## 2 Materials and Methods  
In this study, diatomite powder (flux calcined, Celite 499, Celite Corp, Lompoc, CA, USA, 92.0% SiO\({}_{2}\) as referred to in Table 1) and sodium alginate (Daejung Chemicals and Metals, Gyeonggi-do, Republic of Korea) were used as raw materials for the preparation of porous diatomic granules. The manufacturing process of the porous diatomite granules was a dropwise granulation process, which was described in previous works [6; 11; 40]. Diatomite-based slurries were prepared by ball-milling (5 mm-sized alumina balls, 200 rpm, 4 h) different amounts of powders, ranging from 4 to 44 g (diatomite solid content: 3.8 to 30.5 wt.%) in 100 mL of distilled water (DI water) with the addition of 1 wt.% of Dolapix CE64 (Zschimmer and Schwarz Chemie GmbH, Lahnstein, Germany) as a dispersant. The compositions were designated as \"DX\", where \"D\" represents diatomite and \"X\" denotes the mass of the diatomite used to prepare the batches (Figure S1). Subsequently, diatomite/sodium alginate dispersions were obtained by mixing the diatomite slurries with a fixed content of 1.5 wt.% of sodium alginate. The mixing process was carried out for 4 h at 300 rpm, followed by overnight stirring at 200 rpm to de-foam the gels. The sodium alginate content was fixed considering the minimum concentration required to achieve high sphericity (sphericity \(\sim\)1, sphericity factor \(\sim\)0), as reported in previous studies of sodium alginate droplet gelation [40; 41]. The resulting dispersions were transferred dropwise through a syringe tip with a diameter of 1 mm into a column containing a 10 wt.% CaCl\({}_{2}\) solution (aq) (Daejung Chemicals and Metals, Gyeonggi-do, Republic of Korea). The collection distance between the syringe tip and the surface of the CaCl\({}_{2}\) bath was set to 1 cm. The wet-gel droplets were allowed to age for 1 h in the CaCl\({}_{2}\) solution, after which they were separated by simple filtration and washed with DI water. The resulting granules were dried at 80 \({}^{\circ}\)C overnight and subsequently heat-treated at 1200 \({}^{\circ}\)C for 1 h in air. The granules obtained with a selected batch composition (sphericity \(\sim\)1, sphericity factor \(\sim\)0) were heat-treated at different temperatures, in this case, 900 \({}^{\circ}\)C, 1000 \({}^{\circ}\)C, and 1100 \({}^{\circ}\)C. Granules derived from the selected processing conditions were labeled as \"DX-Y\", where \"D\" represents diatomite, \"X\" denotes the mass of the diatomite used to prepare the dispersion, and \"Y\" represents the first one or two digits of the heat-treatment temperature. In this case, \"0\" refers to dried granules, i.e., green body, \"9\" refers to 900 \({}^{\circ}\)C, \"10\" refers to 1000 \({}^{\circ}\)C, and so on. A diagram illustrating the different processing steps is provided in Figure 1. Specific resulting properties of the materials, dispersions, and porous diatomite granules were characterized throughout the manufacturing process. Figure 1: Diagram of the steps and mechanisms involved in the processing of porous diatomite granules, including (**a**) preparation of the diatomic/sodium alginate dispersion, (**b**) gelation of dispersion droplets in a Ca\({}^{2+}\) bath, (**c**) evaporation of encapsulated water through drying, and (**d**) bonding of diatomic particles after a heat treatment. The average particle size distributions of the processing powders were determined using a particle size analyzer (LSTM 13 320 MW, Beckman Coulter, Brea, CA, USA). The viscosity curves of the diatomic/sodium alginate dispersions were measured using a rotary viscometer (ViscoQC300, Anton Paar GmbH, Graz, Austria). The quantitative measure of the granule shape was calculated according to the sphericity, as described in the literature [6; 42].