Modeling the Steady-State and Dynamic Characteristics of Solid-Oxide Fuel Cells

From Fundamental Interfacial Reaction Kinetics to Macroscopic Current–Voltage Characteristics: Case Study of Solid Acid Fuel Cell Limitations and Possibilities

“…The local volumetric concentrations, C i , depend on the local molar fluxes (in further analogy to charge transport in the solid phase). This relationship is treated using a modified Stefan‐Maxwell diffusion model assuming no pressure gradient exists in the cathode: [ 14 ] $$$$\begin{equation}\frac{{ - d{C_{\mathrm{i}}}}}{{dx}} = \sum\nolimits_{k \ne i}^n {\frac{{{y_{\mathrm{k}}}{N_{\mathrm{i}}} - {y_{\mathrm{i}}}{N_{\mathrm{k}}}}}{{D_{{\mathrm{ik}}}^{{\mathrm{B,eff}}}}}} + \frac{{{N_{\mathrm{i}}}}}{{D_{\mathrm{i}}^{{\mathrm{K,eff}}}}}\end{equation}$$$$where y i is the local mole fraction of the species, $$D_{{\mathrm{ik}}}^{{\mathrm{B,eff}}}$$ is the effective binary diffusion coefficient of species i , and k (defined for i ≠ k ), and $$D_{\mathrm{i}}^{{\mathrm{K,eff}}}$$ is the effective Knudsen diffusion coefficient of species i . The assumption of a negligible pressure gradient is shown below to be justified.…”

“…In brief, the binary diffusion coefficients were obtained from reference sources, [ 25,26 ] to which the Hirshfelder correlation [ 25 ] was applied to account for the operating temperature, 250 °C, and pressure, 1 atm. Knudsen diffusion, which accounts for the interaction of gas molecules with pore walls, was computed using the well‐known Knudsen diffusivity expression [ 14b ] and the measured mean pore radius, r pore . The effective diffusion coefficients were taken to scale with the porosity according to the Bruggeman correction: [ 14b,27 ] $$$$\begin{equation}{D^{{\mathrm{eff}}}} = {\varepsilon ^{\frac{3}{2}}}D\end{equation}$$$$…”

“…Knudsen diffusion, which accounts for the interaction of gas molecules with pore walls, was computed using the well‐known Knudsen diffusivity expression [ 14b ] and the measured mean pore radius, r pore . The effective diffusion coefficients were taken to scale with the porosity according to the Bruggeman correction: [ 14b,27 ] $$$$\begin{equation}{D^{{\mathrm{eff}}}} = {\varepsilon ^{\frac{3}{2}}}D\end{equation}$$$$…”

Computational modeling of sodium-iodine secondary batteries

“…where i • is an empirical fitting parameter for the exchange current density, and the reference concentrations of [Na + ] * is taken to be 1 M. Because the Butler-Volmer equation represents the net charge-transfer rates rather than the elementary mass-action kinetics [17,18], the exponent for the sodium-ion concentration [Na + ] is usually different from the stoichiometric coefficient of the charge-transfer reaction.…”

Optimal design of a micro-tubular fuel cell

“…where (u D , X D ) are the velocity of the air and the concentration of O 2 at the inflow boundary Γ D , e is the electron charge and R(X ) is the Butler-Volmer reaction term [30], which can be simplified [42,11] to…”