## 3 Results and Discussion
### Sorption Capacity of Beech and Birch Barks  
Two sorption models such as the Langmuir and Freundlich isotherms were used to describe the sorption capacity of beech and birch barks. The experimental data and sorption isotherms as well as the constants determined from both models are shown in Figures 7 and 8 and Table 8.  
The Langmuir isotherm, which describes the single-layer adsorption of sorbate on the sorbent, clearly better describes the obtained experimental data. The R\({}^{2}\) values presented in Table 8 show that regardless of the type of sorbent, its fineness or the type of dye, the R\({}^{2}\) values obtained for the Langmuir isotherm were higher and ranged from 0.999 (BBiC-BR46) to 0.991 (BBiC-BV10), while for the Freundlich isotherm, the R\({}^{2}\) values ranged from 0.896 (BBiC-BR46) to 0.7761 (BBeF-BV10). This suggests that bark-based sorbents, regardless of their type, adsorb dyes in a single layer. \begin{table}
\begin{tabular}{c c c c c c c c c c c} \hline \hline \multirow{2}{*}{**Type** **(Initial Conc.)**} & \multicolumn{3}{c}{**PHASE 1**} & \multicolumn{3}{c}{**PHASE 2**} & \multicolumn{3}{c}{**PHASE 3**} \\ \cline{3-11}  & \multirow{2}{*}{**Sorbent**} & \(\mathbf{k_{d1}}\) & **Time** & \(\mathbf{R^{2}}\) & \(\mathbf{k_{d2}}\) & **Time** & \(\mathbf{R^{2}}\) & \(\mathbf{k_{d3}}\) & **Time** & \(\mathbf{R^{2}}\) \\ \cline{3-11}  & & \(\ast\) & **[min]** & **-** & \(\ast\) & **[min]** & **-** & \(\ast\) & **[min]** & **-** \\ \hline \multirow{3}{*}{BR46} & BBeC & 5.940 & 30 & 0.9895 & 1.758 & 60 & 0.9501 & 0.472 & 210 & 0.9804 \\  & BBeF & 6.553 & 30 & 0.9811 & 1.638 & 90 & 0.9449 & 0.353 & 180 & 0.9724 \\ (50 mg/L) & BBiC & 4.278 & 45 & 0.9990 & 2.308 & 75 & 0.9923 & 0.810 & 180 & 0.9634 \\  & BBiF & 4.461 & 60 & 0.9908 & 1.621 & 120 & 0.9721 & 0.467 & 120 & 0.9973 \\ \hline \multirow{3}{*}{BV10} & BBeC & 0.314 & 20 & 0.9823 & 0.213 & 40 & 0.9997 & 0.069 & 120 & 0.9901 \\  & BBeF & 0.344 & 45 & 0.9949 & 0.118 & 45 & 0.9824 & 0.029 & 90 & 0.9044 \\ (5 mg/L) & BBiC & 0.287 & 10 & 0.997 & 0.174 & 35 & 0.9955 & 0.082 & 135 & 0.9964 \\ \cline{1-1}  & BBiF & 0.222 & 20 & 0.9967 & 0.164 & 70 & 0.9889 & 0.071 & 90 & 0.9652 \\ \hline \hline \end{tabular}
\end{table} 
Table 7: Rate constants of BR46 and BV10 diffusion determined from a simplified intraparticular diffusion model (sorbent dose = 5 g/L); \(\ast\) [mg/(g-min\({}^{0.5}\))]. \begin{table}
\begin{tabular}{c c c c c c c c c c} \hline \hline  & \multirow{2}{*}{**Isotherm**} & \multicolumn{3}{c}{**Basic Red 46**} & \multicolumn{3}{c}{**Basic Violet 10**} \\ \cline{3-11}  & & **BBeF** & **BBeC** & **BBiF** & **BBiC** & **BBeF** & **BBeC** & **BBiF** & **BBiC** \\ \hline \multirow{3}{*}{Langmuir} & \(Q_{\mathrm{max}}\) [mg/g DM] & 131.5 & 123.0 & 111.7 & 111.2 & 18.0 & 17.3 & 16.5 & 15.9 \\  & \(K_{\mathrm{C}}\) [L/g DM] & 0.088 & 0.066 & 0.091 & 0.056 & 0.286 & 0.229 & 0.145 & 0.130 \\  & \(R^{2}\) & 0.998 & 0.995 & 0.994 & 0.999 & 0.994 & 0.998 & 0.994 & 0.991 \\  &  
Figure 8: Experimental data and isotherms determined from the Langmuir and Freundlich equations for dye BV10: (**a**) beech fine particles, (**b**) beech coarse particles, (**c**) birch fine particles and (**d**) birch coarse particles. Figure 7: Experimental data and isotherms determined from the Langmuir and Freundlich equations for dye BR46: (**a**) beech fine particles, (**b**) beech coarse particles, (**c**) birch fine particles and (**d**) birch coarse particles. As far as sorption capacity is concerned, such general conclusions cannot be drawn. The research carried out showed a clear dependence of the sorption capacity obtained on the type of dye, which is much weaker than the type of sorbent. The highest sorption capacities were obtained for the beech bark sorbent and BR46 dye. The sorption capacity of fine fraction of the beech bark in relation to the BR46 dye was 131.5 mg/g DM, and for the coarse fraction of the beech bark was 123.0 mg/g DM.