## 3 Results and Discussion
### Experimental Study on Isothermal Adsorption Characteristics of Solute  
#### 3.2.1 Isothermal Adsorption Test of _S. pasteurii_  
According to the isothermal adsorption test of _S. pasteurii_ at 20 \({}^{\circ}\)C, the OD\({}_{600}\) value concentration was converted into the mass concentration of bacteria by Formula (3), and the isothermal adsorption line of _S. pasteurii_ in the layer 3 fine sand in Shanghai was obtained, as shown in Figure 11. It can be seen that when the concentration of _S. pasteurii_ is OD\({}_{600}\) = 1.35 (mass concentration 7.32 g/L), the capacity of the fine sand to adsorb _S. pasteurii_ increases with the bacterial solution concentration, which conforms to the Freundlich isotherm equation. The adsorption capacity increased from 59.3 mg/L with OD\({}_{600}\) = 0.35 (mass concentration 1.04 g/L) to 975.7 mg/L with OD\({}_{600}\) = 1.35 (mass concentration 7.32 g/L). In the process of using MICP grouting technology to form a HSRB, the concentration range of _S. pasteurii_ to be used is less than 1.35. Figure 11 shows that the isothermal adsorption of _S. pasteurii_ by Shanghai layer 3 fine sand is basically linear within this range. Therefore, the Freundlich isotherm can be used to describe the isothermal adsorption of _S. pasteurii_ onto the fine sand. The parameters after fitting are as shown in Table 1. \begin{table}
\begin{tabular}{c c c} \hline \hline
**Isotherm Type** & \multicolumn{2}{c}{**Freundlich Isotherm**} \\ \hline Parameter & R\({}^{2}\) & \(K_{d}\) (L/mg) \\ Value & 0.9903 & \(1.5\times 10^{-7}\) \\ \hline \hline \end{tabular}
\end{table} 
Table 1: Parameters of _S. pasteurii_ adsorption model. Figure 11: Adsorption isotherm of _S. pasteurii_. The kinetics of bacterial retention by the porous media was largely influenced by the electrostatic interactions. The greater hydrophobicity of cells and substrata results in greater attractive forces and higher levels of adhesion [40]. The classical Derjaguin-Landau-Verwey-Overbeek (DLVO) theory [41] is used to describe microbial adhesion to solid surfaces; later, [PERSON] developed the extended DLVO theory (XDLVO) [42]. _S. pasteurii_ was proven to show moderate hydrophobic attachment with a non-polar solvent [43]. As the hydrophobicity of the cell increases, it also enhances the adhesion property to the sand. This is consistent with the extended XDLVO theory [42], which points out the importance of \"hydrophobic attraction\" between hydrophobic and hydrophilic surfaces in aqueous media. The results showed the good attachment ability of _S. pasteurii_ to this type of sand. According to the isothermal adsorption test of CaCl\({}_{2}\) at 20 \({}^{\circ}\)C, the isothermal adsorption line of Ca\({}^{2+}\) in the layer 1 fine sand from Shanghai was obtained, as shown in Figure 12. The figure shows that when the concentration of Ca\({}^{2+}\) is below 32 g/L, the _S. pasteurii_ adsorption capacity of Shanghai layer 1 fine sand increases with the bacterial solution concentration. When the concentration of Ca\({}^{2+}\) exceeded 32 g/L, the maximum _S. pasteurii_ adsorption capacity of Shanghai layer 1 fine sand was 2.4 g/kg, and the adsorption capacity did not increase. The isothermal adsorption capacity of Ca\({}^{2+}\) is described by linear isothermal adsorption (Equation (6)) and Langmuir isothermal adsorption (Equation (7)), as shown in Table 2. The range of Ca\({}^{2+}\) concentration may be 20-60 g/L in the process of using MICP technology to form a HSRB. Figure 12 shows that, within this concentration range, the maximum adsorption capacity of Ca\({}^{2+}\) by Shanghai layer 1 fine sand is 2404.8 mg/kg, and Ca\({}^{2+}\) will not be adsorbed indefinitely. Therefore, the Langmuir isotherm can truly reflect the adsorption of Ca\({}^{2+}\) by the layer 1 fine sand from Shanghai during the migration process.