## 2 Materials and Methods
### Effect of Flowrate  
In general, a breakthrough curve (BTC) is represented by a graph with \(C_{\mathit{effluent}}\) or \(C_{\mathit{effluent}}/C_{\mathit{effluent}}\) versus the experimental time or the treated volume. The BTC tendency and time required to reach the breakpoint are important factors for the fixed-bed column design and to check the practical application in industry. The shape of the curve can vary with sorbent characteristics, inlet adsorbate concentration, inlet flowrate, bed height, or diameter of the column. Thus, the analysis of the BTC is essential for the effective design of the column [25].  
The flow rate is a critical variable to determine the efficiency of the adsorbent for application in a large-scale continuous process. The influence of the flow rate on dye adsorption on the PSAC was investigated by varying the flow rate (7.7 and 30.8 mL min\({}^{-1}\)  
\begin{table}
\begin{tabular}{c c} \hline \hline
**Parameters** & **PSAC** \\ \hline BET surface area N\({}_{2}\) (m\({}^{2}\) g\({}^{-1}\)) & 2826 \(\pm\) 8.97 \\ BET surface area CO\({}_{2}\) (m\({}^{2}\) g\({}^{-1}\)) & 910 \(\pm\) 11.80 \\ Total pore volume (cm\({}^{3}\) g\({}^{-1}\)) & 1.54 \\ Mesopore volume (cm\({}^{3}\) g\({}^{-1}\)) & 1.07 \\ Micropore volume (cm\({}^{3}\) g\({}^{-1}\)) & 0.47 \\ Average pore diameter (nm) & 2.18 \\ Average pore diameter N\({}_{2}\)/CO\({}_{2}\) (nm) & 1.10 * \\ \hline \hline \end{tabular}  
* Determined simultaneously with N\({}_{2}\) at \(-196\)\({}^{\circ}\)C and CO\({}_{2}\) at 0 \({}^{\circ}\)C isotherms.  
\end{table}
Table 1: Surface characterization of the activated carbon prepared.  
Figure 3: Pore size distribution of the PSAC.  
at fixed values of the inlet dye concentration and bed height. The results are shown in Figure 4.  
It is observed that, by increasing the flow rate, the breakthrough curve became steeper and the breakthrough time decreased (Table 2) due to the increased mass-transfer rate in the adsorption zone. Similar results were obtained by [PERSON] et al. [33] for the removal of dye-contaminated effluent with sewage-sludge-based biochar, [PERSON] and [PERSON] [34] for the adsorption of textile industry effluent using activated carbon prepared from agro-waste materials, and [PERSON] et al. [35] for the adsorption of tartrazine anionic dye with synthesized polystyrene/magnetic nanocomposite. Additionally, except for the red dye, the adsorption capacity decreased with an increasing flow rate. This is because, at high flow rates, the residence time of the dyes in the column is reduced, which results in less contact time between the dye and the adsorbent, and intraparticle diffusion may be limited [25]. Furthermore, it is observed that, by increasing the flow rate fed to the column, higher values of \(C/C_{0}\) tend to be reached. This fact may be caused by an increase in turbulence generated by using a greater flow rate and, therefore, an increase in mass-transfer processes.  
The variation that can be observed in the slope of the curves and in the adsorption capacity can be explained by limitations on the mass transfer [36].  
Figure 4: Breakthrough curves for blue (**a**), red (**b**), and black (**c**) dye adsorption onto the PSAC at different flow rates (inlet dye concentration: 500 mg L\({}^{-1}\) for blue and red and 100 mg L\({}^{-1}\) for black dye; bed height 4 cm; temperature: 20 \({}^{\circ}\)C).