## 2 Structure, Theory, and Numerical Model  
### Model Structure and Mesh  
In Figure 1a, the schematic diagram of a one-cell SOFC stack with an interdigital fuel flow rib channel design and conventional paralleled line-type rib channels of the air flow path is displayed. The core part, SOFC unit, includes the porous anode, dense electrolyte, and porous cathode; their corresponding reaction area is 100 \(\times\) 100 mm. The fuel and air flow paths are two important study parts. The fuel and air flow arrangement in Figure 1a is a counterflow type. The fuel and air flow manifold configurations are both '1 in 2 out' with radii of 5 mm. The '1 in 2 out' here means one inlet manifold at one side and two outlet manifolds at the other side. Fuel and air flows are further distributed over the anode and cathode surfaces, respectively, by the rib channels. Figure 1b shows the conventional paralleled line-type rib channels over the porous cathode surface. This design type was reported to have a lower pressure drop throughout the stack compared with the other structure designs [23]. As shown in the figure, the air rib channels are separated by 39 solid ribs. The length of each flow channel is 100 mm, and the width and height of the ribs are 2 mm and 2 mm, respectively. This configuration is considered to be a proper choice for the cathode side. The reason is that the mole fraction of O\({}_{2}\) within the supplied air flow gas is only 21% and the air flow utilization within SOFC stacks may be only around 30% [24]. Thus, there is a large amount of air flow mass supply rate on the stack level. Adopting a lower flow resistance design is good to achieve a relatively lower pressure drop between the stack entrance and exit [18; 23]. Different from the air flow path, high resistance-designed fuel flow path is recommended to achieve high fuel utilization due to the relative light molecular mass of fuel and the low fuel flow mass supply rate of the stack. Figure 2a shows the fuel flow path structure with the interdigitated feature. There are 20 rib channels for the fuel input and 19 rib channels for collecting the exhaust gas. Figure 2a displays the schematic diagram of the interdigitated design in the y-direction view. Obviously, the fuel entering the fuel input channels is not directly connected with the exhaust channels of the outlet. In other words, the gas transmission between the fuel input and exhaust channels depends mainly on the connection of the porous anode. As further illustrated in Figure 2c, the gas can be carried out through the porous anode in both the lateral and longitudinal directions, simultaneously. Fuel from the input rib channels can be diffused to the electrochemical reaction sites within the porous anode and over the anode/electrolyte interface through the porous anode structure. Then, the exhaust gas, such as the electrochemical reaction production (i.e., vapor) and the unused fuel will be transported back into the exhaust collecting channels directly through the porous anode structure. The gap between the fuel flow channels is only 0.5 mm, which can increase the gas penetration cross-section to improve the effective reaction area of the SOFC unit. This interdigitated design for the fuel flow path is expected to improve both the fuel and vapor management qualities within the SOFC stack. Figure 1: (**a**) Schematic diagram of the typical one-cell solid oxide fuel cell (SOFC) stack model with an interdigital fuel flow rib channel design; (**b**) The conventional air flow rib channels with parallel line-type configuration. The meshing process is one of the key steps to ensuring the calculation accuracy of the numerical simulation [25]. In Figure 3, meshes of the whole stack and the partial enlargement picture are displayed to illustrate the meshing quality. The meshes include sub-channel, cell unit, manifold, and interconnector zones. The mesh number of each rib channel is 4 \(\times\) 4 in the height and width directions.