## 3 Results and Discussion
### Simultaneous Evaluation of Washing Time and Solid-Solution Ratio in Heavy Metal Removal Efficiency  
So far, the effect of the type of washing solution, washing time, and the solid-solution ratio was evaluated through batch-type experiments. Additionally, other ions interacted with the washing solution, and the interaction depended on metal forms, ion affinity and surfactant structure [39]. Among them, the optimum washing time and solid-solution ratio, which represent the maximum amount of heavy metal removal, were calculated through CCRD arrangement for the washing time and solid-solution ratio, which were determined to have a complex effect on heavy metal removal (Table 2). Through the multiple regression and predictive second-order polynomial equation, a model equation representing the maximum \(\tau^{2}\) for each heavy metal was calculated (Table 3). In addition, the results are presented as 2D-contour and 3D-mesh plots, and the optimum solid-solution ratio and washing time, which indicate the maximum removal efficiency of each heavy metal, were suggested using the maximum value option in the solver method (Figures 9 and 10). Figure 8: The effect of the solid-solution ratio on the heavy metal removal efficiency by pH 0.5 acid solution (**a**), 50 mM EDTA (**b**). Asterisk indicates significant difference from maximum removal efficiency. Red dotted line indicates the minimum removal efficiency of heavy metals to meet the legal standards. \begin{table}
\begin{tabular}{c c c c c c} \hline \hline  & **Code** & **Cd** & **Cu** & **Pb** & **Zn** \\ \hline
**SSR 1** & **Washing Time** & \multicolumn{4}{c}{**mg kg\({}^{-1}\)**} \\ \hline \(-1\) & \(-1\) & 12.4 \(\pm\) 0.5 & 189.2 \(\pm\) 8.6 & 575.9 \(\pm\) 30.9 & 1254.6 \(\pm\) 57.9 \\ \(-1\) & \(1\) & 12.6 \(\pm\) 0.7 & 196.3 \(\pm\) 9.6 & 595.8 \(\pm\) 24.4 & 1351.7 \(\pm\) 47.2 \\ \(1\) & \(-1\) & 12.5 \(\pm\) 0.2 & 185.1 \(\pm\) 3.7 & 591.4 \(\pm\) 17.6 & 1248.5 \(\pm\) 20.9 \\ \(1\) & \(1\) & 13.1 \(\pm\) 0.9 & 197.1 \(\pm\) 14.9 & 620.8 \(\pm\) 51.6 & 1360.0 \(\pm\) 104.6 \\ \(2\) & \(0\) & 127 \(\pm\) 1.0 & 187.6 \(\pm\) 16.4 & 580.4 \(\pm\) 52.2 & 1288.2 \(\pm\) 109.3 \\ \(-2\) & \(0\) & 135.5 \(\pm\) 0.9 & 209.9 \(\pm\) 19.6 & 602.5 \(\pm\) 52.3 & 1354.9 \(\pm\) 121.1 \\ \(0\) & \(-2\) & 12.1 \(\pm\) 0.3 & 178.6 \(\pm\) 2.4 & 537.9 \(\pm\) 5.70 & 1097.1 \(\pm\) 17.8 \\ \(0\) & \(2\) & 12.5 \(\pm\) 0.6 & 188.1 \(\pm\) 10.4 & 574.0 \(\pm\) 28.7 & 1274.5 \(\pm\) 98.7 \\ \(0\) & \(0\) & 12.5 \(\pm\) 0.8 & 184.4 \(\pm\) 14.4 & 559.0 \(\pm\) 63.8 & 1205.2 \(\pm\) 125.9 \\ \(0\) & \(0\) & 13.4 \(\pm\) 0.5 & 203.1 \(\pm\) 8.2 & 631.6 \(\pm\) 32.9 & 1348.8 \(\pm\) 31.9 \\ \(0\) & \(0\) & 13.5 \(\pm\) 0.7 & 202.5 \(\pm\) 10.8 & 641.5 \(\pm\) 42.4 & 1345.5 \(\pm\) 66.6 \\ \(0\) & \(0\) & 13.0 \(\pm\) 0.8 & 196.1 \(\pm\) 12.6 & 619.4 \(\pm\) 41.1 & 1334.8 \(\pm\) 89.1 \\ \hline \hline \end{tabular} 1  
\end{table} 
Table 2: Removal amount by heavy metals according to treatment code. \begin{table}
\begin{tabular}{c c c c} \hline \hline  & **zdj-r2** & **Model 1** \\ \hline Cd & 0.391 & 0.200 & RE(\%) = 74.7 \(-\) 1.94x\({}_{1}\) + 1.14x\({}_{2}\) - 1.81x\({}_{1}\)2 \(-\) 0.68x\({}_{2}\)2 \({}^{2}\) + 0.03x\({}_{1}\)x\({}_{2}\) \\ Cu & 0.479 & 0.317 & RE(\%) = 74.5 \(-\) 2.93x\({}_{1}\) + 1.67x\({}_{2}\) - 1.62x\({}_{1}\)2 \({}^{2}\) - 0.84x\({}_{2}\) + 0.38x\({}_{1}\)x\({}_{2}\) \\ Pb & 0.443 & 0.269 & RE(\%) = 84.2 \(-\) 1.86x\({}_{1}\) + 2.02x\({}_{2}\) - 2.78x\({}_{1}\)2 \({}^{2}\) - 1.25x\({}_{2}\)2 \({}^{2}\) + 0.29x\({}_{1}\)x\({}_{2}\) \\ Zn & 0.498 & 0.341 & RE(\%) = 76.6 \(-\) 2.23x\({}_{1}\) + 3.35x\({}_{2}\) - 1.87x\({}_{1}\)2 \({}^{2}\) - 1.22x\({}_{2}\)2 \({}^{2}\) + 0.63x\({}_{1}\)x\({}_{2}\) \\ \hline \hline \end{tabular} 1  
\end{table} 
Table 3: The model equation for the evaluation of the maximum heavy metal removal efficiency (RE). Figure 9: The effect of the solid-solution ratio and washing time on heavy metal removal efficiency using 1 M citric acid through CCRD using 2D contour plot.