## 3 Results and Discussion
### Kinetics of Dye Sorption  
In the study, the equilibrium time of sorption of BR46 and BV10 dyes on the bark of beech and birch trees was determined as a function of the fraction. The sorption processes were carried out at an optimum pH value, which was pH = 5 for Basic Red 46 and pH = 3 for Basic Violet 10. The studies to determine the sorption equilibrium time for both dyes were carried out for the BR46 solution at a concentration of 50 mg/L and for the BV10 solution at a concentration of 5 mg/L (Figure 4). Based on the studies carried out, the equilibrium time of 300 min for BR46 and 240 min for BV10 was assumed (Figure 4). The longer sorption time of the BR46 dye (300 min) may be due to its lower molar mass, which led to a longer time of filling the sorption centres by dye molecules. On the other hand, the shorter sorption time of the BV10 dye may indicate a higher molar mass, which had a limited ability to reach the sorption centres due to the size of the molecules. Experimental data from studies on the sorption kinetics of BR46 and BV10 on bark-based sorbents were described using pseudo-first- and pseudo-second-order models (Table 6, Figure 5). In each series of experiments, regardless of the type of sorbent and dye, the best agreement with the obtained data was demonstrated by the pseudo-second-order model, which is typical for the sorption of cationic dyes on plant biomass. \begin{table}
\begin{tabular}{c c c c c c c c c} \hline \multirow{3}{*}{\begin{tabular}{c} **Dye** \\ **(Initial Conc.)** \\ \end{tabular} } & \multicolumn{3}{c}{**Pseudo-First-Order Model**} & \multicolumn{3}{c}{**Pseudo-Second-Order Model**} & \multirow{3}{*}{**Exp. Data**} & \multirow{3}{*}{**Equil. Time**} \\ \cline{3-4} \cline{6-9}  & & **k\({}_{1}\)** & & & & & & \\ \cline{3-9}  & & **[1/min]** & **[mg/g]** & **-** & **[g/mg \(\times\) min]** & **[mg/g]** & **-** & **[mg/g]** & **[min]** \\ \hline \multirow{3}{*}{\
\begin{tabular}{c} BR46 \\ (50 mg/L) \\ \end{tabular} } & BBeC & 0.0564 & 42.55 & 0.9665 & 0.0018 & 46.19 & 0.9975 & 45.10 & 300 \\  & BBeF & 0.0678 & 44.33 & 0.9669 & 0.0021 & 47.80 & 0.9980 & 46.99 & 300 \\  & BBiC & 0.0277 & 40.89 & 0.9773 & 0.0008 & 46.45 & 0.9969 & 43.01 & 300 \\  & BBiF & 0.0328 & 43.12 & 0.9712 & 0.0009 & 48.24 & 0.9955 & 45.34 & 300 \\ \hline \multirow{3}{*}{
\begin{tabular}{c} BV10 \\ (5 mg/L) \\ \end{tabular} } & BBeC & 0.0373 & 2.50 & 0.9842 & 0.0899 & 2.79 & 0.9986 & 2.62 & 180 \\  & BBeF & 0.0418 & 2.69 & 0.9951 & 0.0195 & 2.97 & 0.9946 & 2.74 & 180 \\ \cline{1-1}  & BBiC & 0.0409 & 1.98 & 0.9425 & 0.0271 & 2.18 & 0.9858 & 2.10 & 180 \\ \cline{1-1}  & BBiF & 0.0277 & 2.04 & 0.9764 & 0.0159 & 2.30 & 0.9926 & 2.11 & 180 \\ \hline \end{tabular}
\end{table} 
Table 6: Kinetic parameters of dye sorption onto BBeC, BBeF, BBiC and BBiF. Figure 4: Sorption equilibrium time for (**a**) BR46 and (**b**) BV10. Figure 5: Sorption kinetics of BR46 onto (**a**) beech fine particles, (**b**) beech coarse particles, (**c**) birch fine particles and (**d**) birch coarse particles and sorption kinetics of BV10 onto (**e**) beech fine particles, (**f**) beech coarse particles, (**g**) birch fine particles and (**h**) birch coarse particles. Pseudo-first-order model and pseudo-second-order model. The data from studies on the kinetics of dye sorption on BBeF, BBeC, BBiF and BBiC were also described using an intraparticular diffusion model. The analysis of the constants determined from a specific model showed that the sorption of dyes on the sorbents tested took place in three phases in each test series (Table 7, Figure 6). Figure 6: Intraparticular diffusion model of the sorption of BR46 onto (**a**) beech fine particles, (**b**) beech coarse particles, (**c**) birch fine particles and (**d**) birch coarse particles and sorption of BV10 onto (**e**) beech fine particles, (**f**) beech coarse particles, (**g**) birch fine particles and (**h**) birch coarse particles. The first phase of sorption was the shortest but was characterised by the highest efficiency.