Local Diffusion Convective Impedance

The nonsteady part of the mass balance equation (13.12) may be written as  

The spatial dependence of the sinusoidal perturbation is evident in the definition 

As contains a dependence on the space coordinates, it is necessary to derive first the local solution. A solution in the form of a series can be obtained as 

For this solution the number of terms that play a role in the series increases with the frequency. Generally the solution given by equation (13.25) is used for the low-frequency solution, and the high-frequency solution is derived by another method. 

with the dimensionless frequency K, - given by equation (13.23). (Taken from Delouis et 

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The dimensionless impedance of a small electrode can be defined by summing the effects of die local convective-diffusion impedance, i.e.. 

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