Channel and tubular electrodes

In these electrode configurations, the solution moves past the electrodes embedded in the wall of a tube or channel. It turns out, as is to be expected, that for high Schmidt numbers (thin diffusion layer) the mass transport in the appropriate dimensionless variables is virtually identical for both electrodes. 

Laminar fluid flow in tubes has been described by Levich [ 3 ]. An entry length, le, is necessary to establish Poiseuille flow, given approximately by 

Making the assumption of a thin diffusion layer compared with the tube radius, we approximate 

Analogously to rotating electrodes, we take p = 1 for the upstream of two electrodes (generator) and p = 3 for the downstream (detector). Since, in electrochemical experiments, radial diffusion will be much less than axial convection, we can say that 

This equation is of exactly the same form as the dimensionless convective-diffusion equation at the RDE (p. ). Furthermore, in dimensionless 

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For use with tubular and channel electrodes (Fig. 8), no extra special... 

EC reactions at tubular and channel electrodes have been considered [208]. An analytical solution is not possible due to the non-uniformly accessible nature of the electrode. However, an approximate equation for the half-wave potential can be written, for a reduction, as... 

There is no absolute distinction in the literature between flow cells and channel electrodes. We shall say here that a flow cell contains a tubular electrode (often termed an annulus), while a channel electrode system contains a flat (or occasionally curved) electrode. Figure 7.6 shows a typical flow cell with an annular electrode. In contrast, the channel electrode illustrated in Figure 7.7 is flat and embedded inside a rectangular cavity. 

The aims of this chapter are to suggest that the channel (or tubular) electrode meets the criteria, set out above, more successfully than the other available hydrodynamic electrodes and to illustrate, by way of practical examples, that the channel electrode and channel electrode methodology can be applied to the study of a diverse range of electrochemical and other interfacial phenomena. By way of introduction, we will firstly consider the channel electrode in the light of the preceding criteria before proceeding with more detailed discussion. 

CO = rotation speed (rad s-1) Vf = volume flow rate (cm3 s 1 ) rT = radius of wall-tube U = linear velocity of solution (cm s 1 ) 0 = angle between cone surface and rotation axis x = length of tubular/channel electrode w = width of channel electrode d — width of channel h = half-height of channel co = rotation speed of solution (rad s 1) co" = rotation speed of rotating disc (rad s-1). 

The construction of tubular electrodes may be divided into two basic types integral and demountable. Channel electrodes are only of the latter type. Final dimensions must satisfy the entry length criterion for Poiseuille flow (pp. 370 and 372). 

The electrochemical impedance may be obtained from potentiostatic or galvanostatic experiments. Alternating current voltammetric techniques are well documented at the DME, as are various kinds of pulse techniques. The former has also been developed at rotating and tubular/channel electrodes. 

Convection terms commonly crop up with the dropping mercury electrode, rotating disk electrodes and in what has become known as hydrodynamic voltammetry, where the electrolyte is made to flow past an electrode in some reproducible way (e.g. the impinging jet, channel and tubular flows, vibrating electrodes, etc). This is discussed in Chap. 13. 

This chapter is concerned with channel electrodes, which have their origins in the latter concept, forced convection being employed as a variable, by moving the solution over a stationary electrode embedded in the wall of a channel. The aim of the chapter is to show that, of the presently available hydrodynamic systems, the channel electrode (or the closely related tubular electrode) is the most satisfactory in the study of a diverse range of electrochemical and other interfacial problems. 

Fig. 2. Co-ordinate system for (a) the channel electrode and (b) the tubular electrode.

Elbicki etal. 984) reviewed the optimum configurations for each of the above electrodes (thin-layer, tubular, and wall-jet) based on a mathematical treatment of the diffusive and convective phenomena in force. Boundary conditions on such physical restraints as electrode area, cell dimensions, and inlet configuration were established. Some confusion in the past has resulted from misinterpreting these equations (Weber, 1983) they are derived for cells in which the boundary layer may freely grow unencumbered. In certain cells (e.g., low-volume wall-jet or long-channel electrodes), walls, nozzles, etc. may impede the growth of the diffusion layer and bias the output current expected. Under these conditions, the wall-jet electrode behaves virtually as a thin-layer cell (if the nozzle spacing is small and the nozzle acts as a point source). Both detectors were concluded to yield output currents of... 

