Reduced System of Equations and Solutions

Ideal ionic transport in the CCL means that the overpotential gradient is small. Setting in the system (4.53H4.55) — i o and omitting Equation 4.54 yields 

Differentiating Equation 4.69 with respect to x and eliminating dc/dx with the help of Equation 4.70, one arrives at 

Using Equation 4.73 here yields the x shape of the oxygen concentration 

By definition, the dimensionless rate of the electrochemical conversion (the ORR rate) is 

the higher rjo, the smaller Id, that is, the conversion domain shrinks with the 

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