Equations for Oxygen Transport

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, 

In writing Eq. (10.61), Dy was taken to be constant. Strictly speaking, Dy may decrease slightly when the oxygen-deficiency increases (i.e., towards decreas- 

The relation between Dy and the tracer diffusion coefficient D can be expressed as 

When electronic conduction predominates, one may derive the following relationship between Dy and the chemical diffusion coefficient D (by combining Eqs. (10.12) and (10.60)), 

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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... 

One of the first analytical models of CCL was developed by Springer and Gottesfeld [6], based on Pick s equation for oxygen transport and Tafel law for the rate of ORR. A similar approach was then used by Perry, Newman and Cairns [5] and by Eikerling and Komyshev [7]. 

In this chapter the scope of our discussion was restricted by the macrohomogeneous model of CL performance and its derivatives. The first numerical macrohomogeneous models of CCL for a PEM fuel cell were developed by Springer and Gottesfeld (1991) and by Bernard and Verbrugge (1991). These models included the diffusion equation for oxygen transport, the Tafel law for the rate of ORR and Ohm s law for the proton transport in the electrolyte phase. A similar approach was then used by Perry, Newman and Cairns (Perry et al., 1998) and by Eikerling and Kornyshev (1998) for combined numerical and analytical studies. 

A simple linear diffusion equation for oxygen transport in the GDL leads to the following relation between the oxygen concentration at the CCL/GDL interface Cox,i and the oxygen concentration in the channel... 

Equations for oxygen transport throughout and across the acinar tree... 

Localized vs. Delocalized Electrons Oxygen Desorption and Perovskite Stability Equations for Oxygen Transport Electronic Conductivity... 

Equations for oxygen transport can be derived from the point defect equilibria discussed in Section V.B.2. This provides ns with some general insight into the transport behavior of oxygen-deficient perovskites. Strictly speaking, the equations presented below are valid at low defect concentrations only, i.e., assuming oxygen defects to be randomly distributed. 

The following equation is derived for oxygen transport and consumption in the tissue cylinder ... 

The aforementioned models include three governing equations (i) mass transport equation for oxygen, (ii) proton current conservation equation with the Tafel rate of electrochemical reaction on the right side and (iii) Ohm s law, which relates proton current to the gradient of overpotential. Due to the exponential dependence of the rate of ORR on overpotential this system is strongly non-linear. 

In this section, a model for the PEFC cathode impedance is discussed, including oxygen transport in the channel (Kulikovsky, 2012d). The model is based on the transient CCL performance model from the section Basic Equations linked to the nonstationary extensions of the models for oxygen transport in the GDL and in the channel, discussed in the section Performance Modeling of a Fuel Cell. ... 

The functions c (z) and yo(z) in Equation 5.156 are the steady-state oxygen concentration in the channel and the local cell current density, respectively. These functions result from the solution of the steady-state problem for oxygen transport in the cathode channel (the section Oxygen Transport in the Channel ). 

Write a balanced equation for the reduction of molecular oxygen by reduced cytochrome e as carried out by complex IV (cytochrome oxidase) of the electron transport pathway. 

PEST. This code ( 3) was developed within the framework of Rensselaer Polytechnic Institute s CLEAN (Comprehensive Lake Ecosystem Analyzer) model. It includes highly elaborated algorithms for biological phenomena, as described in this volume (44). For example, biotransformation is represented via second-order equations in bacterial population density (Equation 5) in the other codes described in this section PEST adds to this effects of pH and dissolved oxygen on bacterial activity, plus equations for metabolism in higher organisms. PEST allows for up to 16 compartments (plants, animals, etc.), but does not include any spatially resolved computations or transport processes other than volatilization. 

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... 

Equation (2.19), which concerns a situation without processes in the biofilm, can be extended to include transformation of a substrate, an electron donor (organic matter) or an electron acceptor, e.g., dissolved oxygen. If the reaction rate is limited by j ust one substrate and under steady state conditions, i.e., a fixed concentration profile, the differential equation for the combined transport and substrate utilization following Monod kinetics is shown in Equation (2.20) and is illustrated in Figure 2.8. Equation (2.20) expresses that under steady state conditions, the molecular diffusion determined by Fick s second law is equal to the bacterial uptake of the substrate. 

Current densities in the cathode are mainly determined by the respective value of oxide anion conductivity compared to the electronic conductivity (/Co" and ice", coupled to each other in Wagner diffusion). Equation (34) describes the current density limit for coupled transport of oxygen anions and electrons (777) ... 

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... 

In addition to the gravitation of Earth a rocket launched from earth must also overcome the air resistance of the atmosphere, which means that the rocket equation for such cases is only an approximation. Planes, RAM and SCRAM jets which are propelled by jet engines, transport their fuel with them, but they also suck air in and use the oxygen from the air for the combustion of the fuel. They only carry the fuel but not the oxidizer with them. The rocket equation is not valid for such vehicles, which are referred to as air-breathing engines. 

Similarly, phenothiazine may be oxidized to the cation radical species which then dimerizes forming the 3,10 -diphenothiazinyl species (Tsujino, 1969). The product of the electron-transfer step may react, via a second-order process, with a species in solution to form a new product. An example of this type of mechanism involves the reduction of anthraquinone and its derivatives in the presence of oxygen (Jeziorek etal., 1997). To understand quantitatively an EC and EC2 process, the concentration and scan-rate dependence of the associated cyclic voltammograms is matched with theory deriving from the mass transport/kinetic equations for each species. 

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. 

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