Kinetics of Dissolution and Recrystallization of Sodium Chloride at Controlled Relative Humidity †

Both producers and users of divided solids regularly face the problem of caking after periods of storage and/or transport. Particle agglomeration depends not only on powder water content, temperature and applied pressure, but also on the interactions between the solid substance and water molecules present in the atmosphere, i.e. on relative humidity (RH) at which the product is stored. Ambient humidity plays an important role in most events leading to caking: capillary condensation of water at contact points between particles, subsequent dissolution of a solid and formation of a saturated solution eventually followed by precipitation of the solid during the evaporation of water. Here, we focus on the kinetics of dissolution followed by evapo-recrystallization of a hygroscopic sodium chloride powder under controlled temperature and RH, with the aim of anticipating caking by predicting rates of water uptake and loss under industrial conditions. Precise measurements of water uptake show that the rate of dissolution is proportional to the difference between the imposed RH and deliquescence RH, and follows a model based on the kinetic theory of gases. Evaporation seems to be governed by more complex phenomena related to the mechanism of crystal growth from a supersaturated salt solution.


INTRODUCTION
Water being ubiquitous in the atmosphere, the influence of moisture on the chemical and physical stability of many dispersed systems and its impact on product manufacturability, quality and shelf-life is of great concern.In particular, the presence of water in an atmosphere where formulated products containing deliquescent hygroscopic substances are manipulated can have a pronounced effect on their end-use properties such as particle aggregation and ability of powder to flow.Many industrial formulations, especially food products, contain sodium chloride, a deliquescent substance with a deliquescence relative humidity, DRH, of 75% at 25℃.Examples of systems at risk include also cosmetics, agricultural chemicals, explosives and pharmaceuticals.Caking of such powders is generally strongly influenced by dissolution followed by recrystallization of the hygroscopic solid substance present.A crystalline substance is said to deliquesce if it forms an aqueous solution when the ambient relative humidity reaches a certain threshold value.Below this critical RH, crystal surrounded by water vapor is thermodynamically favorable 1,2) while above the critical RH, the aqueous solution is the thermodynamically favored phase.It is of fundamental interest to understand events taking place when particles containing a hygroscopic substance are exposed to the atmosphere containing water vapor.For example, it is well known that adsorbed water cannot cause the dissolution of the solid substrate while condensed liquid water can.Capillary condensation of water vapors leads to the formation of pendular liquid bridges at the contact points between particles.This liquid water is likely to dissolve deliquescent crystalline substances present in the particles.Disso-lution gives rise to the formation of a saturated solution from which recrystallization of solute follows if water is evaporated, for example due to the changes of ambient conditions of relative humidity and/or of temperature.Usually the re-crystallized solid bridges mechanically bind the particles in contact more efficiently than the pendular liquid bridges between them.The mechanical strength of solid bridges depends not only on temperature, humidity and pressure, but it depends also on the mass transfer, the solubility of the powder in water and the number of contact points, i.e. on the coordination number of particles in the powder bed 3) .A schematic representation of the adsorption of water molecules followed by capillary condensation and dissolution of the solid phase is proposed in Fig. 1.The time sequence of phenomena taking place when hygroscopic crystals are brought in contact with an atmosphere containing water vapor is the following: adsorption of water molecules on the solid surface at low vapor pressure (steps 1 and 2), followed by the multilayer formation and capillar y condensation at contact points/lines/surfaces at intermediate vapor pressures (step 3).In the case of good wetting of the solid by liquid water, capillary condensation can occur at quite low vapor pressures, i.e. at low RH, but the quantity of liquid water, determined by the socalled Kelvin radius, will remain small.At higher RH, both Kelvin radius and the corresponding quantity of liquid water will increase rapidly.Deliquescence of the solid takes place if RH becomes equal or higher than DRH, i.e. when the ambient vapor pressure becomes equal or higher than the vapor pressure of the saturated solution of NaCl (steps 4 to 6).When a mix-ture of small individual particles and agglomerates of a hygroscopic substance is subjected to high RH, small particles might completely dissolve long before large agglomerates are dissolved (as presented in step 5).This means that not all parts of the solid sample are in equilibrium with their environment.In order to better understand the kinetics of the deliquescence of hygroscopic substances under well-controlled ambient conditions, we propose the use of Dynamic Vapor Sorption (DVS) apparatus.We examine dissolution of a solid followed by its recrystallization via the precise measurements of water uptake and water loss at variable conditions of ambient relative humidity.In such a way we provide an original method for the precise determination of deliquescence relative humidity.Modeling the dissolution of a solid and the evaporation of water from a solution so obtained is tempting on the basis of the kinetic theory of gases with the aim of predicting the corresponding kinetics at different ambient conditions of RH similar to those met in industrial applications.This work will focus on the partial dissolution and recrystallization of sodium chloride, a classic model hygroscopic solid.Sodium chloride is present in atmospheric aerosols where it represents the majority of solid particles 1) .For that reason, a significant quantity of highly reliable data concerning NaCl-water binar y systems, as well as various other mixtures relevant to atmosphere science, has been published in the last few decades 1,4,5) .Moreover, salt dissolution in water is of particular interest also because of its occurrence in food and other industrial products.Yet these formulations are often complex mixtures of ingredients influencing each otherʼs behavior.Issues Fig. 1 Hygroscopic crystals in water vapors: adsorption of water vapor and condensation of liquid water followed by dissolution of a solid (adapted from Peters 4) , Zasetsky

