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

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3.2. Coupling water and ionic transport

To model the transport of ions under the influence of capillary suction, it would seem straightforward to substitute Eq. (28) in Eq. (84). However, the development of the water transport equations was made for the case of pure water in a porous material. When ions are in solution, the vapor pressure above a solution is lower than in pure water [36]. This effect is quantified through Raoult's law. Accordingly, the relationship should instead be written as:

(85)

because the presence of ions in solution is likely to disturb the equilibrium between the aqueous and gaseous phases in a pore. To evaluate to what extent the presence of ions will affect the vapor pressure of water, one can use Raoult's law to calculate the vapor pressure change between pure water and a 500 mmol/l NaCl solution with water as solvent. According to Raoult's law [36], the vapor pressure change is given as:

(86)

where X_solute is the molar fraction of solute (NaCl) in the solution and

is the vapor pressure of pure water. At 25 °C, the vapor pressure of bulk water is 3.17 kPa [36]. Knowing that in 1 l of water there are 56 mol:

(87)

This gives a change in vapor pressure of Δp_v=0.03 kPa, which is obviously very weak. According to the result of this simple calculation, the effect of ionic concentration on the capillary pressure is neglected. It was also neglected in previous models presented in Refs. [23], [24], [25] and [28].

Substituting Eq. (28) in Eq. (84) gives:

(88)

This equation can be used to model the transport of ions in unsaturated cement-based materials when the pore fluid is in movement because of capillary suction. To complete the model, an equation must be considered to evaluate the potential Ψ, as well as an expression to calculate the chemical activity coefficients. These topics are addressed in the following sections.

Next: Calculation of the potential Up: Ionic transport Previous: Transport of ions