Time Evolution Study of the Electric Field Distribution and Charge Density Due to Ion Movement in Salty Water

Abstract

Desalination and water purification through the ion drift of salted water flow due to an electric field in a duct is perhaps a feasible membrane-free technology. Here, the unsteady modulation of ion drift is treated by employing the Poison–Nernst–Plank (PNP) equations in the linear regime. Based on the solution of the PNP equations, the closed-form relationships of the charge density, the ion concentration, the electric field distribution and its potential are obtained as a function of position and time. It is found that the duration of the ion drift is of the order of one second or less. Moreover, the credibility of various electrical circuit models is examined and successfully compared with our solution. Then, the closed form of the surface charge density and the potential that are calculated without the linear approximation showed that the compact layer is crucial for the ion confinement near the duct walls. To test this, nonlinear solutions of the PNP equations are obtained, and the limits of accuracy of the linear theory is discussed. Our results indicate that the linear approximation gives accurate results only at the fluid’s bulk but not inside the double layer. Finally, the important issue of electric field diminishing at the fluid’s bulk is discussed, and a potential method to overcome this is proposed.