Migration versus Diffusion through Porous Media: Time-Dependent Scale Analysis

Abstract

This paper presents a fundamental study of enhanced ionic transport in the case when an electrical field is applied through a saturated porous medium. The study focuses on the very first moments when the potential difference is applied. Scale analysis is used in order to highlight the existence of two different regimes: initially, pure diffusion prevails in spite of the electrical field that will overtake diffusion-driven transport after a transition time. It is shown that the reason for this change in mechanisms is the search for the maximization of the ionic transfer. In the numerical part, the impact of already contaminated porous medium on the amount of ionic species transferred is studied, together with the effect of the concentration and concentration gradients levels. Finally, an optimization method is proposed in order to maximize the transport of species by applying an electrical field increasing in time.