## 3 Results and Discussion
### Adsorption Efficiency in Batch System
 \tag{7}\]  
For continuous systems, regression model equations were generated too, and these are as follows: Equation (8) is for YSR-Cr (VI), Equation (9) is for YSR-Ni (II), Equation (10) is for PSR-Cr (VI), and Equation (11) is for PSR-Ni (II). Where \(H\) is the beg height (cm), \(T\) is the temperature (\({}^{\circ}\)C), and \(R\) is the efficiency of removal (%). \[ \begin{array}{c}R=3.42*10^{-6}-6.94*T-3.62*10^{8}*T-3.61*10^{9}*H+2.76*10^{6}* T^{2}\\ +4.73*10^{7}*T*H+5.069*10^{7}*H^{2}\end{array}  \tag{8}\]  
\[R=23.11+1.22*T+10.90*H-0.006*T^{2}-0.081*T*H-0.41*H^{2} \tag{9}\]  
\[R=-75.343+1.442*H^{2}+3.384*T-0.006*H^{2}-0.006*H*T-0.020*T^{2} \tag{10}\]  
\[R=93.001+0.043*T+0.092*H-0.0002*T^{2}-0.0006*T*H-0.0003*H^{2} \tag{11}\]  
The equations make it possible to establish the influence of each evaluated effect and their interactions as standardized values. The removal efficiencies were calculated by Equation (1) after the adsorption process shown in Figure 5. PSR biomass reported high removal efficiencies (>80%) for the removal of Cr (VI) and Ni (II) ions, which can be attributed to the high surface area and small pore size enhancing adsorption properties of such materials [62], consistent with the EDS after the adsorption process reported in Figures 4 and 5, as well as the irregular morphologies evidenced in the SEM micrographs, which is a desirable characteristic of adsorbents due to the availability of active sites for adsorbing heavy metal ions [63]. The kinetic study was carried out to analyze the effect of time on the adsorption capacity at the best experimental conditions found for each process (Table 7). According to these best experimental conditions, a gap of 10 \({}^{\circ}\)C between optimum conditions for removing Ni (II) onto both bio adsorbents. This fact could be explained because the structure of PSR is dominated by the presence of mesopores (Table 4 and Figure 3), while the size of the pores of YSR is macro (Table 4 and Figure 4); these results suggest an excellent adsorbent capacity by PSR, as it could offer a larger contact area between the metal ions and the biomaterial [64]. On the other hand, the increase in temperature is possibly explained by the endothermic nature of the Ni (II) adsorption process, and it may be due to the increase in the ionization of the lignocellulosic components, which act as adsorption sites, thus promoting the increase in the rate of diffusion of Ni (II) through the outer boundary layer into the pores [65; 66]. The fit parameters of the pseudo-first-order and pseudo-second-order models were estimated by nonlinear fitting and are summarized in Table 8. It was found that the pseudo-second-order model best describes the adsorption kinetics of the two metals under study on YSR and PSR according to the correlation coefficient obtained; this indicates that the removal of metals occurs by chemisorption or chemical adsorption due to the formation of chemical bonds between adsorbent and adsorbate [67]. The value of the \(k_{2}\) constant evidences the selectivity of the materials for Cr (VI) relatively to Ni (II), which could be explained by the difference in the electronic configuration, ionic radius, and first ionization potential of the two metals. [68]. According to the pseudo-second-order parameter \(k_{2}\), it was observed that Cr (VI) ion was adsorbed at a faster rate than Ni (II). This fact may be explained by considering the ionic radius of both metals: Ni (II) (0.72 A) y Cr (VI) (0.52 A). Since Cr (VI) ions have a smaller ionic radius, it could be reasonable that their faster diffusion could be possible through the adsorbent pores [69]. Additionally, it showed the selectivity of PSR by Ni (II) ions, which has been speculated to the availability of limiting binding surface sites [70].