Theoretical background
We propose to describe the dissolution and crystallization of NaCl on the basis of a simple model taken from the kinetic theor y of gases which was already successfully applied to another hygroscopic salt, ammonium nitrate 8,9) .The well-known Knudsen formula links the flux of molecules impinging on the surface of a condensed phase with the pressure of the ambient gas, P, linearly.The proportionality coefficient is dependent on temperature, molar mass of the condensed phase and exchange surface.It is represented by a "Knudsen coefficient", KKnudsen.If we define the sticking-coefficient as the probability for a water molecule to remain at the surface after impact, and considering that the condensed phase has a nonnegligible pressure, ps, the net flux of molecules, dm/ dt, entering the condensed phase is: Moreover, as P corresponds to the relative humidity and ps corresponds to the deliquescence relative humidity, one can write: Eq. ( 2) where aw is the water activity of the substance in solution and aw the water activity of the saturated solution of the same substance at the same conditions of pressure and temperature.Note that water activity is linked to relative humidity: a w = RH 100 and to the imposed vapor pressure, P, via the saturated pressure of pure water P0 a w = P P 0 Accordingly, the rate of uptake of water molecules from the vapor phase should be proportional to the water activity of the binary mixture water-NaCl.

EXPERIMENTAL Dynamic Vapor Sorption (DVS)
Sodium chloride cr ystals of about millimeter in size and a purity of 99.5% were used as provided by Merck.Samples, typically of 8 to 25 mg, were submitted to the continuous gas flow of 200 cm 3 /min containing pure nitrogen and water-vapor-saturated nitrogen in proportion corresponding to the desired relative humidity.Mass variations due to the uptake of water from the gas phase were measured by an accurate microbalance system (DVS, Surface Measurement Systems) with a precision of 0.1 µg; its variation with respect to time, dm/dt, was calculated on a lapse of time of 10 min with an acquisition every minute.Temperature and humidity were controlled to 0.1℃ and 0.5% RH, respectively.A schematic representation of the apparatus is shown in Fig. 3.

Environmental Scanning Electronic Microscopy
The Environmental Scanning Electron Microscopy (ESEM) instrument allows the examination of particles under moderate vacuum (up to 50 Torr for low magnifications).In addition, the sample observation can be carried out in an environment of controlled temperature, pressure and humidity, allowing observation of wetting and drying, with no damage to the material and no need for any special preparation or metal coating.As one can see from Fig. 2, by keeping the tem-perature at 2℃ and by varying the pressure of the water vapor between about 3 and 5 Torr (400 and 666 Pa), significant variations of RH can be imposed in the observation chamber.Under such conditions, dissolution of NaCl crystals can be observed if the imposed RH is greater than 75% RH, while recrystallization can be observed when the pressure of water vapor is lowered to the values corresponding to RH< 75% RH.

