Fractal theory and regression analysis were employed for the first time to investigate the effect of pore size and pore distribution on high-temperature mechanical properties of porous alumina ceramics (PAC). In the present work, PAC with the comparable porosity, different pore sizes and pore distributions were prepared using carbon black as the pore-forming agent. Particular emphasis in this study was placed on the establishment of correlation between the thermal shock resistance and pore properties. The relationship between fractal dimension ( $D_{\text{f}}$) and thermal shock resistance parameter ( $R_{\text{st}}$) in specimens presented the negative power function, indicating that low $D_{\text{f}}$ could benefit the improvement of thermal shock resistance in specimens. The results showed that the increase of pore size and pore sphericity leads to a reduced $D_{\text{f}}$, the enhanced hot modulus of rupture (HMOR) and $R_{\text{st}}$. The decrease of proportion of micro-pores below 2 µm, the increase of mean pore size and pore sphericity could result in the decrease of $D_{\text{f}}$, and then improve $R_{\text{st}}$ and HMOR of specimens. Based on the correlation between $R_{\text{st}}$ and pore characteristics, PAC with improved thermal shock resistance could be achieved when their pore structure meets the above features.

Low-cost porous ceramic microspheres from waste gangue were prepared by simple spray drying and subsequent calcination. Effects of calcination temperature on phase and microstructure evolution, specific surface area, pore structure, and dye adsorption mechanism of the microspheres were investigated systematically. Results showed that the microspheres were spherical, with some mesopores both on the surface and inside the spheres. The phase kept kaolinite after calcined at 800 and 900 ℃ and transformed into mullite at 1000 ℃. The microspheres calcined at 800 ℃ showed larger adsorption capacity and removal efficiency than those calcined at higher temperatures. Methylene blue (MB) and basic fuchsin (BF) removal efficiency reached 100% and 99.9% with the microsphere dosage of 20 g/L, respectively, which was comparable to that of other low-cost waste adsorbents used to remove dyes in the literature. Adsorption kinetics data followed the pseudo-second-order kinetic model, and the isotherm data fit the Langmuir isotherm model. The adsorption process was attributed to multiple adsorption mechanisms including physical adsorption, hydrogen bonding, and electrostatic interactions between dyes and gangue microspheres. The low-cost porous microspheres with excellent cyclic regeneration properties are promising absorbent for dyes in wastewater filtration and adsorption treatment.