## 2 Materials and Methods
### Calculation Methods  
The amount of sorbed dye on the sorbent calculated according to Formula (1):  
\[\text{Qe}=\frac{(\text{C}_{\text{o}}-\text{C}_{\text{s}})\cdot\text{V}}{\text{m}} \tag{1}\]  
Qe--Mass of the sorbed dye [mg/g DM];  
C\({}_{\text{o}}\)--Initial dye concentration [mg/L];  
C\({}_{\text{s}}\)--Concentration of dye after sorption [mg/L];  
V--Volume of solution [L];  
\begin{table}
\begin{tabular}{c c c c c c c} \hline \hline
**Sorbent** & **Dye** & **Con. of Dye** & **Sorbent Dose (for** & **Sampling Time** & **Mixing** & **Temp.** \\  & **[mg/L]** & **pH of Dye Solutions** & **All Series)** & **(for All Series)** & **Speed** & **[\({}^{\circ}\)C]** \\ \hline BBeF & BV10 & 5 & & & & \\ BBeC & BR46 & 50 & Optimal, determined & & 0, 5, 10, 20, 30, 45, & & \\ BBiF & BV10 & 5 & for each dye in point & 1 & 60, 90, 120, 150, & & \\ BBiC & BR46 & 50 & 2.5 & & 180, 240, 300, 360 & & \\ \hline \hline \end{tabular}
\end{table}
Table 4: Test parameters—the sorption equilibrium time.  
\begin{table}
\begin{tabular}{c c c c c c c} \hline \hline
**Dye** & **Con. of Dye** & **SPH of Dye Solutions** & **SPH Dose** & **Mixing Speed** & **Sorption Time** & **Temp.** \\  & **[mg/L]** & **pH of Dye Solutions** & **[g DM/L]** & **[z.p.m]** & **[min]** & **[\({}^{\circ}\)C]** \\ \hline BV10 & 5 & 2/3/4/5/6/7/8/9/10/11 & 1 & 120 & 120 & 22 \\ BR46 & 50 & 2/3/4/5/6/7/8 & 1 & 120 & 120 & 22 \\ \hline \hline \end{tabular}
\end{table}
Table 3: Test parameters—influence of pH on the efficiency of dye sorption.  
\begin{table}
\begin{tabular}{c c c c c c c} \hline \hline
**Sorbent** & **Sorbent Dose** & **Dye Conc. [mg/L]** & **Dye Conc. [mg/L]** & **pH of the Solutions** & **Sampling Time** & **Mixing Speed** & **Time** \\  & **[g/L]** & & & & & \\ \hline BBeF & & & & & & \\ BBeC & & & & & & \\ BBiF & & & & & & \\ BBiF & & & & & & \\ BBiC & & & & & & \\ \hline \hline \end{tabular}
\end{table}
Table 5: Test parameters—determination maximum sorption capacity.  
M--Sorbent mass [g DM].  
The kinetics of dye sorption onto tested sorbents was described using pseudo-first-order (2), pseudo-second-order (3) and intraparticular diffusion (4) models:  
\[q=q_{e}\times\left(1-e^{(-k_{1}\times l)}\right) \tag{2}\]  
\[q=\frac{\left(k_{2}\times{q_{e}}^{2}\times t\right)}{\left(1+k_{2}\times q_{e} \times t\right)} \tag{3}\]  
\[q=k_{id}\times l^{0.5} \tag{4}\]  
q--Instantaneous value of sorbed dye [mg/g];  
q--The amount of dye sorbed at the equilibrium state [mg/g];  
t--Time of sorption [min];  
k1--Pseudo-first-order adsorption rate constant [1/min];  
k2--Pseudo-second-order adsorption rate constant [g/(mg \(\times\) min)];  
kid--Intraparticular diffusion model adsorption rate constant [mg/(g \(\times\) min\({}^{0.5}\))].  
In this study, two sorption models were used to describe the data:  
Langmuir's isotherm (5):  
\[\text{Qe}=\frac{\text{Q}_{\text{max}}\text{-}\text{K}_{\text{C}}\text{-}\text{ C}_{\text{e}}}{1+\text{K}_{\text{C}}\text{-}\text{C}_{\text{e}}} \tag{5}\]  
Qe--Equilibrium amount of sorbed dye [mg/g DM];  
Qmax--Maximum sorption capacity [mg/g DM];  
Kc--Constant used in the Langmuir's equation [L/mg];  
Ce--Concentration of dye remaining in the solution [mg/L].  
[PERSON]'s isotherm (6):  
\[\text{Qe}=\text{K}\text{-}\text{C}_{\text{e}}^{\text{n}} \tag{6}\]  
Qe--Actual sorption of sorbate on the sorbent [mg/g DM];  
K--Sorption equilibrium constant used in [PERSON]'s model;  
Ce--Concentration of dye remaining in the solution [mg/L];  
n--Heterogeneity parameter.