Several mathematical models have been developed to predict the movement of ions in cement-based materials. Most of these approaches are single-ion models, considering only chloride and its detrimental effect on the durability of the material. Most of the time, such models consider the transport of ions under the effect of diffusion and advection (fluid flow). Also considered is the effect of the chemical reactions involving the considered species, although in a very simple way. For example, Saetta et al. [23], Nagesh and Bhattacharjee [24], and Gospodinov et al. [25] published such models.
However, these models oversimplify some basic physical phenomena. For instance, the electrical coupling between the ions [18] and its effect on their movements is often overlooked. This is particularly true for cement-based materials because they contain concentrated porous solution. The electrical coupling between the ions for concentrated solutions was recently put in evidence in two papers by Snyder [26] and [27] that report on diffusion experiments through nonreactive ceramic frits. Multiionic models taking into account electrical coupling were recently published by Masi et al. [28] and Truc et al. [29].
Unfortunately, as it was the case with Richards' equation, there is a lack of agreement with regard to the definition and the use of some parameters in these models. For example, the diffusion coefficient is sometimes called the intrinsic diffusion coefficient, the apparent diffusion coefficient, or the effective diffusion coefficient. Once again, the averaging procedure is used to generate an ionic transport model. The method will clarify some of the basic concepts behind the modeling of ionic transport. Such a work was previously published [4] but was applied only to nonreactive saturated materials. The model presented in the following sections is more general.