Potentiometric Mode of the Oxygen Pump

The relative quantity of the removing oxygen from the liquid metal can be expressed by the following equation  

If the density of the electrical current i corresponds to the diffusive flow on the metal-electrolyte interface j, then the electrochemical balance equation can be presented as follows  

The equation for the oxygen flow can be obtained by the differentiation of correlation (4.46) by time x with consideration of Equation (4.47)  

The diffusive purification flow from the liquid-metal flat layer with thickness 5 will follow the jc coordinate toward the metal-electrolyte interface, where the condition Cl = const should be fulfilled. Coordinate x = 0 will be combined with the free surface of the liquid-metal layer. Then, the relative change of the oxygen concentration can be found from the solution of the following nonstationary diffusion equation  

The average relative oxygen concentration in metal can be expressed as follows  

---