Mass-Transfer-Controlled Current Distributions

The tertiary current distribution also takes into account the variation of current density when there are significant changes in the concentration of electroactive spedes across the surface the largest variation must occur when the overpoten-tial is so high that the current is mass transfer controlled. 

The rotating disk electrode, described in Section 11.6, has the advantage that the fluid flow is well defined emd that the system is compact and simple to use. The rotation of the disk imposes a centrifugal flow that in turn causes a radially uniform flow toward the disk. If the reaction on the disk is mass-transfer controlled, the associated current density is imiform, which greatly simplifies the mathematical description. As discussed in sections 5.6.1 and 8.1.3, the current distribution below the mass-transfer-limited current is not uniform. The distribution of current and potential associated with the disk geometry has been demonstrated to cause a frequency dispersion in impedance results. The rotating disk is therefore ideally suited for experiments in which the disk rotation speed is modulated while im-der the mass-transfer limited condition. Such experiments yield another t)q)e of impedance known as the electrohydrodynamic impedance, discussed in Chapter 15. 

Another difference between classical electrochemistry and electrochemical engineering lies in the size of the electrode. Conventional electrochemistry most commonly employs micro electrodes of well defined area operating under carefully controlled current and mass transfer conditions. Conversely, electrochemical engineering typically employs large surface area electrodes, where, moreover, the surface area and electrode activity varies constantly as metal is deposited. In addition, there are usually difficulties in maintaining uniform potential control and current distribution over the electrode surface. It is also necessary to consider the reverse stripping process of recovering the metal after collection. 

These MEC experiment were performed in absence of aeration control and it is difficult to define the cathodic reaction from this curve. Nevertheless the curve corresponding to the MAOI containing an IM particle confirms that the cathodic reaction is mainly distributed on the IM particle for such an aluminium alloy (6xxx). The IM particle represents 6 % of the capillary area and the cathodic current is more than 50 times higher, but does not exhibit a mass transfer control which is probably due to the non-controlled aeration of the capillary (see Fig. 6b). 

The dimensionless limiting current density N represents the ratio of ohmic potential drop to the concentration overpotential at the electrode. A large value of N implies that the ohmic resistance tends to be the controlling factor for the current distribution. For small values of N, the concentration overpotential is large and the mass transfer tends to be the rate-limiting step of the overall process. The dimensionless exchange current density J represents the ratio of the ohmic potential drop to the activation overpotential. When both N and J approach infinity, one obtains the geometrically dependent primary current distribution. 

On the submicron scale, the current distribution is determined by the diffusive transport of metal ion and additives under the influence of local conditions at the interface. Transport of additives in solution may be non-locally controlled if they are consumed at a mass-transfer limited rate at the deposit surface. The diffusion of additives in solution must then be solved simultaneously with the flux of reactive ion. Diffusive transport of inhibitors forms the basis for leveling [144-147] where a diffusion-limited inhibitor reduces the current density on protrusions. West has treated the theory of filling based on leveling alone [148], In his model, the controlling dimensionless groups are equivalent to and D divided by the trench aspect ratio. They determine the ranges of concentration within which filling can be achieved. 

In the previous section, the velocity and concentration distributions have been established and two transfer functions were considered. The explicit form of the third function which relates the fluctuating interfacial concentration or concentration gradient to the potential or the current at the interface, requires to make clear the kinetic mechanism composed of elementary steps with at least one of them being in part or wholly mass transport controlled. 

The tertiary current distribution Ohmic factors, charge transfer controlled overpotential effects, and mass transport are considered. Concentration gradients can produce concentration overpotentials. The potential across the electrochemical interface can vary with position on the electrode. 

Therefore let us instead consider the more practical case of the tertiary current distribution. Based on the dependency of the Wagner number on polarization slope, we would predict that a pipe cathodically protected to a current density near its mass transport limited cathodic current density would have a more uniform current distribution than a pipe operating under charge transfer control. Of course the cathodic current density cannot exceed the mass transport limited value at any location on the pipe, as said in Chapter 4. Consider a tube that is cathodically protected at its entrance with a zinc anode in neutral seawater (4). Since the oxygen reduction reaction is mass transport limited, the Wagner number is large for the cathodically protected pipe (Fig. 12a), and a relatively uniform current distribution is predicted. However, if the solution conductivity is lowered, the current distribution will become less uniform. Finite element calculations and experimental confirmations (Fig. 12b) confirm the qualitative results of the Wagner number (4). 

