In this study we focussed on the salt transport during the drying of a salt-contaminated material, as this induces crystallization at the surface of the material. Here we consider single-sided drying of a material saturated with a NaCl solution. Drying experiments were performed on various types of fired-clay brick. These bricks showed almost no adsorption of ions at the pore wall. In all drying experiments, with the drying rates used in this study, it was observed that the moisture profiles were almost homogeneous, and within the time of these experiments, that is, up to 14 days, no receding drying fronts were observed. We attribute this to the wetting properties of the NaCl solution. In Fig. 1, an example for a drying experiment of a 3 M NaCl solution is shown.


Figure 1. NaCl concentration profiles measured during drying of a fired-clay brick sample
of 45 mm length after 0, 1, 3, 6, 9, 12, and 15 days.

During the initial drying, Na ions are advected to the surface (position 0 mm) and the NaCl concentration slowly increases to 6 M, which is the saturation value for a NaCl solution. At this point additional advection will result in crystallization at the top of the sample, which is observed as a white efflorescence. From this point on the NaCl concentration profile in the sample starts to level off until the total sample is at 6 M. During a drying experiment there will be a competition between advection, which transports ions to the top of the sample and thereby causes accumulation, and diffusion, which levels off any accumulation. For the drying of a porous material a Peclet number can be defined as:

where h is the drying rate, L the length of the sample,  thetam maximum fluid content by capillary saturation, and D the diffusion coefficient of Na in the porous material. For Pe<<1 diffusion dominates and the ion-profiles will be uniform, whereas for Pe>>1 advection dominates and ions will be accumulated at the drying surface. Initially the drying rate gives rise to Pe~ 3, corresponding to the accumulation of the 6 M peak at the surface, whereas  after two days Pe~ 0.7, corresponding to the leveling off of the NaCl profile
 This quantity CavgSavg is proportional to the total amount of dissolved ions in the solution (observed by NMR), since in our. From the measured profiles it is found that initially this amount decreases rapidly, indicating that salt is crystallizing. As the drying rate decreases also the crystallization rate decreases at the top. In order to get a better representation of this experiment and also to include the crystallization we have introduced the efflorescence pathway diagram (EPD), as plotted in Fig. 2.


Figure 2.  Efflorescence pathway diagram: CavgSavg, which represents the total amount of NaCl present in  the solution, as a function of the average saturation Savg.  EPD for the experiment plotted in Fig. 1. Indicated are the points corresponding to the profiles plotted in Fig. 1

In an EPD the total amount of NaCl present in the solution CavgSavg ,that is, the amount directly measured by NMR, is plotted against the average saturation Savg. In this diagram two limiting situations can be distinguished:

Line A, B :   In the case of very slow drying (i.e., Pe<<1), the ion profiles stay homogeneous and for some time no crystallization will occur. The average NaCl concentration slowly increases (line A) until the complete sample has reached 6 M. From this point on any additional drying will result in crystallization (line B).

Line C    : In the case of very fast drying of the samples (i.e., Pe>>1). Now ions are directly advected with the moisture to the top of the sample and a 6 M peak will build up with a width so small that the average concentration is not significantly affected. If the rate of crystallization is high enough, that is, if there are enough nucleation sites at the top, the average NaCl concentration in the
solution in the sample itself will remain constant at nearly the initial concentration

From any point within the region bounded by the lines A-C only moisture removal will result in an increase of the
NaCl concentration. A decrease of CavgSavg can only take place by crystallization. This requires that ions
are transported to a region with a local concentration of 6 M peak, that is, the drying surface in our experiments. Because the transport is driven by evaporation, crystallization always involves a (small) change of Savg.


For the experiment shown in Figs. 1 the corresponding pathway is plotted in Fig. 2. This pathway indicates  that during the first 9 12 days a peak in the NaCl concentration is present and salt will crystallize at the top; that is, there is salt efflorescence. Thereafter the concentration in the sample is 6 M. More measured pathways can be found in the Applied Physics Letters 81, 2893-2895 (2002)

Conclusion
The EPD diagrams reflect the competition between advection to the surface and redistribution by diffusion, but also take into account the crystallization. The EPDs indicate that in general, crystallization at the surface cannot be avoided.