Fluxes in a Mixed Proton, Oxygen Ion, and Electron Conductor Revisited

Fluxes in a Mixed Proton, Oxygen Ion, and Electron Conductor Revisited 

In ambipolar diffusion of protons and oxygen ions, the two types of ions move in the same direction for charge compensation, and the net result is permeation of water. If we also have electronic transport, then the transport of hydrogen and oxygen ions may be de-coupled. They may move in the same direction or in opposite directions and at different ratios. 

In the case discussed here, where three or more species (e.g.. A, B, C) provide charge transport, it may, as mentioned earlier, be important to keep the pairwise ambipolar conductivities in the correct form, and to be aware of the inequality  

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