Other One-Dimensional Electrode Geometries

Thus far we have considered only the case of planar macroelectrodes. Although these are widely used for electrochemical experiments, they have some drawbacks mainly due to the distorting effects arising from their large capacitance and ohmic drop. In addition, mass transport in linear diffusion is quite inefficient such that in the case of fast homogeneous and heterogeneous reactions, the response is diffusion-limited and therefore it does not provide kinetic information. 

In both cases, we normalise the spatial coordinate against the radius of 

Note that the simulation space is now constrained to the region 1 i 1 + VTmax, R = 0 is the point at the centre of the electrode (its interior) so naturally the simulation space begins at i = 1 (r = rg), the electrode surface. The time is likewise normalised against the radius  

If we turn now to the discretisation of Pick s second law, the use of the second-order central difference approximation for the first derivative leads to 

Taking into account the above definitions and following the procedure detailed in Chapter 3, we obtain the following expressions for the a, jd and 7 coefficients for the Thomas algorithm of species j  

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