# Two-Dimensional Modelling Approach for Electrokinetic Water Transport in Unsaturated Kaolinite
## 4 Conclusions  
In this paper, a new conceptual model and a simulation tool were developed that allow for the simulation of water flow in partially saturated soils in 2D domains under electrokinetic treatments. With a simple formulation and state functions based on the extensive characterisation that has been developed over time for kaolinite, different operational alternatives were analysed. This has allowed for the identification of behavioural trends and the optimisation of treatment strategies on a lab scale. Relevant differences in performance were observed between operation with electrolyte wells, which provide unlimited fluid supply, and operation with electrodes inserted in the ground. In the first case, saturation of the soil is almost inevitable, and a higher fluid flow in the soil is reached after this point. This configuration is particularly suitable for electroosmotic flushing of contaminants or for the delivery of reactants in ground improvement techniques in low-permeability soils. In the second case, there is only a redistribution of water within the soil, so this arrangement  
Figure 7: Time to saturation depending on the (**a**) number of total electrodes, (**b**) minimum distance between the anode–cathode, and (**c**) ratio of electrodes/minimum distance. Energy consumption to saturation depending on the (**d**) number of total electrodes, (**e**) minimum distance between the anode–cathode, and (**f**) ratio of electrodes/minimum distance. \(\
abla\psi=50\) Vcm\({}^{-1}\) is indicated by empty markers and \(\
abla\psi=1\) Vcm\({}^{-1}\) is indicated by filled markers. is ideal for soil dewatering and drainage, which can be advantageous in improving the mechanical properties of the ground. In addition, a detailed analysis of various operating alternatives with several electrolyte wells and varying spatial distributions was carried out. It was found that the ratio of the number of electrodes to the minimum distance between them primarily determines both the time to saturation and the energy consumption. It has been shown that electrical potential gradients do not particularly favour rapid saturation of the soil, and greatly increase the energy cost. This implies that there is an important task of optimisation in the design of these kinds of treatments. Optimal designs are also expected to be dependent on the properties of the soil to be treated, its volume, the available energy sources, and the type of treatment to be conducted. The role of numerical models is therefore fundamental in the process of fine-tuning and optimising electrokinetic treatments, although practical experience in the field will always be irreplaceable. However, the presented numerical model still suffers from limitations. In particular, more tests are needed for its validation. In general, most of the tests thus far have focused on evaluation of the reduction in pollutant concentration (electrokinetic remediation) or the variation in the soil void ratio (electroconsolidation). In future works, it will be essential to have reliable results on the spatial distribution of water content in situations with well-defined initial and boundary conditions. Furthermore, an additional extension to 3D conditions and more realistic geometries will be required to fully exploit the capabilities of this model. The following supporting information can be downloaded at: [[https://www.mdpi.com/article/10.3390/app13010519/s1](https://www.mdpi.com/article/10.3390/app13010519/s1)]([https://www.mdpi.com/article/10.3390/app13010519/s1](https://www.mdpi.com/article/10.3390/app13010519/s1)), Figure S1: 2D maps of the current density and electric potential gradient for the configuration presented in Figure 1a. Figure S2: 2D maps of hydraulic and electroosmotic volumetric fluxes for the configuration presented in Figure 1b. Table S1: Values of the physical parameters as a function of the void ratio range studied. Conceptualization: R.L.-V. and A.Y. ; methodology: R.L.-V. and A.Y. ; software: R.L.-V. and A.Y.