Adhesion Force Arising from Solid Salt Bridge Formed after Drying of Liquid Bridge t

Water bridges formed among particles in industrial process often contain soluble impurities such as salts. When such bridges are exposed to dry air, water in the bridges vaporizes and the salts crystallize to form solid bridges. Solid bridges between two glass spheres were formed from NaCJ, KCl, KN0 3 and Na:z50 4 solution by controlling the humidity, and their tensile strength was measured. It was found from these experiments that 1) the adhesion force of a solid salt bridge which was uniformly formed in the gap between two spheres was one to two orders of magnitude larger than that of a water bridge without crystallization; 2) the average adhesion force of solid bridges was proportional to the 1/2 power of the product of salt volume and particle radius; and 3) the adhesion force of bridges of NaCl and KCl was influenced by the surrounding humidity, which it was below their deliquescent points, because they adsorbed water until complete recrystaJJization took place.


Introduction
Liquid bridges formed among fine particles m Industrial processes often contain a small quantity of soluble impurities. When such soluble impurities are contained in a liquid bridge, depending on the kind and quantity of the solute, the liquid bridge may easily grow in size in comparison with the size of a liquid bridge formed by pure water (approximately 0.15 to 100 nm in neck radius of the bridge) 2 l. This has been confirmed by experiments using several types of fine particles that have been industrially employed 3 l. In connection with the problem associated with such phenomenon, we have studied the adhesion forces acting between particles when liquid bridges containing soluble impurities are exposed to dry air, and the solutes in the liquid bridge are crystallized.
In the experiments, liquid bridges were formed from aqueous solutions containing NaCI, KCl, KN0 3 and Na 2 S0 4 between two glass spheres of identical size, then solid bridges were formed by keeping the liquid bridges in an atmosphere of low humidity, and their adhesion force was measured. Additionally, a relation between the adhesion force arising from the initial liquid bridge and that of the solid bridge after crystallization was theoretically studied, and the results of the experiments were discussed.
In most previous studies on such solid bridges, the strength in a consolidated state of a powder bed consisting of deliquescent particles as NaCI was studied 1 · 5 • 7 · 8, 10-12), and the adhesion force of a solid salt bridge formed by vaporizing water from a liquid bridge containing a small amount of soluble salts has never been studied.

