## 3 Results and Discussions  
Practically and easily obtainable PPI of reticulated porous ceramics is limited to the value of approximately 45. Therefore, the above-mentioned literatures mostly focused on the study of reticulatedporous ceramics with less than 45 PPI. For example, reticulated porous alumina ((5 PPI) [31] and (20 PPI) [32; 33; 33]), reticulated porous alumina-zirconia composite (20 PPI) [34], reticulated porous aluminum nitride (20 PPI) [4], reticulated silicon nitride (10 PPI) [5], reticulated porous silicon carbide ((8 PPI) [6] and (10 PPI) [7]), reticulated porous zirconia (45 PPI) [8], reticulated porous cordierite (10 PPI) [9], reticulated porous yttrium disilicate (60 PPI) [10], and reticulated porous mullite (20 PPI) [11] have been reported. The detailed reasons are as follows. (1) As the value of PPI increased above approximately 45 PPI, it was difficult for a sacrificial polymer template to completely fill the internal pores with ceramic slurry. It was also very difficult to remove the excessive ceramic slurry while maintaining the formation of thin and uniform ceramic coatings over the strut walls of the sacrificial polymer template. Consequentially, several blocked inter-connected pores were generated by the remnants of excessive ceramic slurry, which should have participated in the ceramic coating on the strut walls of the sacrificial polymer template. It should have been removed completely, but remained even after the squeezing process. It can severely degrade the two main advantages of reticulated porous ceramics: low density and high permeability. (2) When PPI was relatively low, such as 10 or 25 PPI, it was favorable to increase the viscosity of ceramic slurry to coat the strut wall of sacrificial polymer template firmly, minimizing any defects that could be generated by the un-coated strut wall owing to the low adhesiveness, induced by the low viscosity of ceramic slurry, which enhanced the compressive strength of reticulated porous ceramics. However, when PPI approached approximately 45 PPI, a highly viscous ceramic slurry could not easily penetrate and remove the narrow pore channels of the sacrificial polymer template. Therefore, it was difficult to enhance the compressive strength of reticulated porous ceramics by increasing the PPI or viscosity of ceramic slurry. To demonstrate the difficulty faced during the preparation of reticulated porous ceramic specimen with high PPI, reticulated porous alumina specimens were prepared. Figure 1 shows the compressive strengths of the reticulated porous alumina specimens that were prepared by two different types of alumina slurry compositions, which were sintered at 1600 \({}^{\circ}\)C for 1 h. They had pore densities of 60 and 80 PPI. In Figure 1, the compressive strength of reticulated porous alumina prepared using the optimized alumina slurry, with the well-established composition of binder, solid loading, and dispersant, was higher than that of the reticulated porous alumina prepared using alumina slurry with the un-optimized slurry composition (in which the content is identical, minus the dispersant). Generally, if the viscosity of un-optimized alumina slurry was too high, it could not penetrate the narrow pore channel of the sacrificial polymer template. There were voids inside the reticulated porous alumina and many pore channels of the surface were blocked by the excessive alumina slurry which should have been penetrated the surface instead. If the viscosity of un-optimized alumina slurry was too low, it could not form a firm and defect-free coating layer on the surface of strut walls of the sacrificial polymer template. To evaluate the coating quality, generally, the applied mass (the amount of coated ceramic slurry after the squeezing process) can be easily measured. However, it is not certain whether the applied mass is properly coated on the strut walls or distributed non-uniformly deep-inside the reticulated porous ceramic specimen.