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Effect of interfacial supersaturation on secondary nucleation
Journal of the Taiwan Institute of Chemical Engineers 40 (2009) 439–442
Contents lists available at ScienceDirect
Journal of the Taiwan Institute of Chemical Engineers journal homepage: www.elsevier.com/locate/jtice
Effect of interfacial supersaturation on secondary nucleation Clifford Y. Tai *, Chia-Der Tai, Ming-Hui Chang Department of Chemical Engineering, National Taiwan University, Taipei 10617, Taiwan
A R T I C L E I N F O
A B S T R A C T
Article history: Received 29 February 2008 Received in revised form 23 January 2009 Accepted 31 January 2009
A stirred tank was used to study the effect of interfacial supersaturation on secondary nucleation. The experiment was performed by the injection of solution to a seed crystal surface and thus to induce secondary nuclei. The distance between the jet and the seed crystal and the stopping time, which was the time interval between starting injection and stopping agitation, were varied to show the difference in the number of crystals generated by secondary nucleation. From the two-step crystal growth model, the interfacial supersaturation decreases with an increase in stopping time, thus the secondary nucleation is influenced by the interfacial supersaturation. ß 2009 Taiwan Institute of Chemical Engineers. Published by Elsevier B.V. All rights reserved.
Keywords: Interfacial supersaturation Secondary nucleation Fluid shear Injection induction period
1. Introduction Nucleation is generally defined as the formation of nuclei from a homogeneous phase under supersaturation. There are two types of nucleation, i.e., primary nucleation and secondary nucleation, depending on the absence or presence of solute crystals in the system. In the former system, a shower of nuclei bursts out at high supersaturation, then the supersaturation decreases and the magma density increases drastically on a sudden. On the other hand, when secondary nucleation dominates at low supersaturation, nuclei are generated gradually and the changes in supersaturation and magma density are rather slow. Thus, the control of supersaturation in the solution is possible for the secondary-nucleation system. As a result, large single crystals with different morphology can be prepared as required by chemical industries. The effect of supersaturation on the secondary nucleation thus attracts great attention in the crystallization community. The state of supersaturation is a necessary but not sufficient condition for the generation of particles within a homogeneous phase. A supersaturated solution may last forever without disturbance or seeding. Such a solution is under metastable condition. The secondary nucleation will occur in the metastable region. A key to understand secondary nucleation is the identification of the source of secondary nuclei or clusters. Experimental evidences showing the existence of clusters in supersaturated solutions were reported in the literature over a long period of years (Larson and Garside, 1986; Mullin and Leci, 1969; Rusli and Larson, 1987). The results were summarized and
explained by Larson (1991) for a variety of common inorganic and organic solutes in aqueous supersaturated solutions; the clusters might exist as large as 100 A˚ containing molecules of an order of hundreds. Meanwhile, hypothesis concerning the source of secondary nuclei was proposed. Clontz and McCabe (1971) suggested that the adsorption layer existing between the stagnant film and crystal surface consisted of clusters entity from which crystals were generated. Larson (1982) re-emphasized the possibility of the solution/crystal interface as a source of secondary nuclei as proposed earlier by Clontz and McCabe (1971). The dual role of supersaturation in the determination of secondarynucleation rate was proposed by Garabedian and StricklandConstable (1972), i.e., the supersaturation will affect the number of nuclei or clusters forming at the solution/crystal interface, and the fraction of nuclei surviving in the bulk solution after being detached from the interface. However, no differentiation was made between the two supersaturations. Building on the perspective of these researchers, Tai et al. (1992) postulated a hypothesis that clusters queued up to incorporate into the growing crystal formed the adsorption layer, where the interfacial supersaturation acted as a key variable in the formation of secondary nuclei. The actual role of interfacial supersaturation is unclear, but it might determine the cluster size or concentration at crystal surface. The interfacial supersaturation is referred to that appeared in the two-step model of crystal growth, which can be described mathematically by the following equations: G ¼ K d ðs s i Þ
diffusion
(1)
and * Corresponding author. Tel.: +886 2 23620832; fax: +886 2 23623040. E-mail address: [email protected] (C.Y. Tai).