Dissolution mechanism
The images in Fig. 4 illustrate the phenomenon of capillary condensation at the contact area between two crystals at RH close to DRH.Fig. 4a shows two NaCl cr ystals in contact at 72% RH, i.e.RH<DRH.Even if liquid water condenses at the contact area, its volume is too small to be obser ved at micrometric scale.However, when RH is elevated to 83% RH, a significant volume of condensed liquid water is observed at the contact surface (Fig. 4b).The shape of the liquid/vapor interface indicates that the solid substrate is well wetted by liquid water, which is to be expected for high-affinity substances such as hygroscopic solids and water.Such events constitute the starting point of caking phenomena: the solid phase dissolves into liquid bridges formed by the condensation of water, and a saturated solution embedding solid particles is formed, as can be observed in Fig. 4b.DRH and measuring the increase of sample mass due to the absorption of water.Subsequently, the same sample is exposed during the same period of time to a chosen constant RH<DRH.This gives rise to evaporation of absorbed water and recrystallization of the solid substance.Fig. 6 shows the quantity of water measured as a function of time: left-hand side of the graph corresponds to water absorption at three different RH>DRH, while the right-hand side corresponds to the evaporation and recrystallization of the solid at three different RH<DRH.Several samples containing between 12.5 and 13.5 mg of NaCl were analyzed.

Dry
First of all, one can notice that except at the very end of the evaporation step, i.e. the last 2 000 to 3 000 s of each experiment, both the water uptake and water loss seem to be directly proportional to the time of exposure to water vapors.Moreover, the dissolution rate, i.e. the slope of absorbed quantity versus time cur ve, increases at increasing relative humidities while the evaporation rate increases at decreasing relative humidity.One can also note that the quantity of water absorbed during 4 hours (14 400s) is strongly influenced by the imposed RH: it amounts to 4.46 mg for 85% RH, 7.76 mg for 90% RH and 10.76 mg for 95% RH for a comparable initial mass of NaCl.Moreover, the kinetic curves of water uptake and water loss look approximately symmetrical with respect to the axis t=14 400s, suggesting the linearity between water uptake or loss and the difference between the imposed relative humidity and the deliquescence point, RH-DRH, in accordance with the prediction of the Knudsen law (see Eq. ( 2)).The imposed RHs were chosen so that the differences between RH and DRH are identical (in absolute value) during dissolution of a solid and solution evaporation.
From the data presented in Fig. 6 and from similar measurements at other imposed relative humidities, the rate of water uptake or water loss is calculated for different samples of the order of 12.5 to 13.5 mg of NaCl.The obtained values corresponding to water absorption (2 points situated on the right-hand side of point M at 75% RH) and evaporation (7 points situated on the left-hand side of point M) are shown in Fig. 7.
The unquestionable linearity between the rate of water uptake or water loss and the imposed relative humidity is in agreement with the Knudsen law.It allows the determination of an experimental value of KKnudsen equal to 1.30 10 -12 kg.s -1 .Pa -1 with a relative error inferior to 10 -2 .By taking the rate of water uptake equal to zero one can determine the deliquescence point at 76% RH (with an accuracy of 0.5% RH), which is in good agreement with literature data.Graphically, the same result can be obtained by two means.The easy way is to take the abscissa for the null rate because it corresponds to the point where equilibrium is reached.Other wise, as the Knudsen coefficient can be obtained from the slope of water uptake versus RH curve (proportionality coefficient of the graph),

