A simplified model for the combined wicking and evaporation of a NaCl solution in limestone
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Salt weathering is one of the major causes of the damage both in cultural heritage as well as in civil engineering constructions. A special case develops when there is a continuous wicking of a salt solution into a material in combination with evaporation of the moisture at its surface. In this study we are interested in the case where the absorption rate is much higher than the evaporation and as a result a salt concentration will build up at the drying surface resulting in crystallization. To this end we propose a simplified model to describe this mechanism. In order to check the model the NaCl concentration profiles were measured non-destructively by Nuclear Magnetic Resonance during a combined wicking and evaporation experiment with limestone. A good correlation was found between the model and the measured NaCl concentration profiles.
KeywordsDiffusion Advection Wick action NMR
Salt weathering is one of the major causes of the destruction of our cultural heritage. Ions such as chlorides, sulphates and nitrates are well known to be the cause; the damage is by the crystallization of these soluble salts within the pores. These salts can only be transported within liquid. Therefore the liquid transport processes are dominant in determining where the accumulation will take place and therefore where salt crystallization and possible damage can occur. Often there is a continuous wicking of a salt solution. This can be encountered if the construction is in contact with groundwater or as often seen in marine environments when it is in contact with seawater. In these circumstances ions will be advected along with the capillary moisture flow into the material (see. e.g., [1, 2]).
When there is continuous wicking of a solution into a material in combination with evaporation of the moisture at the surface of the material an equilibrium will develop between wicking of the salt solution and the evaporation flux at the drying surface. Based on the sharp front model Hall  has shown, in the case the influence of gravity can be neglected, the evaporation front will lie either near one of the boundaries, i.e., the absorption or the drying interface. In this study we are interested in the case when the absorption rate is much higher than the evaporation. Hence, the material is saturated all the time and the drying front will be at the evaporation surface. This reflects the majority of the cases found in cultural heritage and civil engineering. A well-known example is the housing along the canals in the historic city of Venice where this process gives rise to continuous salt damage. This situation is not only encountered in cultural heritage but also for instance in concrete elements in a tunnel. Whereas cases in a marine environment can be identified quite easily, one should also consider monuments in contact with natural groundwater. Ground water contains dissolved salts coming from natural sources such salts in soil, rock, and organic material, or human activities, e.g., agricultural chemicals etc. Although the salt concentration might be very low, salts can still accumulate over many years or decades at the drying surface and give rise to crystallization damage. It has been recognized that this combined wicking and evaporation is an important process and as such lab tests have been used to look at the damage potential of various types of salts [4, 5].
One of the very first studies about combined wicking and evaporation action was carried out by Lewin . Although his model gives some insight, it is an oversimplification. A more detailed study in one dimension has been done by Puyate et al. . However in their model there is no explicit dependence on the drying rate. Most studies have focused on the boundary conditions trying to determine the effect of salt on the evaporation in order to get a better understanding of especially the type of the crystallization, i.e., efflorescence and subflorescence [8, 9, 10].
In this study the focus was on the NaCl transport in a porous material, i.e., limestone, along with the moisture flow and in particular on the build-up of the concentration near the drying surface. To this end we will first discuss a simplified model to describe the concentration build up. The model was checked by performing non-destructive measurement of the concentration build up using Nuclear Magnetic Resonance (NMR). This setup will be briefly discussed in the next sections, as well as the influence of the one-dimensional resolution of the NMR on the measured concentration profiles. Finally the results of the measurements will be presented and discussed.
Hence it can be seen that as long as the liquid speed is constant, the concentration rise at the surface will increase linearly with time.
Hence as the ion diffusivity is constant, the peak width is fully determined by the liquid velocity and as the liquid velocity increases the peak width near the surface will decrease.
3.1 NMR setup
The sample is moved through the NMR with the help of a stepper motor. The moisture is first measured at the center of the NMR, after which the NMR machine is switched over to sodium and its content is then measured in order to determine the NaCl concentration. Subsequently the sample is moved to a new position and the procedure is repeated until a complete moisture and NaCl concentration profile is measured. Measuring the moisture content takes in the order of 40 s, where as it takes about 120 s to measure the Na concentration. With the NMR relaxation parameters used in the NMR experiment no signal is obtained from salt crystals and only free moving ions are measured. The measurement time of a complete profile takes is in the order of 3 h, whereas the total experiment took 50 days; hence variations of the profile during a measurement can be discarded.
3.2 One-dimensional resolution
The material used in these experiments is a biomicritic limestone from Sardinia. This limestone is very widespread in the Mediterranean basin and has been much used in buildings and monuments because it can be easily carved. These materials are characterized by a high porosity of 34% and poor mechanical properties so it weathers easily [18, 19, 20]. The average pore size has a maximum distribution at 1.6 µm (as measured by differential scanning calorimetry and Mercury intrusion porosimetry methods). The specimens were initially oven dried and then vacuum saturated with water before the experiments were carried out.
4.3 Combined wicking and evaporation
As can furthermore be seen from fitted profile as provided in Fig. 6, as soon as at the surface the concentration of the fitted profiles reaches 6 m crystallization starts and the concentration levels off. This indicates that in the current experiment no large supersaturation was measured, in contrast to experiments in glass capillaries where supersaturation ratios up to 1.6 were measured . One could argue that the one-dimensional resolution is too low to measure the supersaturation in this particular experiment. However the buildup of such a supersaturation peak should also comply to the advection–diffusion model and hence to the fitted profiles. Moreover as indicated by Naillon et al.  as the crystallization initiates the supersaturation will be consumed very fast and indeed within the time resolution of this experiment no supersaturation was observed.
As can be seen as soon as the 6 m is reached and crystallization starts, the measured NaCl profiles does not significantly change. This indicates that crystallization must take place at the top of the sample. Indeed after the experiment was performed, a thick layer of salt was found on the top of the sample and no mechanical damage to the stone was observed, showing that the crystallization rate is high enough to compensate for the ion influx.
5 Conclusion and discussion
The aim of this paper was to investigate the ion transport during combined wicking and evaporation; a situation which is often encountered in situ. It has been demonstrated by NMR that the NaCl concentration profiles can be measured non-destructively and quantitatively. The measured NaCl concentration profiles can be described by a simplified model, which only takes into account the liquid flow speed and the diffusivity of the ions in the material. This model reveals that although this combined wicking and evaporation is a slow process the concentration will continue to increase for many years, giving rise to salt crystallization and eventual damage. This combined process is dependent on the evaporation at the surface and therefore will strongly depend on the external condition during the yearly cycle in situ (see e.g. ).
We would like to thank Hans Dalderop and Jef Noijen for their help in performing the experiments. This research is supported by the Dutch Technology Foundation STW, which is part of the Netherlands Organization for Scientific Research (NWO), and which is partly funded by the Ministry of Economic Affairs.
This study was funded by Dutch Technology Foundation STW.
Compliance with ethical standards
Conflict of interest
The authors declared that they have no conflict of interest.
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