Modeling ion and fluid transport in unsaturated cement systems in isothermal conditions

The electrical potential in Eq. (88) arises in the material to enforce the electroneutrality condition. If two species are diffusing in a material, with one of the species having a greater self-diffusion coefficient, then in order to maintain a neutral solution, the potential created slows the fastest ions and accelerates the slowest ones.

The mathematical relationship that relates electrical potential to electrical charge in a given medium is given by Poisson's equation [18]

where ρ is the electrical charge density and ∈ is the medium permittivity. The charge density can be related to the ionic concentration through:

It may seem awkward to have an equation from electrostatics in a model where the ions are moving through time. However, because the electromagnetic signal propagates much more rapidly than the ions do, Poisson's equation is perfectly suitable.

To use Eq. (91) in the transport model, it has to be averaged over the REV. As it was done previously, it is assumed that the boundary effects at the liquid/solid and liquid/gas interfaces are negligible. Following the same average rules as in the previous sections, we get the following relationship:

3.3. Calculation of the potential