Time, t [s]
Fig. 6 Water uptake for samples containing between 12.5 and 13.5 mg of NaCl exposed to 95% RH ( ■ ), 90% RH ( • ) and 85% RH ( ▲ ) and water loss at 55% RH ( ■ ), 60% RH ( • ) and 65% RH ( ▲ ) at 25℃ Experimental data suggest that, in the case of partial dissolution followed by evaporation; both processes can be described by a simple model: water uptake/ loss is dependent on the dif ference between the imposed relative humidity and the deliquescence relative humidity, RH-DRH.Moreover, according to ESEM obser vations at high relative humidity, dissolution seems to be a homogeneous process where all particles, individual crystals as well as aggregates, take up water simultaneously.However, detailed study of recrystallization after partial dissolution will show the complexity of the mechanism at issue.In particular, ESEM obser vations provided the proof of the existence of two perceptible successive stages during recrystallization.Keeping in mind practical aspects of the present study, one can use the measured rates of dissolution/ recrystallization to determine the amount of hygroscopic powder dissolved or the time required for its caking by recrystallization.For example, let us imagine a product containing NaCl which is stored during four days of rainy weather followed by a period of dry weather.In this case (and by taking the simplifying assumption that there is no interaction with other constituents present in the product), the amount of dissolved NaCl and the required time for recrystallization as a function of relative humidity can be calculated.Some values are reported in Table 1:

Recr ystallization at RH<DRH
In order to better understand the phenomena taking place during recrystallization of the solid phase, ESEM observations at imposed RH<DRH were also performed.After partial dissolution shown in the sequence in Fig. 5, two partially dissolved aggregates (lower left-hand side of Fig. 8a) bathing in a large non-spherical drop and the spherical drop issued from dissolution of small individual crystals (upper right-hand side of Fig. 8a) can be observed.The recrystallization of the large aggregate of crystals can be witnessed from Fig. 8a to Fig. 8d, where water is Fig. 7 Water uptake/loss rate at different constant relative humidities at 25℃ during partial dissolution followed by recrystallization of NaCl; point M corresponds to DRH.
-  rapidly evaporating from the agglomerate while the size of spherical solution droplet seems unchanged.
The cluster looks completely dry on Fig. 8d, while the drop did not yet show the appearance of a solid.Only in Fig. 8e can one see the beginning of faceting on the periphery of the droplet.Fig. 8f shows the emergence of the solid phase while the agglomerate seems unchanged.The image in Fig. 8f reveals the final stage of drying: from the spherical solution droplet, one unique compact crystal has re-crystallized with a shape different from the initial cr ystal before dissolution (initial crystal can be seen in the insert on the top left-hand side of Fig. 8f).
The importance of modifications induced by partial dissolution followed by recr ystallization is further illustrated in Fig. 9 where the shape of NaCl aggregates before dissolution and after recr ystallization is compared.It shows clearly that starting from two separate clusters (Fig. 9a), one bigger but more compact cluster is obtained after recr ystallization (Fig. 9b).The ensemble of ESEM obser vations proves that due to the dissolution/recrystallization of crystals, caking is accompanied by significant changes with respect to initial size and shape of particles.
By means of ESEM obser vations of sample dr ying at microscopic scale, two distinct phenomena responsible for caking can be identified: the first one corresponds to the crystal growth from partially dissolved bigger aggregates, while the second one represents the formation of a crystal from homogeneous aqueous solution formed previously by complete dissolution of the small crystal.In order to verify this qualitative observation, one can perform quantitative analysis of dissolution and recrystallization kinetics.
The drying experiments shown in Fig. 10 were performed on the same sample but at different RH.Each drying sequence was preceded by partial dissolution at 90% RH, meaning that one single NaCl sample was subjected to partial dissolution seven times.
The rate of water uptake or loss is deduced from quantitative measurements of sample mass as a function of time (such as data shown in Fig. 6).One should note again that negative signs for water loss rates come from the fact that water evaporation is measured.The first part of the cur ves represents seven experiments at imposed RH=90% (time scale between 0 and 14 400s) carried out on one single sample submitted to multiple cycles of partial dissolution followed by drying.The fact that the dissolution rate remains constant is in accordance with Eq. ( 2), and its remarkable reproducibility suggests that the Knudsen coefficient remains constant.By contrast, the kinetics of recrystallization at variable RH between 60% and 0% RH are all divided into two distinct periods: during the first one following the adjustment of RH to the imposed RH below DRH (t >14400s), the loss of water taking place at approximately constant rate is observed.Subsequently, the rate of evaporation seems to slow down slightly, goes through a minimum (in absolute values) followed by a sequence where the rate seems to accelerate.
Coming back to the pictures obtained by ESEM (Fig. 8), one can suppose that the constant rate of evaporation corresponds to the evaporation of water from solution bathing partially dissolved aggregates.The process is governed by the imposed driving force for evaporation, i.e.DRH-RH.A subsequent decrease of the evaporation rate suggests that the solution in liquid drops becomes more concentrated, similarly to what was observed earlier for ammonium nitrate 9) .In such a case, the nucleation of a solid phase takes place when the solution reaches a critical concentration and is followed by the growth of crystals at a rate which depends on the degree of supersaturation of the solution contained in a drop.Indeed, ESEM observations (Fig. 8c) show that the spherical droplet remains liquid even though all water seems to be evacuated from the aggregate.
One can also observe that during drying, the time for total evaporation of the water is dependent on the imposed RH: it is short for RH=0% ( ◆ ) and much longer for RH=60% ( • ).Likewise, the evaporation rate during the first phase of crystallization and acceleration during the second phase both increase with decreasing imposed RH (i.e. by increasing the difference between DRH and imposed RH).Finally, the shoulder which appears more intensely at high RH (50 and 60% RH) at the end of evaporation can be interpreted as the loss of residual water in the crystal matrix, which is more difficult to evacuate at low driving force for crystallization (DRH-RH).Careful examination of the kinetics of evaporation will allow a better insight into the mechanism of recrystallization.

