# Two-Dimensional Modelling Approach for Electrokinetic Water Transport in Unsaturated Kaolinite
## 3 Results and Discussion  
### Influence of the Electrode Positioning Type  
#### 3.1.1 Void Ratio Sensitivity  
Three simulations were carried out by setting the void ratio at 0.7, 0.9, and 1.2. As the initial water content was the same in the three cases (0.25, see Table 1), the initial degree of saturation for each simulation was 0.946, 0.736, and 0.552, respectively. The electric potential gradient applied was 1 Vcm\({}^{-1}\) in the three cases. First, progressive saturation of the soil was observed in the simulations when electrolyte reservoirs were considered. To explain this behaviour, it is important to bear in mind that, in general, a constant electrolyte level is maintained in the reservoir during the process. In the experimental setups, this is achieved with level controllers coupled with solenoid valves that allow for the addition/extraction of electrolyte. Considering this, and starting from a partially saturated state, a liquid pressure gradient was induced from the electrolyte reservoirs to the soil in contact with them, producing a significant hydraulic flow that generates soil saturation. This behaviour has been observed in previous experimental tests focused on electrokinetic remediation of pesticide-contaminated soils. Two-dimensional moisture distribution maps show a progressive and homogeneous increase in this variable [50; 51]. Different time intervals are needed to reach full saturation depending on the initial degree of saturation. For a time of 86,400 s (1 d), the case with \(e=0.7\) presented an average saturation degree of 0.963, while for the cases with e = 0.9 and e = 1.2, the values were 0.841 and 0.721, respectively. By inspecting Figure 2, it is apparent that water transport by electroosmosis is not relevant, since no asymmetries in the isolines of the degree of saturation can be observed. When an analysis of the net volume change of electrolytes was carried out (Figure 3), a loss of volume from both the anolyte and catholyte to the soil was observed in the first stages. The trend was more pronounced in the case where saturation was lower. However, while this volume loss was maintained in the case of anolyte reservoirs, a turning point appeared in the variation of the volume of the catholyte. From that moment onwards, an increase in the volume of catholyte was associated with a net transport of water from the soil to this reservoir. This indicates a change in the predominant type of water transport phenomenon, switching from hydraulic to electroosmotic. To explain this behaviour, it is useful to analyse the evolution of the volumetric fluxes (Figure 4). Figure 2: 2D maps of the degree of saturation evaluated at two times, 0 and 86,400 s (1 d), and three void ratios, 0.7, 0.9, and 1.2, when the electrodes were placed into the electrolyte reservoirs corresponding to the configuration presented in Figure 1a. Electric potential gradient: 1 Vcm\({}^{-1}\). In the cases of void ratios of 0.9 and 1.2, at t = 86,400 s (1 d), it can be observed that the hydraulic volumetric flow was much higher than the electroosmotic flow. However, at t = 864,000 s (10 d), the time at which full saturation was reached in all three simulated cases, the liquid pressure remained constant and equal to atmospheric pressure in both the soil and the electrolyte reservoirs. Consequently, there is no liquid pressure gradient, and therefore, the Darcian transport is negligible compared to the electroosmotic flow, whose direction is from anode to cathode, as shown in Figure 4. In addition, the direct influence of the degree of saturation on the magnitude of electroosmotic flow can be verified. The electroosmotic transport was higher when the soil was saturated (t = 864,000 s) than when it was in a state of partial saturation (t = 86,400 s). On the other hand, increases in both the electroosmotic and hydraulic volumetric fluxes associated with an increase in the void ratio were also observable, fundamentally due to the dependence of the saturated conductivities on the void ratio.