Distribution in Three-Dimensional Electrodes

Three-dimensional electrodes were mentioned in Section 5.1.1.2. Table 5.4 indicates a potential advantage, namely a high space-time yield. Such electrodes differ from their two-dimensional counterparts in the distribution of potential and current density in the matrix of the electrodes. Rigorous analysis would require evaluation of three-dimensional potential distributions. Fortunately this is often unnecessary one-dimensional approximate models or simplified two-dimensional models are sufficient. A comprehensive treatment of three-dimensional electrodes is beyond the scope of the present text (the reader has already been referred to the review in Ref. 5, particularly for information on fluidized bed electrodes. Further information can be found in Refs. 42-44.) We will concentrate on two limiting types of operation of packed-bed electrodes to illustrate the current distributions encountered and their relationship to scale-up. 

FIGURE 5.31. Schematic diagram of packed bed electrode. = potential in the liquid phase, = potential in the particulate phase. 

The total current density i at any cross-section is equal to the sum of current density in the metal phase and current density in the electrolyte phase i/. 

The complexity of Eq. (5.25) depends on the order of the electrochemical reaction and the spatial dependence of the concentration terms. For a first-order reaction you can use a form of the Butler-Volmer Eq. (3.83). We shall use the Tafel approximation, assuming that the reaction is cathodic see Eq. (3.84)  

6 and ij/ are integration constants found by trial and error from  

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From the standpoints of potential, and current, distribution in three-dimensional electrodes, the following comments may be made ... 

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