Secondary current distribution [85, 86], Here, mass transfer effects are not controlling, bnt reaction kinetics are considered because of a non-negligible electrode polarization (i.e., electrode reactions that require an appreciable surface overpotential to sustain a high reaction rate). Once again, Laplace s Equation (Equation [26.120]) is solved for the potential distribution, but the boundary condition for O on the electrode surface (y = 0) is given by... 

On the other hand, the selectivity of the electrochemical deposition of the metal on the substrate must be 100% of the current efficiency, with no interference from the other metal deposition processes. Therefore, the potential distribution needs to be presented for any serious electrochemical reactor study and the electrocatalyst selection problem. The major problem of current distribution depends on the type of the process that controls the entire reaction rate, such as charge transfer, ohmic contributions, or mass transport to or from the electrode. Many parameters have to be evaluated in the course of an electrochemical process to obtain the desired uniform potential and current distributions. One of the conditions that has to be fulfilled is the continuity equation for the current density vector, j ... 

If we consider again the equation of charge transfer, but for a mass transport-controlled process, the change in the current distribution at a radius r will be... 

The current distribution, in terms of t>, is illustrated by Fig. 54. Large current densities at the upstream and downstream edges of the electrode result because the potential distribution is controlled by the ohmic resistance (large ), as illustrated in Fig. 53. As the solution velocity is increased (TV, or Nt taking on larger values), the current density over the whole of the electrode surface decreases. Eventually, at a sufficiently high rate of mass transfer, the curent density at all points on the surface is lower than that needed for saturation of the adjacent solution. 

Since the focus of this paper is on pollution control applications of metal recovery, the complex and as yet incompletely told story of the early development of electroplating, surface finishing and early electrowinning techniques will not be discussed further. The development of electrolytic cells for pollution control applications of metal recovery dates from the mid-1960 s when several major advances in electrochemical engineering took place. Advances in potential and current distribution theory, mass transfer processes, coupled with the introduction of new materials, created a stimulus for the introduction of novel cathode designs with improved mass transfer characteristics. 

Current distribution through the electrode which controls the current efficiency Is also dependent on the mass-transfer characteristics of the system and on the control of potential over the working electrode surface. Thus In bulk, porous or three-dimensional electrodes It Is usually mass-transfer characteristics which control most situations. The Nernst diffusion model (Fig. 1) gives a simplified picture of the electrode-solution Interface conditions. This simplified picture, however, does not account for real operating conditions since the stationary diffusion layer thickness Is strongly dependent on the solution flow characterIcs. Most modern hydrodynamic treatments take these factors Into account. 

Davis, Ouwerkerk and Venkatesh developed a mathematical model to predict the conversion and temperature distribution in the reactor as a function of the gas and liquid flow rates, physical properties, the feed composition of the reactive gas and carrier gas and other parameters of the system. Transverse and axial temperature profiles are calculated for the laminar flow of the liquid phase with co-current flow of a turbulent gas to establish the peak temperatures in the reactor as a function of the numerous parameters of the system. Also in this model, the reaction rate in the liquid film is considered to be controlled by the rate of transport of reactive gas from the turbulent gas mixture to the gas - liquid interface. The predicted reactor characteristics are shown to agree with large-scale reactor performance. For the calculations of the mass transfer coefficient in the gas phase, kg, Davis et al. used the same correlation as Johnson and Crynes, but multiplied the calculated values arbitrarily by a factor 2 to include the effect of ripples on the organic liquid film caused by the high SOj/air velocities in the core of the reactor. 

Reaction engineering parameters. The achievement of a correct rate and selectivity of production requires control and uniformity of the potential and current distribution. In turn, very high rates will usually involve a uniformly high mass transport over the electrode, achieved by provision of the required hydrodynamics. The electroactive area per unit reactor volume may need to be high if the available current density is low and a compact design is required. Adequate heat transfer must be available between the reactor and its environment. 

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