## 3 Results and Discussion  
The specific surface areas of the dendritic lattices were calculated according to the aspect ratios, as shown in Figure 5. These numerical values were obtained under the geometric conditions of a uniform lattice constant. The maximum amounts were individually exhibited at specified aspect ratios of 1.17, 0.90, 2.34 and 2.18 on the lattice patterns with coordination numbers 4, 6, 8 and 12, respectively. These optimized model parameters were used in the structural modeling of the numerical simulations. The specific surface area was maximized in the 12-coordinated lattices, compared to those of the other lattices. However, the fluid flow profiles of molten salts should be considered to optimize the YSZ lattice patterns and increase the separation efficiencies of oxygen ions. Figure 4: A schematic illustration of process sequences in stereolithographic additive manufacturing (STL-AM). An ultraviolet (UV) laser beam was scanned on spread resin pastes with fine particles, to draw cross-sections. A solid component was automatically formed through layer lamination and interlayer bonding. Figure 3: A lithographic test pattern to systematically optimize the laser drawing conditions. A round hole (1.0 mm in diameter) was opened at the center of a square sheet (5.0 mm in edge length). The hole diameters and sheet thicknesses were defined as the dimensional tolerances and curing depths, respectively. The streamline distributions of molten salts were visualized to represent fluid movements as graphical contrasts with the YSZ lattice models, as shown in Figure 6. These line densities corresponded with the flow rates, and the color tones indicate the flow velocity. The molten salts were spatially distributed in the 4-coordinated lattices, as shown in Figure 6a. However, the construction points with high streamline densities were formed in the vicinities of the lattice junctions. Straight streamlines were formed in the 6-coordinated lattices, as shown in Figure 6b. The relatively brief contact of the molten salts with the YSZ lattice did not contribute to the oxygen ion absorption at the interface. Smooth meandering streamlines were formed in the 8-coordinated lattices, as shown in Figure 6c. However, retention points with low streamline densities were formed between the nodal lattices. Molten salt streamlines surrounded the 12-coordinated lattices, as shown in Figure 6d. Oxygen ions were absorbed on the YSZ lattice surfaces and conducted the following electric field. Figure 5: Calculated specific surface areas of the modulated dendritic lattices. The aspect ratios were defined as the numerical proportions of the lattice lengths to diameters. The curved solid lines (a–d) indicate the maximum specific surface areas on the 4-, 6-, 8-, and 12-coordinated lattices, respectively. Figure 6: Streamline distributions of high-temperature liquids in the dendritic lattices visualized by computer fluid dynamics (CFD). The flux densities and color variations indicate the fluid amounts and velocities, respectively. The fluid profiles (**a–d**) were simulated in the 4-, 6-, 8- and 12-coordinated lattices, respectively. The 12-coordinated lattices with an aspect ratio of 2.18 were mathematically verified to exhibit the maximum specific surface areas and high liquid permeabilities. The stress distributions loaded from the molten salts for the YSZ lattice surfaces were visualized, as shown in Figure 7. The mechanical stresses were concentrated on the side facing the inlet and vicinity of the nodal points of the cylindrical lattices. The maximum amounts were lower than 400 MPa in the fracture stress of the sintered YSZ at temperatures above 1000 \({}^{\circ}\)C [11]. The temperature distributions were visualized in the cross-section parallel to the fluid flow direction, as shown in Figure 8. The lattice temperature gradually decreased away from the electrode surfaces by thermal radiation inside the electrode.