Electrochemistry mesoscale approach

In SOFC modeling, the electrochemistry of the fuel cell can be included in the model at various levels of detail. In a continuum-scale approach, empirical current-potential (f-V) relations are typically used to model the electrochemistry of the SOFC. In a mesoscale approach, the electrochemical reactions and the transport of electrons and ions in the SOFC can be modeled explicitly. The continuum-scale approach allows for a quick evaluation of the I-V performance of the SOFC by assuming that the electrochemistry occurs only at the interface of the electrode and electrolyte. In the mesoscale approach, the electrochemistry of the SOFC is resolved through the thickness of the electrodes based on the local conditions in the cell. In this section, we discuss the details of both approaches. 

Both mesoscale electrochemistry modeling approaches calculate the potential distribution in the tri-layer based on the local Earadaic current density via Poisson s equation ... 

This is followed in Section 26.4 by a discussion of mesoscale modehng of the SOFC electrodes in which the SOFC electrodes are explicitly resolved and the detailed reactive transport and electrochemistry is modeled. Section 26.5 briefly describes nanoscale approaches for modeling the transport and reactions of species in the SOFCs, which are suitable for elucidating kinetic and mechanistic issues relevant to SOFC performance. 

There are two approaches to modeling the SOFC electrochemistry at the mesoscale an elementary kinetics-based model and a modified Butler-Volmer model. In the elementary kinetics-based model, the electrochemical reactions of the SOFC are modeled exactly, whereas in the modified Butler-Volmer model, the phenomenological Butler-Volmer equation is solved based on the local Faradaic current density. 

Many SOFC models chose not to model explicitly the electrochemical reactions. Instead, a modified Butler-Vohner relation based on the local conditions within the tri-layer can be used to solve for the current density of the fuel cell in a mesoscale electrochemistry approach [25]. The local Faradaic current density can be calculated from the modified Butler-Vohner relation as [31]... 

Cell-level models solve the species [Eq. (26.1)], momentum [Eq. (26.5)], and energy [Eq. (26.7)] conservation equations using the effective properties of the electrodes and can include the electrochemistry using a continuum-scale (Section 26.2.4.1) or a mesoscale (Section 26.2.4.2) approach. Traditionally, cell-level models use a continuum-scale electrochemistry approach, which includes the electrochemistry as a boundary condition at the electrode-electrolyte interface [17, 51, 54] or over a specified reaction zone near the interface. The electrochemistry is modeled via the Nernst equation [Eq. (26.12)] using a prescribed current density and assumptions for the polarizations in the cell. The continuum-scale electrochemistry is then coupled to the species conservation equation [Eq. (26.1)] using Faraday s law ... 

Recently, several groups have taken cell-level macroscale models a step further to investigate the electrochemistry through the thickness of the electrodes using the mesoscale electrochemistry approach [19, 27, 31]. In these models, no assumptions are made about a reactive zone for the electrochemical reactions instead, the electrochemistry is modeled through the thickness of the electrodes based on a mesoscale electrochemistry approach (Section 26.2.4.2) in which the explicit charge-transfer reactions [27] or a modified Butler-Volmer approach [19, 31] are modeled. This extends the effects of the electrochemical reactions away from the electrolyte interface into the electrodes. In these cell-level models, the electrochemistry is coupled to the local species concentrations, pressures, and temperatures, and provides a more detailed view into the local conditions within the fuel cell and how these local conditions affect the overall SOFC performance. 

We begin with the discussion of cell thermodynamics and electrochemistry basics (Chapter 1). This chapter may serve as an introduction to the field and we hope it would be useful for the general reader interested in the problem. Chapter 2 is devoted to basic principles of structure and operation of the polymer electrolyte membrane. Chapter 3 discusses micro- and mesoscale phenomena in catalyst layers. Chapter 4 presents recent results in performance modeling of catalyst layers, and in Chapter 5 the reader will find several applications of the modeling approaches developed in the preceding chapters. 

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