# Two-Dimensional Modelling Approach for Electrokinetic Water Transport in Unsaturated Kaolinite
## 3 Results and Discussion
### Influence of the Applied Electrode Configuration  
In a previous study, it was found that under the operating conditions set when using electrolyte reservoirs, kaolinite tends to saturate. At that point, the electroosmotic flow becomes the most relevant contribution to the total flow. Two magnitudes were selected as reference indicators to elucidate the influence of the electrode arrangement on the saturation process: (i) the amount of energy required to reach a fully saturated state and (ii) the time required to do so. Twelve configurations were selected (together with the basic distribution used in the previous sections of this work, Figure 1a,c-n), which are the most common configurations found in the literature [27, 40, 41, 42, 43, 44]. Simulations were carried out by applying electric potential gradients of 1 and 50 Vcm\({}^{-1}\). To establish a common criterion that facilitates comparison, the electric potential applied in the anolyte reservoir (\(\psi_{\text{anode}}\)) was estimated by considering the minimum distance between anode/cathode pairs. Table 3 presents the main features of the simulations conducted in this study. Figure 6: 2D maps of the degree of saturation evaluated at 86,400 s and three electric potential gradients of 5, 10, and 50 Vcm\({}^{-1}\): 0.7, 0.9, and 1.2 when the electrodes were in the electrolyte reservoirs and inserted into the soil corresponding to the configurations presented in Figure 1a and 1b, respectively. The void ratio of soil was 0.9. There is a decreasing trend in the time required to achieve full saturation of the soil as the total number of electrolyte reservoirs increases (Figure 7a). Furthermore, even when the electrical gradient was applied and the number of electrodes were the same, there were cases with very different saturation times. For example, in a system with 6 electrodes, specifically 3 anodes and 3 cathodes, the configuration corresponding to Figure 1e (2 rows of 3 electrodes facing each other) presented a saturation time almost double that obtained in the configuration illustrated in Figure 1j (hexagonal geometry with alternating anodes and cathodes). This reveals that, in addition to the number of electrolyte reservoirs, the geometrical configuration also has a significant influence. If the saturation time is analysed as a function of the minimum distance between anodes and cathodes, small interelectrode distances result in shorter saturation times. Even so, in this case, the trend is not clear, as there was greater dispersion among the results obtained. This dispersion decreases if the saturation time is analysed as a function of the electrode/minimum distance ratio, where a well-defined decreasing trend in saturation time was observed as the ratio increases. Of all the electrode configurations used, one (corresponding to the diagram in Figure 1d) displayed a behaviour discordant with the general trend. This may indicate that the number of electrodes has a more important role than the minimum distance between anode-cathode pairs in the time needed to reach saturation. Regarding the energy consumption in the saturation process, the trends observed coincide with those corresponding to the time needed. It is important to highlight the energy increase observed (up to three orders of magnitude) when a potential gradient of 50 Vcm\({}^{-1}\) was applied. However, the reduction in the time needed to saturate the soil was not as relevant compared to the simulations carried out at 1 Vcm\({}^{-1}\). From the above results, it could be stated that for the simulated cases, the type of electrode configuration used has a greater relevance in the transport of water through a partially saturated soil than the applied electric potential gradient.