Anode-pore tortuosity in solid oxide fuel cells found from gas and current flow rates

The effect of solid oxide fuel cell (SOFC) anode thickness, porosity, pore size, and pore tortuosity on fuel and exhaust gas flow is calculated. Also determined is the concentration of these gases and of diluent gases as a function of position across the anode. The calculation is based on the dusty-gas model which includes a Knudsen (molecule–wall) collision term in the Stefan–Maxwell equation which is based on unlike-molecule collisions. Commonly made approximations are avoided in order to obtain more exact results. One such approximation is the assumption of uniform total gas pressure across the anode. Another such approximation is the assumption of zero fuel gas concentration at the anode–electrolyte interface under the anode saturation condition for which the SOFC output voltage goes to zero. Elimination of this approximation requires use of a model we developed (published elsewhere) for terminal voltage V as a function of electrolyte current density i. Key formulae from this model are presented. The formulae developed herein for gas flow and tortuosity are applied to the results of a series of careful experiments performed by another group, who used binary and ternary gas mixtures on the anode side of an SOFC. Our values for tortuosity are in a physically reasonable low range, from 1.7 to 3.3. They are in fair agreement with those obtained by the other group, once a difference in nomenclature is taken into account. This difference consists in their definition of tortuosity being what some call tortuosity factor, which is the square of what we and some others call tortuosity. The results emphasize the need for careful design of anode pore structures, especially in anode-supported SOFCs which require thicker anodes.