Effect of osmotic pressure on desalination

Many studies up to now on poulticing have focused on the salt and moisture transport solely in terms of advection and diffusion. However in salt extraction, as
there are salt gradients present so too will there be osmotic pressure gradients which can have a large influence.For a single capillary pore the capillary pressure pc is
given by:
γ (N/m) is the surface tension of the liquid/vapor interface, φ the contact angle between the liquid/air and liquid/solid interface and r the pore size. During drying, the pattern of liquid water migration is very much affected by the different capillary forces. Where micropores are interconnected with macropores, water is preferentially drawn into the micropores due to capillary pressure gradients. Thus, the surface macropores begin to empty of liquid water, while the micropores remain full. Hence when two different saturated porous materials are placed in hydraulic contact with each other and dried, the material with the largest pores will start to drain first. Therefore, during drying water is removed first from the material with the largest pores. Consequently, in the case of poultice/substrate systems, the poultice will dry first if it has larger pores than the substrate.Hence there will be moisture flow, and thereby an advection of ions, from the substrate into the poultice.In this case there will be an high efficiency of removal of salts from the substrate.
In most porous materials the pores are not uniform, and therefore there is a pore size distribution. Thus the overall macroscopic capillary pressure
ψc of a material is a function of its pore size distribution.  When the substrate/poultice system contains a saline solution there is an additional contribution to the macroscopic capillary pressure of each porous material due to the osmotic pressure, i.e.:

where the osmotic pressure, ψo, is given by:
where R is the universal gas constant, T the absolute temperature and aw the water activity (for pure water aw = 1 and hence the osmotic pressure is zero). When the well known Pitzer’s activity coefficient model is applied the osmotic pressure can be calculated.

    Experiment showing the effect of osmotic pressure
In order to see purely the osmotic effect in an  experiment a Bentheimer saturated with 5 M NaCl solution (representing the poultice) was put on top of a
2 MNaCl solution saturated Bentheimer (representing the substrate). In Fig. 1 the measured moisture profiles are given. Based purely on capillary pressure one does not expect any effect.

Fig. 1. The water profiles in the Bentheimer/Bentheimer system plotted several times during drying. Initially the Bentheimer
on the top was saturated with 5 M NaCl solution and the substrate Bentheimer was saturated with 2 M NaCl solution

In Fig. 2 both the corresponding theoretically derived and measured moisture content relation at the interface are given. In this case due to the higher salt concentration the effective pore size of the Bentheimer with 5 M NaCl solution will be smaller.

Fig. 2 The water saturation of the 2 M NaCl solution saturated Bentheimer at the interface as a function of water
saturation of the 5 M NaCl solution saturated Bentheimer at the interface (see also Fig. 1). The solid line represents the relation
when both materials are water saturated whereas the dashed line represents the relation as determined from the measured
capillary pressure curves and the calculated osmotic pressure

As can be seen indeed the Bentheimer with 5 M NaCl solution dried more slowly indicating that its effective pore size is smaller. After some time there is a deviation from the relationship as predicted on basis of the calculated osmotic pressure. This is due to the salt transport in the Bentheimer saturated with 2 M NaCl solution towards the interface, as a result of which the concentration difference decreased. In this case the difference in drying of the two Bentheimer parts is purely due to the osmotic pressure effect.
      Conclusion and discussion
These drying experiments demonstrate the effect that osmotic pressure has on salt and moisture transport within porous materials. Essentially, a saline solution
in a porous material will exert an osmotic pressure that acts to reduce the effective pore size of the material.
These findings have potential practical implications for the optimisation of poulticing treatments. While the pore size requirements for advection to take place
at the start of the process remain, nevertheless, these constraints need not be quite so severe, as they are gradually overcome by the build up of an osmotic
pressure due to the ongoing migration of salt from the substrate to the poultice. Moreover, it is clear that the longer a poultice stays in contact with the substrate,
the more it will accumulate salt, and thereby the osmotic pressure is increased and its effective pore size will become smaller.

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V. Voronina, L. Pel, K. Kopinga, Effect of osmotic pressure on salt extraction by a poultice, Construction and Building Materials 53 432–438 (2014)