Modeling of electrokinetic processes by finite element integration of the Nernst–Planck–Poisson system of equations

Electrokinetic remediation covers a variety of useful techniques for the mobilization of ionic and non-ionic species from porous materials by means of the application of an external electric field. Due to the large number of physicochemical interactions in the process, designing an electrokinetic remediation process is not simple.

Mathematical models are necessary for a better understanding of its fundamentals.In this study, a model for the electrokinetic transport phenomena based on the strongly coupled Nernst–Planck–Poisson system of equations is described. In the model presented here, the diffusion, the electromigration and the electroosmotic transport contributors are taken into account.

The Poisson's equation of electrostatics is used for the calculation of the electrical potential distribution based on the global charge balance. The effect of the electrode half-reactions is included. In addition to this, water equilibrium is continuously assured and the pH value is monitored. Results from some selected test simulations of the electrokinetic desalination of a sample of porous material are presented, outlining the versatility of the model as well as showing the effect of the counterion in the removal rate of a target ion.