Final Form of the Basic Equation

With the expressions above, Equation 5.201 finally takes the form 

Formally, Equation 5.216 is a Poisson equation with the right-hand side being the difference of normal current densities coming from/to the catalyst layers. Equation 

216 is strongly nonlinear, as the current densities on the right-hand side exponentially depend on through the respective overpotentials (Table 5.10). However, the largest problem with this equation is the small parameter on the left-hand side. Owing to the smallness of this parameter, an accurate numerical solution of Equation 

In the problem discussed, e = 2.5 10 , and, hence, in Equation 5.201, the second derivative 9 l /9z is multiplied by a very small factor = 6.25 10 . The smallness of e allows obtaining the leading-order solution to Equation 5.216, neglecting the left-hand side of this equation. Setting in Equation 5.216 e = 0, one arrives at 

Validity of this approximation can be checked directly using resulting from Equation 5.217 in Equation 5.216.  

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