Conclusion
Aiming at a better understanding of the caking of hygroscopic solids, the role of ambient RH was examined in detail.Several processes participating in caking depend on the water vapor pressure in the ambient atmosphere: condensation of liquid water and subsequent formation of aqueous solution fol-Fig.10 Water uptake/loss rate of the sample of 12.92 mg of NaCl as a function of time at 25℃: dissolution at 90% RH followed by recrystallization at 0% RH ( ◆ ), 10% RH ( ■ ), 20% RH ( ▲ ), 30% RH ( × ), 40% RH ( ), 50% RH ( + ) and 60% RH ( • ) lowed by recrystallization if RH decreases.The behavior of such solutions under industrially relevant conditions was studied on laboratory scale.By means of a model based on the Knudsen law, the amount of dissolved salt as a function of time can be calculated.The required time for dissolution or recr ystallization can also be estimated for RHs corresponding to the storage/transport conditions of industrial powders.Moreover, by coupling the micro-gravimetric measurements with ESEM observations, some light could be shone on the way the recrystallization from aqueous solutions proceeds.Two distinct processes are evidenced: the first one is likely to correspond to the growth of partially dissolved crystals, while the second one should correspond to the formation of crystals in a supersaturated aqueous solution issued from the previous total dissolution of small NaCl cr ystals.Studies currently under way shall allow a better understanding of the behavior of mixtures of several crystalline powders.

Fig. 2
Fig. 2 Pressure-Temperature diagram of water (in dark continued line) (data from Mullinʼs book 6 ) and of saturated aqueous NaCl solution (in light dotted line) (data are adapted from Apelblat and Korin 7).Curves of water vapour pressure at 90%, 80%, 70% and 60% RH are represented in dotted lines from top to bottom, respectively.
deduce the DRH point by means of the ordinate at the origin, which corre-

Fig. 8 Fig. 9
Fig. 8 Time sequence of ESEM images of the recrystallization of NaCl at RH＜DRH (a to f); size bar is 100 µm in all images.

Table 1
Percentage of NaCl dissolved (1a) and time needed for complete recrystallization (1b) as a function of imposed