## 4 Discussion
### Metal Removal Mechanisms and Scale-Dependent Kinetics  
The temporal dynamics revealed through experimental analysis demonstrate a sophisticated three-phase removal process, with distinct characteristics at each stage [24]. The scale-dependent behavior of the treatment system, comparing module-scale (25 L, 30 g biochar) and kinetic studies (100 mL, 10 g biochar), provides crucial insights into removal mechanisms across different operational scales [25]. The distinct volume-to-adsorbent ratios (833:1 vs. 10:1 mL g\({}^{-1}\)) produced markedly different removal patterns that illuminate the underlying processes (Table 4).  
The initial rapid surface adsorption phase (0-4 h) exhibits removal rates of 0.28-0.42 mg g\({}^{-1}\) h\({}^{-1}\), with higher rates observed in the kinetic studies due to greater site availability [26]. During this phase, module-scale experiments showed removal efficiencies of 25-35%, while kinetic studies achieved 45-65% removal, demonstrating the significant impact of the volume-to-adsorbent ratio on initial removal kinetics. The higher ratio in module-scale experiments resulted in more gradual but sustained removal rates, maintaining consistent performance over the 10-day period due to the controlled release of binding sites and reduced competition for adsorption sites.  
The transition to pore diffusion-dominated removal (4-24 h) shows remarkable consistency with molecular dynamics simulations [27], exhibiting a 60-80% rate decrease compared to the initial phase. During this period, removal rates decreased to 0.10-0.15 mg g\({}^{-1}\) h\({}^{-1}\) in module-scale experiments and 0.12-0.18 mg g\({}^{-1}\) h\({}^{-1}\) in ki  
\begin{table}
\begin{tabular}{c c c c c} \hline \hline
**Ions** & **Concentration (mg:L\({}^{-1}\))** & **k\({}_{2}\) (g:mg\({}^{-1}\)-h\({}^{-1}\))** & **q\({}_{e}\) (mg:g\({}^{-1}\))** & **R\({}^{2}\)** \\ \hline Cd\({}^{2+}\) & 0.25 & 0.063 & 0.84 & 0.995 \\  & 2.5 & 0.048 & 7.62 & 0.992 \\  & 12.5 & 0.032 & 35.78 & 0.987 \\ Pb\({}^{2+}\) & 0.05 & 0.095 & 0.18 & 0.997 \\  & 0.5 & 0.078 & 1.74 & 0.995 \\  & 2.5 & 0.052 & 8.35 & 0.991 \\ Cr\({}^{3+}\) & 2.50 & 0.044 & 8.12 & 0.989 \\  & 25.0 & 0.035 & 75.26 & 0.986 \\  & 125.0 & 0.021 & 348.42 & 0.982 \\ Cu\({}^{2+}\) & 5.0 & 0.057 & 16.38 & 0.994 \\  & 50.0 & 0.039 & 154.52 & 0.988 \\  & 250.0 & 0.024 & 715.86 & 0.985 \\ Zn\({}^{2+}\) & 50.0 & 0.042 & 152.60 & 0.990 \\  & 500.0 & 0.028 & 1360.45 & 0.986 \\  & 2500.0 & 0.016 & 5842.64 & 0.983 \\ \hline \hline \end{tabular} Note: All kinetic parameters were calculated based on experimental data from the kinetic studies (10 g biochar in 100 mL solution, 10:1 mL–g ratio). k\({}_{2}\) represents the pseudo-second-order rate constant; q\({}_{e}\) represents the calculated equilibrium adsorption capacity; R\({}^{2}\) represents the correlation coefficient indicating the goodness of fit.  
\end{table}
Table 4: Pseudo-second-order kinetic parameters for heavy metal removal by the ecological concrete–biochar system.  
netic studies. The final chemical fixation phase (>24 h) demonstrates long-term stabilization mechanisms, with removal rates stabilizing at 0.05-0.08 mg g\({}^{-1}\) h\({}^{-1}\) and 0.03-0.05 mg g\({}^{-1}\) h\({}^{-1}\) for module-scale and kinetic studies, respectively.  
These kinetics can be effectively modeled using a modified pseudo-second-order equation [28]:  
\[dq/dt=k_{2}(q_{\rm e}-q)^{2} \tag{3}\]  
where \(dq/dt\) represents the rate of metal uptake, \(k_{2}\) is the rate constant, \(q_{\rm e}\) is the equilibrium uptake capacity, and \(q\) is the uptake at time \(t\). This model has been extensively validated for multi-metal systems.