. For a stationary planar electrode, the relationships worked out above apply directly. For an SMDE, they apply to the extent that /d,oc is the Cottrell current for an electrolysis of duration r and is not disturbed by the convection associated with the establishment of the drop. For a DME, the picture is complicated by the steady expansion of area, but it turns out (47, 48) that (7.3.8) is still a good approximation if /d,DC is understood as the Ilkovic current for time r [(7.3.1) or (7.3.4)] and the pulse width is short compared to the preelectrolysis time [i.e., (r — r )/ t < 0.05]. 

C) A surface redox reaction (II.3.4) on a stationary planar electrode is represented by the system of differential equations (II.3.15) and (II.3.16), with the following initial and boundary conditions [89] ... 

Fig. III.1.2 1 Gradient of dimensionless concentration dc at the stationary planar electrode surface in a calm solution, and 2 the dependence of the ratio c/c on the dimensionless distance jc/5,...

The basic mass transfer processes of interest are migration, diffusion, and convection. We will examine some simple relations in this section. Detailed treatment is beyond the scope of this book. Initially we consider stationary planar electrodes immersed in an unstirred electrolyte. A general treatment is given by Delahay (1954), and a practical approach by Adams (1969). 

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