## 3 Results and Discussion
### Experimental Biosorption Data Modeling in a Dynamic Regime  
The graphical representations of linearized equations of the [PERSON] and Yoon-Nelson kinetic models are illustrated in Figure 3, and the values obtained for the characteristic biosorption parameters of each model are systematized in Table 3.  
Figure 2: The breakthrough curves for the biosorption system in a dynamic regime: BRed dye—residual _Bacillus sp._ biomass immobilized in alginate. Operating conditions: \(T\) = 20 \({}^{\circ}\)C; \(C_{0}\) = 76.72 mg/L; pH = 3.  
\begin{table}
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**Parameter** & **Significance and Characteristics** & & & & & \\ \cline{3-6}  & & & & & & \\ \cline{3-6}  & & & & & & \\ \cline{3-6}  & & & & & & \\ \cline{3-6}  & & & & & & \\ \cline{3-6}  & & & & & & \\ \cline{3-6}  & & & & & & \\ \cline{3-6}  & & & & & & \\ \cline{3-6}  & & & & & & \\ \cline{3-6}  & & & & & & \\ \cline{3-6}  & & & & & \\ \cline{3-6}  & & & & & \\ \cline{3-6}  & & & & & & \\ \cline{3-6}  & & & & & \\ \cline{3-6}  & & & & & \\ \cline{3-6}  & & & & & \\ \hline \hline \end{tabular}
\end{table}
Table 2: Characteristic parameters of the breakthrough curves.  
\begin{table}
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**Parameter** & **Significance and Characteristics** & & & & \\ \cline{3-6}  & & & & & \\ \cline{3-6}  & & & & & \\ \cline{3-6}  & & & & & \\ \cline{3-6}  & & & & & \\ \cline{3-6}  & & & & & \\ \cline{3-6}  & & & & & \\ \hline \hline \end{tabular}
\begin{tabular}{c c c} \hline \hline  & & & & & \\ \cline{3-6}  & & & & & \\ \cline{3-6}  & & & & & \\ \cline{3-6}  & & & & & \\ \cline{3-6}  & & & & & \\ \cline{3-6}  & & & & & \\ \cline{3-6}  & & & & & \\ \hline \hline \end{tabular}
\end{table}
Table 3: Thomas and Yoon-Nelson models applied for BRed dye—residual _Bacillus sp._ biomass immobilized in an alginate biosorption system in a dynamic regime.  
The data presented in Table 3, in association with the graphical representations from Figure 3, underline some findings about the studied biosorption kinetics in the fixed/packed bed (column) reactor (dynamic regime):  
* Because the plot \(ln[(C_{0}/C_{t})-1]\) versus \(V\) gives a straight line (Figure 3a) and the \(R^{2}\) is lower than 0.938 (equal for \(F_{v}=4.5\) mL/min), the viable suggestion is that the [PERSON] kinetic model is relatively well fitted for modeling of kinetic data, especially for \(F_{v}\geq 4.5\) mL/min and the maximum biosorption capacity is of 38.05 mg/g.
* The linearity of plots \(ln[C_{t}/(C_{0}-C_{t})]\) versus \(t\) for all three tested flow rates and the high values of the correlation coefficient, \(R^{2}\) (e.g., 0.947 for \(F_{v}=7.3\) mL/min), suggest that the biosorption kinetic of BRed dye onto residual biomass follows the  
Figure 3: Graphical representation of the linearized equations of the [PERSON] (**a**) and Yoon–Nelson (**b**) models for biosorption in a dynamic regime. Operating conditions: \(T=20\)\({}^{\circ}\)C; \(C_{0}=76.72\) mg/L; pH = 3.  
Yoon-Nelson kinetic model, and the maximum biosorption capacity is of around 34.742 mg/g.
* Both kinetic models (Thomson and Yoon-Nelson) can be used to describe to biosorption kinetics of BRed anionic dye onto immobilised residual biomass when is working with flow rates higher than 4.5 mL/min.  
As pointed out in the previous static study [27], the results show that the biosorption process of reactive BRed anionic dye by the immobilised residual biomass as biosorbent, is a physico-chemical process (based on competitive hydrogen bonding, \(\pi\)-\(\pi\) interactions, electrostatic interactions, ion-exchanges, covalent (coordinative) bonding, hydrophobic interactions) that proceeds properly at acidic pH, moderate dye concentrations in aqueous solution and ambient temperature (20-25 \({}^{\circ}\)C).