Discussion

Estimating the pore solution conductivity is significant to transport models that distinguish between the chemical and the physical behavior. Ionic transport through a porous media is hindered by both the solid microstructure (physical effects) and ion-ion interactions (chemical effects). The physical effects can be uniquely characterized by the formation factor (or tortuosity) and the porosity [3], which are experimentally determined material coefficients. Because macroscopic bulk concrete conductivity measurements can be performed using readily available equipment [6], estimating the pore solution conductivity is vital to estimating the formation factor.

In addition to the material parameters, a transport equation for concentrated electrolytes must also estimate the ionic mobility because an internal diffusion potential will arise due to the differences in self-diffusion coefficients [23]. The internal diffusion potential creates the electrical field necessary to ensure zero total electrical current. The coefficient of proportionality between an electric field and the drift velocity is the mobility, and is proportional to the species equivalent conductivity. Therefore, the magnitude of the mobility determines the resulting diffusion potential and is directly related to the pore solution conductivity.

Furthermore, migration (or driven diffusion) tests that use an external electric field to transport ionic species through a porous material are actually determining the bulk ionic mobility. If the objective is to predict future behavior of concrete exposed to the same external electric field and chemical environment, the observed experimental behavior is indicative of future behavior. By contrast, if the migration test is used to predict future behavior in the absence of an external electric field, the objective of the experiment must be considered carefully.

The response of the migration test is a measure of both the physical microstructure and the concentration dependence of the mobility. Therefore, future predicted behavior based on a transport model that considers chemical and physical effects separately will require a method for extracting the true formation factor from the migration test by accounting for the chemical effects in the test. In the migration experiment, the bulk drift velocity (experimental observation) $\vec{v}$ will be proportional to the external electric field $\vec{E}$:

$$\vec{v_i} = \frac{u_i}{\Upsilon }\vec{E}$$ (10)

The quantity u_i is the mobility of the ion within the pore solution (it incorporates the chemical effects), and the formation factor $\Upsilon$ represents the physical microstructural barrier. The concentration dependence of the mobility ( $Fu_i = \lambda_i$, $F$ - Faraday constant) from Eqn. 3 can be incorporated in the formation factor estimation:

$$\Upsilon = \left(\frac{\lambda_i^\circ}{F}\ \frac{\vec{E}}{\vec{v}}\right)\ \left.\frac{1}{1+G_i\,I_M^{1/2}}\right.$$ (11)

If the chemical effects of the migration test had been neglected, only the quantity within parentheses would have been attributed to the formation factor, as is typically done when estimating the diffusion coefficient from a migration test. Therefore, the true formation factor is a factor of $(1+G_i\,I_M^{1/2})^{-1}$ smaller than what would otherwise be expected; a material with a smaller formation factor would present less of a physical barrier to transport. For the case of a chloride migration test in a pore solution having an ionic strength I_M = 0.75 (as is typical [10]), the quantity $(1+G_{\mbox{\tiny Cl$^-$}}\,I_M^{1/2})^{-1}$ = 0.68. Therefore, neglecting the chemical effects results in a microstructural transport coefficient that is in error by 30 %.