Numerical simulation of multi-species diffusion

Abstract

A B S T R A C T R I~ S u M I~A numerical model has been developed to simulate the transport of several ionic species across a saturated concrete or mortar sample. The chloride binding as well as the electrical coupling between the different ionic fluxes are included in the model by using the NernstPlanck system of equations. This model highlights which parameters affect substantially chloride penetration into reinforced concrete structures and then shows that the use of Fick's first law in a predictive model for chloride penetration is strongly challenged. The simulations are in good agreement with diffusion-cell experiments and membrane potential measurements. iiiiiiiiiiiiii-

Diffusion of ions in unsaturated porous materials

“…Applying the volume-averaging operator, Eq. (19), to the local ionic flux given by Eq. (4) yields an expression for the macroscopic flux of species i,…”

“…In porous materials, the influence of the electrostatic coupling between the ions was discussed more lately by McDuff and Ellis [4], Revil et al [16], Snyder and Marchand [6], and Snyder [17]. Multi-ionic models taking into account electrical coupling were also recently published by Masi et al [18] and Truc et al [19,20], but unfortunately these models do not account for the influence of the electrical double layer, which is responsible for the difference between the so-called diffusion and membrane potentials (see [4,9,21,22]). …”

Anion capture and exchange by functional coatings: New routes to mitigate steel corrosion in concrete infrastructure

“…This 1D-domain of a pristine (i.e., uncracked) concrete section is shown in Figure 6. The concrete section has a thickness of L = 0.2 m, a fraction of which comprises a CAC-based top-layer of thickness x c = 0.025 m. The depth of the reinforcing steel from the upper surface (i.e., the cover depth) is assumed to be x r = 0.050 m. To describe ion transport, the following assumptions were made: The porosity of the concrete and the CAC-based top-layers is saturated with pore solution,Advective transport of ions is negligible as a zero pressure gradient is assumed in the pores, hence the pore solution velocity (and Péclet number) is zero, assuming no moisture transport is induced by cyclic wetting-and-drying [43,77],The effects of ion-activity (i.e., non-ideality of the solution) on transport are not accounted for since this factor exerts second order contributions to the transport response [78,79],The effects of electrical coupling between ions is significant enough to warrant multispecies modeling [42,80], and,The electrical double layer present on the hydrated solids does not affect transport [81], since ion transport takes place dominantly through larger capillary pores which remain percolated, rather than through the nanoscale gel pores, e.g., as present in the C-S-H [68]. …”

“…Several numerical models have been developed to describe mass transport of ions that influence the service life of reinforced concrete infrastructure [23,24,37–42]. These transport models vary in complexity from single-species models governed by Fick’s laws of diffusion [23,37], to multi-species Poisson-Nernst-Planck (PNP) models which account for electric coupling between ions due to their differing mobilities [40,41].…”

Thermodynamic modelling: state of knowledge and challenges

“…Some multi-ionic models dedicated to contaminant ingress in concrete have been developed considering the electrical coupling term in Equation 25. The model presented by Truc et al (2000) takes the electrical coupling into account to model the ingress of chloride in concrete structures. The binding of chloride on the hydrated cement paste is approximated by an isotherm-type relationship.…”