Oxygen transport equations

Here x from Equation 10.4 is changed to the two-membrane domain FOT and SLOT with the depth fixed (the same spin label is distributed between the FOT and SLOT domains). W(FOT) and W(SLOT) are oxygen transport parameters in each domain and represent the collision rate in samples equilibrated with air. Figure 10.9 illustrates the basis of the discrimination by oxygen transport (DOT) method, showing saturation-recovery EPR signals for 5-SASL in membranes... 

The DNS model can be deployed subsequently on the liquid water blocked CL structure pertaining to a saturation level for the evaluation of the hindered oxygen transport. In brief, the DNS model is a top-down numerical approach based on a fine-scale CFD framework which solves point-wise accurate conservation equations for species and charge transport in the CL with appropriate source terms due to the oxygen reduction reaction (ORR) directly on the CL microstructures.25-27 67 The conservation equations for proton, oxygen and water vapor transport, respectively, are given by 25-27 68... 

Similarly, with the 3-D liquid water distribution in the GDL micro structure available from the two-phase LB model and representatively shown in Fig. 15, the DNS model25,27 can be applied to solve the Laplace equation for oxygen transport given below.68... 

The detrimental consequence of liquid water on the CL voltage loss primarily comes from the impeded oxygen transport and reduced electrochemically active area as explained above which can be described by the electrochemical kinetics in terms of the reaction current density,/, through the Tafel equation.27... 

With the evaluated site coverage and pore blockage correlations for the effective ECA and oxygen diffusivity, respectively, and the intrinsic active area available from the reconstructed CL microstructure, the electrochemistry coupled species and charge transport equations can be solved with different liquid water saturation levels within the 1-D macrohomogeneous modeling framework,25,27 and the cathode overpotential, q can be estimated. 

Sometimes the relationship between the rate of the parabolic metal-oxidation process (dnox/dt), limited by oxygen transport through a dense oxide film, is also called the Wagner equation [vi] ... 

If we consider Oj" and h as carriers, we refer, e.g. to chemical diffusion of oxygen in La2CuC>4. Writing down the one-dimensional transport equations (Eq. 103) for ionic and electronic carriers and considering flux coupling and electroneutrality, we immediately obtain for this case (see, e.g., Ref.173)... 

In the models presented by Wang and Lin (1995], the catalytic reaction terms appear in the transport equations for the tube core where methane is introduced. Air flows in the annular region and permeates through the dense oxide membrane to the tube side to react with methane. Transport of oxygen takes place as a result of the defects of oxygen vacancy and electron-hole in the oxide layer. 

Equations for oxygen transport can be derived from the point defect equilibria discussed in Section 10.6.2.2. This provides us with some general insight... 

Oxygen transport in the perovskites is generally considered to occur via a vacancy transport mechanism. On the assumption that the oxygen vacancies are fully ionized and all contribute to transport, i.e., oxygen defects are not associated, the Nernst-Einstein equation reads,... 

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