Theoretical discussion
In this paper, two spheres of identical size as shown in Figure 1 are considered as particles. A liquid bridge containing the soluble salts is formed by the Kelvin effect and the effects of dissolving substances therein (effects of the vapor pressure drop on the surface of the liquid bridge, and as a result increase the size of the bridge) 2 l. Generally, in the case of particles used in industrial processes, the effect of the solutes is greater than the Kelvin effect , which is negligible 3 l, and the size and profile of a liquid bridge are determined by the relative humidity of the atmosphere, the kind and the amounts of solutes in the liquid bridge etc 3 l. The adhesion force F L arising from a liquid bridge formed in such manner can be obtained from the following equation 4 l: where r 2 is the neck radius of the liquid bridge shown in Figure 1, and PL is the pressure deficiency in Liquid bridge Fig. 1 Dimensions of liquid bridge between two spheres the liquid bridge, which depends on the size and profile of the bridge determined in the above manner. Thus, the liquid bridge adhesion force FL is determined by the type and amount of solutes, the surrounding humidity, the size of the particles, the distance between the particles and the like. When a large liquid bridge is formed because of a large amount of solutes contained in the liquid bridge, or when the gap between the particles forming the bridge can be considered ash = 0, for a liquid bridge formed between two spheres of identical size, Eq.
(1) can be approximated by the following equation: (2) where r 0 is the particle radius. Now, we consider that a solid bridge between two identical spheres is formed by crystallization of the solutes contained in the liquid bridge when the humidity becomes lower. It is assumed that the entire amount ( = Ns (4/3) 1r-r 0 3 , where Ns is the number of solute molecules divided by the volume of a particle in the liquid bridge) of solute in the liquid bridge forms a solid bridge between particles in a form similar to that of the liquid bridge in Figure 1. This assumption will be discussed later in Result of Experiments. Now, the adhesion force arising from a solid bridge between particles is defined as the force required to break the solid bridge by separation of two particles as shown in Figure 1. We assume that the breakage occurs at x = 0 in Figure 1, and a relation is derived between the surface area of breakage and the volume of the solid bridge. The volume v of the bridge in Figure 1 is related to a neck radius r 2 for the gap between the particles h = 0 2 > as follows. (3) If the above relation exists also in a solid bridge, the surface area As ( = ;rr/) of breakage can be expressed as follows.
216 (4) Also, as the volume v of the solid bridge is proportional to the number of solute molecules (=Ns (4/3)7r-r 0 3 ), the following equation is obtained from Eq. (4): As a: Ns (4/3) 7rT 0 } (5) Here, if the solid bridge is assumed to have uniform strength at any section, because the tensile breakage force is proportional to the sectional area of breakage, the adhesion force Fs arising from the solid bridge can be expressed by the following formula: (6) Further, if the liquid bridge adhesion force can be obtained by Eq. (2), the following relation is derived from Eqs. (2) and (6): If breakage occurs in a solid bridge, it is expected that the relation between the adhesion force arising from a liquid bridge and that of a solid bridge formed by vaporization of water is given by the above formula. On the other hand, when the amount of soluble salts is reduced, no solid bridge forms in the gap between particles, and the fine crystals are deposited onto the particle surface. In such case, it seems that adhesion force arises from van der Waals force, and the force is smaller than that of the initial liquid bridge. Moreover, if the gap between two particles is increased by deposition of the fine crystal particles in the gap, the van der Waals force becomes even lower.

