3.4.1 Cell Potential

The electrode reactions are assumed to take place in a single step. The charge transfer reaction acts as the rate limiting step for the electrode reactions.

Oxygen is electrochemically reduced at the triple phase boundary at the cathode electrode:

Oxygen is electrochemically re-oxidized at the triple phase boundary at the anode electrode:

In the absence of an electrical load, the oxygen activity on both sides of the electrolyte is fixed and given by their respective chemical potentials. Under equilibrium, the electromotive force, or reversible cell voltage, is given by the Nernst equation:

If hydrogen is present at the anode electrode, then the cell reaction becomes:

At equilibrium, the cell voltage is given by the Nernst equation:

The cell potential measured at equilibrium (i.e., no load), is called the open circuit voltage. The open circuit voltage should be equivalent to the Nernst potential at no load, unless there is leakage across the electrolyte. When the external circuit is closed, then cell voltage drops due to polarization losses at the electrodes.

The electric field and the electrochemistry interact solely at the electrolyte interface. ANSYS FLUENT treats the electrolyte interface as an impermeable wall. The potential field must have a "jump" condition applied to the two sides of this wall to account for the effect of the electrochemistry. To closely couple the electrochemical behavior to the potential field calculation, you need to include all of the electrochemical effects into this jump condition. It encapsulates the voltage jump due to Nernst, the voltage reduction due to activation, the Ohmic losses due to the resistivity of the electrolyte, and a linearized for voltage reduction due to activation. This interface condition relates the potential on the anode side and the cathode side of the electrolyte and has the following form:

where

where $\eta_{\rm ele}$ represents the ohmic overpotential of the electrolyte, and $\eta_{\rm act, a}$ $\eta_{\rm act, c}$ represent the activation overpotential of the anode and the cathode. $\eta_{\rm s}$ represent ohmic losses in the solid conducting regions. $\phi_{\rm ideal}$ represents the Nernst potential.