## 3 Results
### Influence of Electrical Field on the Performance of MFRO Desalination  
To study the effect of an electric field on the rate of desalination, the flux through the membrane, and the _SEC_ in an RO system, the operation pressure was maintained at a fixed value of 0.5 MPa, while the voltage magnitude was systematically varied. The permeate flux impact was analyzed by calculating the permeate flux ratio using Equation (4). Figure 5a illustrates that irrespective of the specific concentration, there was no discernible change in solute rejection following the application of the elevated electric field over the case with no electric field. This result shows that at salt concentrations below 3000 mg/L, the electric field has no significant effect on the desalination of the membrane. Figure 5b shows that the permeate flux ratio increased slightly when an electric field was applied. The values recorded were 1.02%, 1.23%, and 1.37% for salt ion concentrations of 1000, 2000, and 3000 mg/L, respectively. It should be noted that the effect of the electric field on the permeate flux was more pronounced at higher salt ion concentrations and increased voltages, eventually reaching a plateau. According to Equation (2), the amount of produced water is directly influenced by the permeate flux, indicating that water production increases with higher voltages. While water production is typically affected by the operating pressure within the normal range, our study maintained a constant pressure and only varied the electric field. These findings suggest that the electric field can enhance  
Figure 4: Comparing membrane performance of the Multi-field reverse osmosis at different pressure fields under pure brine conditions: (**a**) changing the solute rejection and (**b**) changing the recovery rate. ion migration, reduce ion accumulation on the membrane surface, promote water molecule movement, and thus increase the permeate flux. Figure 5c shows that the _SEC_ in the presence of an electric field is lower at different concentrations than in the absence of an electric field. Specifically, when the salt concentrations are 2000 and 3000 mg/L, the _SEC_ decreases from 0.36 and 0.62 kW\(\cdot\)h/L (0 V) to 0.25 and 0.39 kW\(\cdot\)h/L (25 V), respectively. These reductions correspond to a decrease of 31% and 59%, respectively. However, at a salt concentration of 1000 mg/L, the electrical field has no significant effect on energy consumption. Equations (6)-(8) show that in low-salinity solutions, the current is small, so the electric field's effect on the permeate flux is small. As a result, the rates of power consumption and permeate flux offset each other, leading to a minor change in the unit energy consumption of water production. As the salt concentration increases, the electric field force strengthens, thereby enhancing the effect of the electric field on permeate flux. The growth rate of the permeate flux becomes dominant, leading to a downward trend in energy consumption for water production. However, due to the progressive increase in voltage, the growth rate of power consumption becomes dominant, thereby slowing down the rate of decline in unit energy consumption. Overall, these results suggest that the use of an electric field can greatly decrease the _SEC_, especially at higher salt concentrations. To investigate the correlation between the permeate flux and operating voltage, a linear regression analysis was conducted. The results, presented in Figure 5d, indicate a strong linear correlation between permeate flux and the applied voltage, with R\({}^{2}\) values above 0.9 for all three concentrations tested. The data also reveal that the influence of the voltage on permeate flux varies with the salt concentration. At 3000 mg/L, the permeate flux is most influenced by the applied voltage, followed by 2000 mg/L and then 1000 mg/L.