The mathematical model developed in this paper is first summarized. For materials where the water transport occurs as a result of capillary suction, the water content profile can be calculated with Richards' Eq. (51). The ions will move in the material under the combined effect of diffusion (including electrical and activity effects) and water movement according to Eq. (88). The electrical potential, arising from the electrical coupling between the ions to maintain a neutral solution, is calculated with Poisson's Eq. (92). The chemical activity coefficients, for the highly charged pore solution of cement-based materials, can be evaluated with Eq. (93). Finally, several references were given to address the modeling of chemical reactions occurring in cementitious materials.
The use of the averaging technique clearly helps to clarify the meaning of some important parameters in the model. According to this technique, the water content in Richards' model corresponds to a volumetric water content. The water diffusivity was clearly shown to be a contribution of both liquid water and vapor transport. The diffusion coefficient, the parameter that characterize the ionic diffusion process, is directly related to the geometrical properties of the material through a parameter called the tortuosity.
The averaging technique proved to be a powerful mathematical tool to lay the foundation of transport models in porous media.