The characteristics of the fluid velocity depend on the design of the hydrodynamic cell and the flow pattern. The latter is said to be laminar when the solution flows smoothly and constantly in parallel layers such that the predominant velocity is that in the direction of the flow. Laminar flow conditions are desirable since accurate descriptions of the solution hydrodynamics are available. On the other hand, under turbulent flow conditions the solution motion is chaotic and the velocities in the directions perpendicular to that of the flow are significant. The transition between the laminar and turbulent regimes is defined in terms of the dimensionless Re5molds number, Re, that is proportional to the relative movement rate between the electrode and solution, and the electrode size, but inversely proportional to the kinematic viscosity of the solution. Thus, for low Re values the flow pattern is laminar and it transits to turbulent as Re increases. For example, in a tubular channel the laminar regime holds for Re < 2300. 

Cell Design Albery and coworkers [9-14] used tubular electrodes for ex situ electrochemical EPR experiments. The tubular electrode is equivalent to the channel electrode in all respects, except that the cross section is circular rather than rectangular [82, 137]. Like the later-developed channel flow cell, this setup (shown in Fig. 23) permits the interrogation of electrode reaction mechanisms of relatively long-lived radical species, [9-14] since the convective-diffusion equations are mathematically well defined, which at steady state are given by Eq. (37)... 

In bioanalytical practice the channel systems and tubular electrodes seem to be more useful. Such equipment can be easily attached to a reaction vessel (e.g., fermentation kettle) like a through-flow (bypass) tubing. A general computational approach [73] to the simulation of current-time transients was applied to double-potential step chronoam-perometry at a single-channel electrode. 

Some ISEs containing no inner reference solution, as well as tubular potentiometric sensors, has been used in conjunction with FI systems for the determination of vitamins B, and Bg in pharmaceutical preparations. The membranes used for this purpose were prepared from the vitamin tetra(2-chlorophenyl)borate dissolved in o-nitrophenyloctyl ether and immobilized in PVC. The intrinsic behaviour of the tubular electrodes was assessed by using a low-dispersion single-channel FI manifold and compared with those of conventionally-shaped electrodes using the same membrane the results provided by both were very similar [119]. 

The detector cell was a three-electrode system consisting of a flow-through nickel working electrode, a saturated calomel reference electrode (SCE), and a stainless steel outlet tubing counter electrode. The tubular-type electrode cell housing was constructed of molded Teflon, which was machined to provide the channels and to accommodate the fittings. The working electrode area was... 

Channel and tubular electrodes have been studied in detail without making the assumption of a fast homogeneous reaction [196]. Solution was obtained numerically, but the approximate equation... 

Radicals are generated at a tubular electrode and are then transported by laminar flow into the ESR cavity which, as a downstream detector, is analogous to a second electrode. The theoretical response for the cases where the radicals are stable or decompose by first- or second-order kinetics has been derived and experimentally confirmed [126, 301, 302]. The flow-rate dependence is different for each of the three situations which provides a diagnostic for the type of kinetics. Further information may be obtained from galvanostatic transients which allow the elucidation of electrode and radical surface processes [303]. Very recently, an in situ channel tube electrode has been described for electrochemical ESR which also allows shorter-lived species to be observed and smaller surface coverages to be analysed [304—306]. 

Voltammetry experiments are occasionally undertaken in the form of a tubular or rectangular channel through which the electrolyte solution is pumped at a more or less constant velocity. The electrode may form the channel itself or be embedded in the wall of an inert material, which defines the flow pattern. Sometimes the channel is packed with small particles of electrode material in contact with each other. The latter situation is designed to improve the conversion efficiency of the cell. When all the electroactive molecules are converted during passage through such a porous bed, the efficiency is 100% and the cell is said to be operating coulometrically (see Sec. IV.F). 

SOFC can be manufactured in different geometrical configurations, i.e. planar, tubular or monolithic. Regardless of the geometrical configuration, a solid oxide fuel cell is always composed of two porous electrodes (anode and cathode), a dense electrolyte, an anodic and a cathodic gas channel and two current collectors. For the sake of simplicity the planar configuration is taken as reference, as shown in Figure 3.1. 

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