# A Numerical Study of Chemical Compatibility of GCLs
## 3 The Numerical Results and Discussion
### The Mesoscopic Mechanism of GCLs under Chemical Solution  
GCLs is chemical compatible with liquid to be contained if the hydraulic conductivity of the GCLs remains sufficiently low for the intended application when the GCLs is in chemical equilibrium with the liquid. However, the mechanism of the chemical compatibility of GCLs is difficult to be investigated in a hydraulic conductivity test. Therefore, from the mesoscopic view, the influence of flow path, the pore size, and the mobile porosity on the chemical compatibility and the hydraulic conductivity of GCLs need to be further investigated. Figure 8 illustrates a typical COMSOL model with the initial particle size is 0.075 mm, the initial mobile porosity is 0.4, and the ionic strength is 0 to 0.5 mol/L. Concerning the final mobile porosity and the final pore size changes, the influence of the ionic strength on the hydraulic conductivity of GCLs was explored. The chemical compatibility of GCLs was discussed. All these data were consistent with the experimental data of [PERSON] [6]. This model could screen the effect of the chemical solution and mesoscopic mechanism. Figure 7: The hydraulic conductivity vs. the mobile porosity. Figure 8: COMSOL model diagram (white: bentonite; Color: permeating solution). (**a**) \(I=0.1\) mol/L; \(n_{\rm f}=0.012\); (**b**) \(I=0.5\) mol/L; \(n_{\rm f}=0.0176\); (**c**) \(I=1\) mol/L; \(n_{\rm f}=0.022\). As shown in Figure 8, when the ionic strength of the chemical solution is 0.1 mol/L (the low chemical solution). The \(n_{\mathrm{f}}\) is 0.012, which can be calculated by Equation (11). Therefore, according to the COMSOL model, the final particle size and the final pore diameter of GCLs were 96.5 \(\upmu\)m and 0.3 \(\upmu\)m, respectively, as shown in Figure 8a. The maximum and the average velocities were 2.23 \(\times\) 10\({}^{-8}\) m/s and 8.64 \(\times\) 10\({}^{-9}\) m/s, respectively. Therefore, using this COMSOL model and Equation (3), the hydraulic conductivity, which is 2.29 \(\times\) 10\({}^{-10}\) m/s could be calculated. When the ionic strength increased to 0.5 mol/L, which represents the medium chemical solution [45], the \(n_{\mathrm{f}}\) = 0.0167 could be calculated by Equation (11). Using this final mobile porosity, the COMSOL model, as shown in Figure 8b, could be developed. The swelling of bentonite was inhibited, and the pore size increased. The particle size decreased to 96 \(\upmu\)m while the pore size increased to 0.8 \(\upmu\)m. The maximum velocity was 1.60 \(\times\) 10\({}^{-7}\) m/s, and the average velocity increased to 6.18\(\times\)10\({}^{-8}\) m/s. The average velocity in Figure 8b is 7.15 times that in Figure 8a. Accordingly, the hydraulic conductivity increased by order of magnitude, reaching 4.33 \(\times\) 10\({}^{-9}\) m/s. Compared to those in Figure 8a, it is interesting that although the particle size decreased only 5%, the final mobile porosity and the final pore size increased 150% and 170%, respectively. This phenomenon confirmed that the final mobile porosity and the final pore size are the key factors affecting the hydraulic conductivity of GCLs, as hypothesized in many kinds of research [28; 46; 47]. The COMSOL models proven this mesoscopic mechanism directly. Further increased the ionic strength to 1.0 mol/L, representing a strong chemical solution [4]. As shown in Figure 8c, when the final mobile porosity increased to 0.022 and the particle size decreased to 95.7 \(\upmu\)m, the pore size and the hydraulic conductivity increased to 1.1 \(\upmu\)m and 8.7 \(\times\) 10\({}^{-9}\) m/s, respectively. Comparing the changes from Figure 8a to Figure 8c, it can be found that with the further increase in ionic strength, the particle size decreased 8%, while the final mobile porosity and the final pore size increased 214% and 267%, respectively. This indicated that with the increase in the ionic strength or the solution concentration, particle expansion was inhibited. The final pore size and the finial mobile porosity increased.