Exploring the Impact of Steric Effects on Ion Removal of Water Solutions under the Influence of an Electric Field

In this study, we examine the movement of ions that are in a water solution which flows along a duct, due to the existence of an electric field, taking into account the size of the ions, a phenomenon known as the steric effect. We compare the results from the above model with the classical one (the one that uses the Boltzmann distribution where ions are considered dimensionless) for various parameters such as surface charge density, electric field and differential capacitance. It is shown that for dilute water solutions (10¹⁹ − 10²⁴ ions/m³ final concentration at the center of the duct), with ions of valence z = 1 (let us say saline water), steric effects become important for potentials greater than 1 V, and the phenomenon is more pronounced at higher concentrations. Furthermore, the steric effect model is applied to the calculation of the percentage of reduction in ion concentration in the main volume of the solution as a function of duct width for various electrode potentials and initial ion concentrations. Removal times are also calculated using Modified PNP equations which take into account steric effects. It is found that with a potential of 2.6 V, a 96% reduction in ions is achieved in the main volume of the solution for duct width 0.1 mm for 10²¹ ions/m³ final concentration at the center of the duct within approximately 1.6 s, while the percentage drops to 80% for duct width 1 mm. For smaller potentials, no noticeable decrease in concentration is observed, while for higher potentials, there are more impressive results, but we must be very careful because there is the case of other electrochemical phenomena taking place. The results are better when reducing the width of the duct, but relatively large widths are considered for the method to be practically applicable. With the increase in the concentration of the ions, their reduction percentage in the main volume of the solution decreases but remains significant up to 10²³ ions/m³ final concentration at the center of the duct. In addition, the completion time is shown to be proportional to the duct width. Therefore, for example, with the other parameters the same (2.6 V, 10²¹ ions/m³) but with L ~ 1 mm, the completion time can be estimated to be approximately 16 s. This observation enables us to estimate the completion time for different duct widths, eliminating the need for repeated numerical computation of the MPNP equations.