Models for O2 Semipermeation

In the simplest situation, Eq. (14.18) implemented with Eq. (14.19) can be used for deriving Eq. (14.20) by assuming that the ionic and electronic conductivities are constant with the O2 pressure and do not change within the membrane [27]  

Equation (14.23) can also be deduced from Eq. (14.14) by assuming a zero electrostatic potential gradient (i.e., v p = 0). In such a situation, the O2 flux can be approached to the following expression  

Introducing into Eq. (14.26) the defect equilibrium condition at the feed/mem-brane and permeate/membrane surfaces (Eq. (14.19)), an analogous expression to Eq. (14.23) can be obtained at low fractional coverage of vacancies  

More complex permeation models can be generated for cluster-like oxygen vacancies. In such a situation, two different oxygen vacancies can be proposed in the MIEC material. The exchange between these vacancies can be described 

By developing appropriate charge balances relating the oxygen species and vacancies, Eq. (14.25) can be deduced for the O2 permeance as a function of the molar volume of the perovskite (Table 14.1). Yang and Lin [28]. proposed an isotherm relating the nonstoichiometry of the LSCF perovskite with the O2 pressure  

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