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

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

We can now write the flux of protons (species i) through an oxide with mixed conductivity of protons, oxygen ions and electrons (species k). In this case, the neutral species (n) are hydrogen and oxygen, and we obtain  

We substitute to obtain an expression containing the partial pressures of the molecular neutral species  

It is often practical to insert the equilibrium between hydrogen, oxygen and water in order to express the flux density of protons in terms of the water vapor activity gradient  

This more clearly shows how the proton flux comes about as fluxes of hydrogen and water. 

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