COMPARACIÓN DE LA INFORMACIÓN No existen causas que impidan la comparación

As mentioned briefly in a previous section chemical speciation models can be coupled with transport models in order to predict release of contaminants from S/S wastes. Although determination of equilibrium chemistry is important in order to establish the species available for leaching, modelling of transport of ions in porous cementitious matrices is also essential for determining release of contaminants. Modelling of the transport mechanisms is typically based on diffusion. Molecular diffusion is the process whereby a concentration difference between two points in a stagnant solution is levelled out in time due to the random Brownian movement of molecules. Movement of molecules by diffusion is described by Fick’s laws (Appelo and Postma, 2007). Fick’s first law relates the flux of a chemical species to the concentration gradient:

𝐹 = −𝐷𝜕𝑐

𝜕𝑥 (2.13)

Fick’s second law expresses the change in concentration with time according to the following equation:

𝜕𝑐

𝜕𝑡 = 𝐷_𝑒𝜕²𝑐

𝜕𝑥² (2.14)

where c is the concentration of the contaminant [M/L³], and De is the effective diffusion coefficient, incorporating tortuosity and porosity of the solidified matrix [L²/T]. The equation of the effective diffusion coefficient is:

𝐷_𝑒 = 𝑒

𝜏² 𝐷_𝑑 (2.15)

87 where e is the porosity of the matrix, τ is tortuosity and Dd is the diffusion coefficient of the ion in a dilute solution.

Tortuosity is a measurement of physical retardation and gives an indication of the path length that a diffusing ion must cover in a porous matrix. It is a material property and not ion-dependent (NEN 7375:2004). The basic premise behind the bulk diffusion model is that contaminant release is a result of the concentration gradient between the leachant and the bulk concentration within the monolith (Baker and Bishop, 1997). The main assumptions of the model are (Barna et al, 1994):

o the contaminants are distributed uniformly in the monolith at an initial concentration (C0).

o the monolith remains homogeneous and the effective diffusion coefficient remains constant during leaching.

o no chemical reaction disturbs the physical mass transfer.

The bulk diffusion model is widely used for modelling purposes and forms the basis for leach tests such as the ANS 16.1 and the NEN 7375:2004. Limitations of the bulk diffusion model in describing leachability from S/S wastes have been previously reported. These limitations pertain to the failure of the bulk diffusion model to describe interactions between the leachant and the solids, especially in cases where an acid leachant is used as it will be explained in the following section.

a) Shrinking Unreacted Core Model

According to Baker and Bishop (1997), previous studies on the behaviour of cement in acidic leachants have shown the existence of a calcium depletion zone, with a sharp interface, on the exterior layer of samples leached in acid solution. Depletion of acid-soluble species was also observed in this zone, while an unreacted zone was noted in the interior of the leached specimens. The same authors reported that previous studies on leaching characteristics of S/S wastes leached under acidic conditions observed the following:

 The leached layer was essentially depleted of calcium and soluble contaminants.

88

 The leached layer consisted of an amorphous silica-rich gel with a much higher porosity than the unreacted specimens.

 A thin zone of calcium-rich re-mineralization was noted at the leach front.

 The specimen beyond the leach front remained unchanged.

 A small pH gradient in the leach shell was noted, followed by a large pH change over the very narrow leaching zone. A constant, high pH was observed in the unreacted core.

The shrinking unreacted core model (SUC) was developed to account for the effects of the diffusion acidic species into the leached specimen. In contrast to the bulk diffusion model, where contaminant leaching is considered to be a result from the diffusion from the specimen into the leachant, the SUC model considers the diffusion of acidic species from the leachant into the specimen as the leaching controlling mechanism. Figure 2.5 presents a schematic illustration of the SUC model.

According to the SUC model acid leachant permeates the pore structure of the cement or pozzolanic-based paste. The acid consumes the calcium hydroxide in the paste lowering the pH of the matrix. Reduction in pH results in metal ions dissolving and diffusing in a direction towards the leachant, or towards the unaltered core of the specimen where they precipitate again due to constant high pH. This zone, where metal ions precipitate again as insoluble hydroxides, is called the remineralisation zone.

Figure 2.5 Schematic illustration of the shrinking unreacted core leaching model (Baker and Bishop, 1997).

89 The key elements of the model therefore as shown in Figure 2.5 are the leached shell which is a highly porous structure (Cheng and Bishop, 1990), the leaching front and the unaltered core.

Cheng and Bishop (1990) consider two distinct processes in the SUC model. Diffusion across the leached layer can be considered a steady-state process. At the leaching front however, diffusion of hydrogen ions process as if the medium is infinite and dissolution reactions occur at the same time in the pores. The proton reactions in the leaching front have a half-life of less than milliseconds. The system in such a case could be considered as an unsteady-stated diffusion-controlled fast reactions process.

The shrinking unreacted core model follows a similar rationale to decalcification, apart from the fact that in the latter calcium hydroxide is not neutralized under the effect of an acid but it leaches out of the specimen due to the dissolution of portlandite crystals. In both cases the same zones are observed comprising a leached calcium depleted zone, the leaching front and a sound/unreacted zone or core. The physical properties of cement based materials depend on the amount of calcium present. In both cases, matrix alteration may take place leading to changes in its physical properties during leaching, creating a new porosity.