Channel electrodes turbulent flow

For both flow cells and channel electrodes, we assume that the electrode is solid and absolutely immobile. Its surface is flush with the surrounding insulator in which it is embedded, thereby inhibiting the incidence of turbulent flow. In addition, the electrode is polished, again to prevent turbulence. 

Convection-based systems fall into two fundamental classes, namely those using a moving electrode in a fixed bulk solution (such as the rotated disc electrode (RDE)) and fixed electrodes with a moving solution (such as flow cells and channel electrodes, and the wall-jet electrode). These convective systems can only be usefully employed if the movement of the analyte solution is reproducible over the face of the electrode. In practice, we define reproducible by ensuring that the flow is laminar. Turbulent flow leads to irreproducible conditions such as the production of eddy currents and vortices and should be avoided whenever possible. 

In this section, the discussion centres on the application of double channel electrodes in the study of electrode reaction mechanisms under conditions of laminar flow. (The modifications necessary to what follows when turbulent flow operates can be found in Sect. 6.2.) When employed in this way, the upstream (generator) electrode produces the species of interest, which is then detected on the downstream electrode. This procedure is illustrated schematically in Fig. 37. In general, the detector electrode is held at a potential at which the destruction of the species produced upstream is diffusion-controlled. Kinetic and mechanistic information about the electrogenerated species is then available from "collection efficiency , N, measurements, given by... 

Mass transport to channel and tubular electrodes under a turbulent flow regime... 

Firstly, the effect of both laminar and turbulent flow regimes is readily investigated, as illustrated in Sects. 6.1 and 6.2, and secondly, direct observation of the electrode area under study may be achieved by incorporating a window in the channel cell, permitting light microscopy. In this way, electrochemical measurements can be linked directly to observable events on the surface, such as metal salt film precipitation and pit growth and death. 

Under the assumptions outlined above, the model predicted the current, potential, and concentration distributions on the channel electrode surface for both laminar and turbulent flow as a function of a dimensionless average current and an average saturation current (where the saturation current is the current when the concentration of metal ions on the dissolving electrode is both uniform and equal to the saturation concentration), defined by the parameters , N, and fsc. describes the magnitude of the ohmic resistance of the solution to the charge-transfer resistance and is given by... 

Fig. 54. Current distribution along the channel electrode surface, as calculated by Alkire and Cangellari [169], for various values of N under (a) laminar and (b) turbulent flow regimes. In the former case, the data are for ( = 100, whilst in the latter, they refer to ( = 300.

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. 

The behavior of the boundary layer discussed in Section 2.2 can be used to obtain a quantitative expression for iV, the diffusional flux of solute 0 to the electrode surface. Let us use again the example from Section 2.2, namely that of a channel formed by two parallel solid electrodes. Figure 2.5 replaces the velocity profile of Fig. 2.1 by a concentration profile at the same location of the electrode for a fully developed turbulent flow. There are three regions a near horizontal portion corresponding to the fully mixed turbulent bulk ... 

An electrochemical reactor containing two concentric cylindrical electrodes (Fig. 2.7), with or without a diaphragm, represents a practical and attractive geometry since it offers a uniform primary current distribution (see Chapter 5). Axial flow through the annular space between the two electrodes, or an electrode and a diaphragm, has characteristics between those of a pipe and a rectangular channel. A theoretical analysis for the condition of laminar or turbulent flow is approached in the same way as that for pipes and channels hence, we merely identify appropriate experimental correlations. 

The description of mass transport to channel and tubular electrodes given in Sect. 2 was restricted to laminar conditions. Once Re > 2000, the pattern of flow is no longer smooth and steady fluctuating, irregular (eddying) motions become superimposed on the main stream. Consequently, a complete theoretical description of mass transport, under such a regime, is impossible [149] and, as a result, empirical methods are introduced. In particular, a simplified representation of turbulence is afforded by consider-... 

In an industrial environment, quite different convective diffusion regimes are employed, and some common examples are illustrated in Fig. 4.2. Most commonly, the electrolyte solution is flowed through a channel between parallel electrodes or an electrode and a separator (case a), although in some cases there are turbulence promoters in the channel (case b). These introduce eddies into the flow, increasing mixing and the rate of mass transfer (see below). In bed electrodes (cases c and d) the particles perform the dual role of electrode and turbulence promoters. The last example (case e) is the rotating cylinder electrode. 

Fig. 4.2 — Convective diffusion regimes commonly found in industrial cells, (a) flow through channel formed by two parallel electrode (or by one electrode and a membrane), (b) flow through such a channel but containing a turbulence promoter (e.g. a set of non-conducting bars or a net), (c) fluidised bed electrode, (d) packed bed electrode, (e) rotating cylinder electrode within a concentric tube.

The modification of hydrodynamic aspects is exploited in the falling-film cell [12], where the electrolyte flows as a thin fllm in the channel between an inclined plane plate and a sheet of expanded metal which work as electrodes. Other proposal is to include turbulence promoters in the interelectrode gap in conventional parallel plate electrochemical reactors [13-16], or the use of expanded metal electrodes immersed in a fluidized bed of small glass beads, called Qiemelec cell [17]. Likewise, the Metelec cell [18] incorporates a cylindrical foil cathode concentric arranged around an inner anode, with a helical turbulent electrolyte flow between the electrodes. The electrochemical hydrocyclone cell [19] makes use of the good mass-transfer conditions due to the helical downward accelerated flow in a modified conventional hydrocyclone. 

Sticking to flow in channels (the characteristics of reactors involving three-dimensional electrodes are considered in Chapter 5), turbulence promoters can be divided into two categories which involve electrochemi-cally inert or active materials. 

The flow in the gas channels and in the porous gas diffusion electrodes is described by the equations for the conservation of momentum and conservation of mass in the gas phase. The solution of these equations results in the velocity and pressure fields in the cell. The Navier-Stokes equations are mostly used for the gas channels while Darcy s law may be used for the gas flow in the GDL, the microporous layer (MPL), and the catalyst layer [147]. Darcy s law describes the flow where the pressure gradient is the major driving force and where it is mostly influenced by the frictional resistance within the pores [145]. Alternatively, the Brinkman equations can be used to compute the fluid velocity and pressure field in porous media. It extends the Darcy law to describe the momentum transport by viscous shear, similar to the Navier-Stokes equations. The velocity and pressure fields are continuous across the interface of the channels and the porous domains. In the presence of a liquid phase in the pore electrolyte, two-phase flow models may be used to account for the interaction between the gas phase and the liquid phase in the pores. When calculating the fluid flow through the inlet and outlet feeders of a large fuel cell stack, the Reynolds-averaged Navier-Stokes (RANS), k-o), or k-e turbulence model equations should be used due to the presence of turbulence. 

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