# Adsorption of Coxsackievirus in Sediments: Influencing Factors, Kinetics, and Isotherm Modeling
## 3 Results and Discussion
### Kinetic Modelling  
#### 3.2.1 Fitting of the Kinetic Models with Varied Sediment Particle Sizes  
A series of experiments were conducted to investigate the impact of CA16 adsorption at various sediment particle sizes. The collected data were analyzed using four kinetic models: first-order, second-order, pseudo-first-order, and pseudo-second-order kinetic models. The analysis of the results presented in Figure 4a-d indicates that the pseudo-second-order kinetic model provides the best fit to the experimental data, exhibiting a stronger correlation with the observed adsorption behavior. This validates the reliability of the pseudo-second-order kinetic model in precisely describing the adsorption kinetics of CA16 on clay surfaces at different sediment particle sizes.  
Table 2 presents the kinetic parameters and linear correlation coefficients of CA16 adsorption at varying sediment particle sizes. The coefficient of determination (\(R^{2}\)) values gauge the goodness of fit between the experimental data and the kinetic models. Particularly noteworthy is the superior fit of the pseudo-second-order kinetic model to the experimental data, with \(R^{2}\) values exceeding 0.99 (\(p\) < 0.05). Additionally, the outstanding agreement between the experimental values and the predicted values derived from the pseudo-second-order kinetic model reaffirms its suitability for accurately elucidating the adsorption process. These findings emphasize the robustness and reliability of the pseudo-second-order kinetic model in revealing the mechanisms and kinetics of CA16 adsorption at different sediment particle sizes.  
\begin{table}
\begin{tabular}{c c c c c c c} \hline \hline \multirow{2}{*}{**Factor**} & \multirow{2}{*}{**Kinetic Model**} & \multicolumn{5}{c}{**Adjusted \(R^{2}\)**} & \multirow{2}{*}{\(p\)**} \\ \cline{2-2} \cline{4-6}  & & **First-Order** & & **Secondary-Order** & **Pseudo-First-Order** & **Pseudo-Second-Order** & **Value** \\ \hline \multirow{5}{*}{Sediment particle} & Clay & 0.9602 & 0.8597 & 0.9707 & 0.9985 & \\ \cline{2-6}  & Slit & 0.9637 & 0.8580 & 0.9644 & 0.9974 & \\ \cline{2-6}  & Fine sand & 0.9345 & 0.9734 & 0.9749 & 0.9977 & \\ \cline{2-6}  & Medium sand & 0.8975 & 0.9857 & 0.9471 & 0.9985 & \\ \cline{2-6}  & Coarse sand & 0.8509 & 0.9790 & 0.9069 & 0.9987 & \\ \hline \multirow{2}{*}{Temperature (\({}^{\circ}\)C)} & 10 & 0.9383 & 0.9405 & 0.9728 & 0.9985 & \\ \cline{2-6}  & 25 & 0.9320 & 0.9275 & 0.9648 & 0.9982 & \\ \hline \multirow{5}{*}{pH} & 5.5 & 0.7247 & 0.9647 & 0.8735 & 0.9983 & \\ \cline{2-6}  & 6.5 & 0.8864 & 0.9678 & 0.9362 & 0.9964 & \\ \cline{2-6}  & 8.5 & 0.8497 & 0.9776 & 0.8960 & 0.9999 & \\ \cline{2-6}  & 9.5 & 0.8467 & 0.9854 & 0.9030 & 0.9977 & \\ \cline{2-6}  & 0 & 0.9703 & 0.7438 & 0.9662 & 0.9908 & \\ \cline{2-6}  & 5 & 0.9643 & 0.8703 & 0.9697 & 0.9870 & \\ \cline{2-6}  & 10 & 0.9018 & 0.9664 & 0.9527 & 0.9994 & \\ \hline \hline \end{tabular}  
* Calculating using Analysis of Variance (ANOVA) method [59].  
\end{table}
Table 2: Fitting of the kinetic equation parameters for CA16 adsorption under different factors.  
Figure 4: Kinetic models’ fitting of CA16 adsorption on different sediment particles. (**a**) first-order, (**b**) second-order; (**c**) pseudo-first-order; and (**d**) pseudo-second-order.