## 3 Results and Discussion  
### Multichannel Tubular Support  
In an asymmetric filter configuration, support is a major component that provides overall mechanical strength and stability. The major issue in commercial-grade supports is crack generation during fabrication owing to shrinkage in the final product. To design a support suitable for industrial use with a minimal shrinkage rate, specimens made from various powder mixtures of S-Al\({}_{2}\)O\({}_{3}\) and L-Al\({}_{2}\)O\({}_{3}\) were analysed. Figure 1a shows the effect of the mixing ratio of the starting powder on the linear shrinkage rate. The S-Al\({}_{2}\)O\({}_{3}\) exhibited a high shrinkage rate of approximately 2% without any addition. However, when S-Al\({}_{2}\)O\({}_{3}\) and L-Al\({}_{2}\)O\({}_{3}\) were mixed, the shrinkage rate continuously declined with increasing concentration of L-Al\({}_{2}\)O\({}_{3}\). It consequently stabilised at a ratio of 70:30 for the S-Al\({}_{2}\)O\({}_{3}\) and L-Al\({}_{2}\)O\({}_{3}\), respectively.  
The high shrinkage rate of the S-Al\({}_{2}\)O\({}_{3}\) specimen may be related to the mean particle size. Particles with smaller mean sizes exhibited high sinterability owing to the high surface energy, causing shrinkage in the final product [23]. In contrast, in the mixture of alumina powders, the L-Al\({}_{2}\)O\({}_{3}\) provided skeletal structure to the support, while the S-Al\({}_{2}\)O\({}_{3}\) filled the pores among large particles. This facilitated consistent geometrical dimensions without any shrinkage in the final product [24]. As per the investigation, the final support layer was extruded by S-Al\({}_{2}\)O\({}_{3}\) and L-Al\({}_{2}\)O\({}_{3}\) in the ratio of 70:30, respectively.  
To the best of our knowledge, the obtained average linear shrinkage rate for the final support layer was significantly smaller than the previously reported values, as listed in Table 2. This may be attributed to the fabrication of the support layer with the mixture of small and large alumina particles rather than with single-sized small particles as in previous studies.  
Figure 1b shows an SEM image of an alumina support layer that had been heat treated at 1500 \({}^{\circ}\)C. A microstructure with well-sintered pore channels and an \(\alpha\)-alumina phase can be easily identified. The mercury porosimetry results exhibited a narrow pore-size distribution with an open porosity of 37% and average pore size of 0.8 \(\upmu\)m. As a comparison,  
a SEM image of the alumina support layer composed of only S-Al2O3 particles is given in Figure 1c.  
\begin{table}
\begin{tabular}{c c c c c} \hline
**Alumina Powder** & **Particle Size (\(\mu\)m)** & **Temperature (\({}^{\circ}\)C)** & **Linear Shrinkage (\%)** & **Reference** \\ \hline A300 & 0.3 & 1400 & 14 & [25] \\ A600 & 0.6 & 1300 & 10 & [26] \\ A1100 & 1.1 & 1400 & 12 & [27] \\ AM210 & 4.8 & 1500 & 1.67 & Our work \\ S/L Al2O3 & 4.8/15.66 & 1500 & 1.27 & Our work \\ \hline \end{tabular}
\end{table}
Table 2: Linear shrinkage rate of reported alumina support layer.  
Figure 1: (**a**) Effect of large alumina particle (L-Al2O3) concentration on the linear shrinkage of extruded support layer. (**b**) Typical SEM image of extruded alumina support layer composed of a mixture of S-Al2O3 and L-Al2O3 particles (70:30). (**c**) Typical SEM image of extruded alumina support layer composed of S-Al2O3 particles.