The Nernst diffusion layer and dimensionless variables

It will, in most simulations, be advantageous to transform the given equation variables into dimensionless ones. This is done by expressing them each as a multiple of a chosen reference value, so that they no longer have dimensions. The time variable t, for example, becomes the dimensionless T via the relation 

To illustrate this and, incidentally, to introduce the important and useful concept of S, the diffusion layer thickness, we shall introduce here the diffusion-controlled potential-step experiment. 

Imagine a long thin tube, bounded at one end by an electrode and filled with electrolyte and an electroactive substance initially at concentration Cj (b for bulk )/ as in Fig. 2.3. We place the electrode at X = 0 and the other, counter-electrode, at a large distance so that 

This classical equation with these conditions has an analytical solution for c  

In electrochemical experiments, we usually want the current or, since it is related simply by Eq. 2.9 to 3c/3x at x = 0, we want (3c/3x)q. This 

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