## 2 Materials and Methods
### Cenospheres Separation  
The lignite fly ash sample was subject to wet separation. In this study, the sink-float method was employed to separate the lightweight nanospheres from the bulk fly ash, as the separation efficiency is based on the gravity settling. Water was used as the medium for both methods. Different experimental sets were designed to investigate the maximum cenospheres recovery and the separation efficiency as dependent upon the process parameters. In this study, the effects of process parameters on the cenospheres yield were studied. For the sink-float method, the fly ash sample was added into water at different fly ash-water weight ratios (g/mL). Those varied parameters are fly ash content in water medium (1:5 (20 wt.%), 1:10 (10 wt.%), 1:20 (5 wt.%), 1:40 (2.5 wt.%), 1:80 (1.25 wt.%) fly ash-to-water ratios), stirring method (manually and ultrasonically), and size sieving for the starting fly ash prior to cenospheres separation. For the stirring procedure, mechanical stirring and ultrasonicating (40 Hz) were employed. The mixtures were repeatedly stirred before leaving them to settle. It should be noted herein that a spontaneous imbibition is a measure of particle-level wettability. In this circumstance, water does not experience spontaneous imbibition into dry fly ash; however, wettability of the particles with intra-porous grains and accessible porosity is more pronounced for water to imbibe the ash particles [47]. Thus, in this study mixing procedure was adopted to facilitate such imbibition process for preparing the suspension prior to sedimentation and separation, while the fly ash sample was presumed to have a certain amount of such accessible porosity [18]. The effect of size classification for the starting fly ash before mixing with water was studied. For each experimental batch, the fresh fly ash was screened by wire mesh sieves into four different sizes: \(<\)45, 45-105, 106-250, and \(>\)250 \(\upmu\)m. Then these fractions were subject to cenospheres wet separation to particularly determine the cenospheres content in each size fraction. The cenospheres recovery yield was determined by the weight of cenospheres collected from each batch of size fractions with respect to the sum of cenospheres, \begin{table}
\begin{tabular}{c c} \hline
**Item** & **Unit 12** \\ \hline Density (g/cc) & 2.48 \\ \%Free lime & 1.43 \\ \%SO\({}_{3}\) & 2.72 \\ Average particle size (_D_[_4;3_], \(\upmu\)m) & 41.51 \\ \hline \end{tabular}
\end{table} 
Table 1: General characteristic properties of the fly ash sample. \begin{table}
\begin{tabular}{c c c c c c c} \hline \hline \multirow{2}{*}{**Sample**} & \multicolumn{5}{c}{**Size Distribution (Wt.\%)**} \\ \cline{2-7}  & **\textless{1} \(\upmu\)m** & **1–10 \(\upmu\)m** & **10–50 \(\upmu\)m** & **50–100 \(\upmu\)m** & **100–250 \(\upmu\)m** & **250–500 \(\upmu\)m** \\ \hline Fresh fly ash & 8.13 & 32.66 & 33.08 & 14.33 & 10.89 & 0.91 \\ \hline \end{tabular}
\end{table} 
Table 2: Particle size distribution (wt. %) of the fly ash sample. which was normalized to 100% (see the plots in Figure 1e). The purpose of this experiment is to compare the cenospheres yield with that obtained from the non-sieving condition. The mixtures were stirred to ensure the well mixing between fly ash and water. After stirring, the suspensions were allowed to settle for different time and pH was measured. The separation process was carried out at ambient temperature. Figure 1: Plots of percentage recovery of cenospheres collected by sink-float method, using different ash contents, an eight-day period. The mixtures were (**a**) manually stirred for 10 min; (**b**) ultrasonicated for 30 min. (**c**,**d**) The percent cenospheres recovery obtained from using the starting fly ash being sieved into four sized fractions (<45, 45–105, 106–250, >250 \(\upmu\)m) prior to the cenospheres separation; (**d**) is the zoomed-in plot for the conditions of 106–250 and >250 \(\upmu\)m. (**e**) Plots of weight fraction of the data shown in (**c**,**d**) against ash content.