Experimental Method
Glass spheres of 2. 5, 5. 0 and 7. 5 mm in radius were used as particles. In order to form uniform liquid bridges, the glass spheres were dipped in a concentrated hydrochloric acid solution, held by pincers to avoid any contact with hands, washed in flowing ultrapure water, and dried in a thermo-hygrostat (at 298K and 30% humidity) in a clean tunnel. The glass spheres were set-up as shown in Figure 2 so that the centerline of the two spheres coincided with the vertical direction. Then, liquid bridges of aqueous solution containing solutes (2 x 10 to 4 x 103 molfm3 -ultrapure water) were formed between two glass spheres by means of a microsyringe. The liquid bridge volume is 2 x 10-9 m 3 . Solutes used in the experiment are Nacl, KCl, KN0 3 and Na 2 S0 4 , considering that such ions as N a+ , K + , CI-, N 0 3 -, SO 4 2 -are contained in tap water. The liquid bridge was left in a thermohygrostat operated at various constant humidities below the deliquescent points of the salts shown in Table 1 (at a temperature of 289K) until it reached an equilibrium condition (for about 24 hrs). Once the solid bridge was formed in such manner, the glass spheres set as shown in Figure 2 were removed from the thermo-hygrostat, and placed on an electronic balance, as shown in Figrue 3. Then, the moving stage was slowly moved downward to separate the two spheres. Readings of the electronic balance were constantly inputted to a personal computer, and the highest reading of the balance at breakage of the solid bridge was taken as the adhesion force of the solid bridge. Although the measurement was carried out in a room at a temperature of 293 to 298K and a relative humidity of 60 to 70o/o, it took only a few minutes to measure a sample, and it is considered that no change in crystal conditions such as absorption of moisture occurred during the measurement. range as shown in Figure 4, the adhesion force F 5 of a solid bridge formed by any of the salts tends to comply with the relation given by Eq. (6). In the case of NaCl in Figure 5 (a), the adhesion force decreases, as the humidity increases when the crystals are formed in the solid bridge. As shown in Table 1, NaCl is deliquescent at a humidity of 76%, and deliquescence of crystals begins at a humidity of 76% when the humidity is increased from a low level. However, water is not completely vaporized even if the humidity is reduced below 76%, although crystals are formed, when the humidity is reduced from a level higher than that level. In this case the water is completely vaporized at a humidity of 40o/o 9 · 13 l. Because NaCI has such hysteresis, the results at a humidity of 45 and 60% account for the reduction in the adhesion force due to a small amount of water (undetected by microscopic observation) contained in the crystals. Also, in the case of KCl, a slight difference was found, although it is not as significant as that of NaCI, and it is caused by a hysteresis similar to that of NaCl (KCl is deliquescent at a humidity of 84%, and water is completely vaporized at a humidity of about 45%). In the results of KN0 3 in Figure 5 (c) and Na 2 S0 4 in Figure 5 (d), no difference was detected for different humidities. Since no reference describing the hysteresis of KN0 3 and Na 2 S0 4 was found, changes in weight of the saturated aqueous solution of each salt were examined at various humidities. The hysteresis was not confirmed for both salts within the measurement range. Therefore, the adhesion force for both salts was not affected by humidity as shown in Figures  5 (a) and (d). Figure 6 shows photographs of a NaCl solid bridge formed between glass spheres. In Figure 6 (a) (before breakage), it is recognized that the profile of the solid bridge is similar to that of the liquid bridge in Figure 1, and the solid bridge is formed so as to fill the gap between the glass spheres. A solid bridge of substantially similar profile was formed in other salts, KCl, KN0 3 and Na 2 S0 4 . In Figure 6 (b) (breakage section viewed from above), because the solid bridge has some local voids, and has not a uniform structure, the individual measurement data for adhesive force are distributed within a wide range as shown in Figure 4. Although the adhesive forces A condition for the formation of a solid bridge between glass spheres is that the liquid bridge be kept in an atmosphere at the deliquescent point shown in Table 1 or at a higher humidity. The liquid bridge force FL can be calculated from Eq. (2). In Figure 7, FL is compared with the solid bridge force F 5 shown KONA No. 13 (1995) Relative humidity 30% 45% 60 1 ' 7o 80% In the experiment, the measurement of the adhesion force in a section with a smaller amount of crystals was not achieved, because the solid bridge was broken by a very small force before measurement of adhesion force. When the amount of crystals was much smaller, deposits of small crystals on the particle surface were observed, in which the van der Waals force is the main mechanism of adhesion between particles, as described in the Theoretical Discussion. The adhesion force in such state should be studied in the future.

Conclusions
A solid bridge formed after drying a liquid bridge containing such water-soluble salts as NaCl, KCl, KN0 3 and Na 2 S0 4 in a low humidity atmosphere, was experimentally studied. The results of the experiments are described below. 1) When a large amount of solutes was contained in an initial liquid bridge, it was found that a solid bridge forms so as to fill the gap between particles, and its adhesion force is one to two orders of magnitude higher than that of the liquid bridge before crystallization. 2) Although the adhesion forces of individual solid bridges were distributed within a wide range, the average value of such forces was proportional to about 1/2 power of the product of the volume of crystals forming the solid bridge and the particle radius. This could be explained by a theoretical model. 3) It was found that the adhesion forces arising from NaCl and KCl bridges increase as the humidity decreases (below their deliquescent points), because they adsorbed water until complete recrystallization took place.

Author's short biography Yasuo Kousaka
The author is Professor of Chemical Engineering Department at University of Osaka Prefecture since 1979. His major research interests are dynamic behavior of aerosol particles, sizing techniques of aerosol particles and powders, and dispersion of aggregate particles in air and water. He is currently editor in chief of Journal of the Society of Powder Technology, Japan, and vice president of Japan Association of Aerosol Seience and Technology.

Y oshiyuki En do
The author is Research Associate of Chemical Engineering Department at University of Osaka Prefecture since 1991. His research interests are almost same as those of Professor Kousaka.