G ¼ K r s ni
surface reaction
1876-1070/$ – see front matter ß 2009 Taiwan Institute of Chemical Engineers. Published by Elsevier B.V. All rights reserved. doi:10.1016/j.jtice.2009.01.006
(2)
C.Y. Tai et al. / Journal of the Taiwan Institute of Chemical Engineers 40 (2009) 439–442
440
Fig. 1. Schematic diagram of two-step model for crystal growth (after Tai et al., 1992).
where Kd and Kr are mass-transfer and surface-reaction coefficient, respectively, n is the surface-reaction order, s (=c/c* 1) is the over-all supersaturation and si (=ci/c* 1) is the interfacial supersaturation as shown in Fig. 1. The magnitude of interfacial supersaturation, which cannot be measured by any instrumentation at the present time, was influenced by Kd, Kr and n under the constraint of constant s as postulated by Tai et al. (1992). Accordingly, operation variables, such as temperature, agitation rate, and impurity concentration, which affected Kd, Kr and n, would influence the interfacial supersaturation and thus the nucleation rate and crystal growth rate. Based on the postulation they were able to rationalize experimental data, some of which appeared to be conflicting, reported in the literature in a qualitatively manner. In addition, after a long argument they reached a conclusion that fluid shear (Jagannathan et al., 1980; Sung et al., 1973) acted as the same manner as a contacting rod (Clontz and McCabe, 1971; Johnson et al., 1972; Tai et al., 1975) to induce the secondary nucleation, i.e., for both cases energy was transmitted to a crystal surface for detaching clusters that queued up in the solution/crystal interface. Nevertheless contacting rod was more effective than fluid shear in producing secondary nuclei, because the impact force caused by contact would give a more rigorous disturbance to the adsorption layer (Tai et al., 1992). To demonstrate the role played by interfacial supersaturation, Tai and Shih (1997) conducted a fluidized-bed experiment to measure the crystal growth and secondary-nucleation rates under the same supersaturation. The crystal growth rate data were analyzed by the two-step growth model to determine the interfacial supersaturation. Then the secondary-nucleation rate data were correlated with the following two forms, i.e., with or without the interfacial supersaturation. B0 ¼ 9:55 104 Re2:4 s i 1:4 s 1:0
(3)
and B0 ¼ 4:8 104 Re2:5 s 2:1 0
(4)
where B is the nucleation rate and Re is the Reynolds number. Eq. (3) fits experimental data much better than Eq. (4) does, with an error of 15.9% and 34.2%, respectively, defined as
{S{[B0(exp) B0(cal)]/B0(cal)}2}1/2. Viewing that the Re has a similar effect on B0, the interfacial supersaturation, si, should play a role in the process of secondary nucleation. It implies that the number of nuclei generated by contact, which comes from solution/crystal interface, is influenced by the interfacial supersaturation; however, the fraction of nuclei which survives in development stage is determined by the over-all supersaturation. The system they worked with was potassium alum, which is a readily soluble salt. Another experimental evidence to show the importance of interfacial supersaturation was presented by Qian and Botsaris (1997). They proposed a nucleation model, so called embryos coagulation secondary nucleation, to provide an explanation for an experimentally observed type of secondary nucleation, which is termed catastrophic secondary nucleation. This type of secondary nucleation has a kinetic characteristic of a primary nucleation; at a certain critical supersaturation a shower of nuclei appears suddenly from the solution/crystal interface. The system they worked with was potassium chloride, which is a readily soluble salt. For a sparingly soluble system, Tai et al. (2005) found that addition of seed crystal of CaCO3 to a supersaturated solution has the effect of reducing the induction period. They postulated that nuclei was induced by an increase in the concentration of clusters in the vicinity of seed crystal surface, due to the van der Waals attractive force existing between the clusters and seed crystals. It means that the supersaturation at the crystal/solution interface becomes higher to induce nucleation due to the presence of seed crystals. In this report experiments were further conducted in a stirred tank to examine the number of crystal generated by fluid shear at various interfacial supersaturations. The interfacial supersaturation was varied by changing Kd but keeping the same size of seed crystals or constant Kr. The idea of generating nuclei by shear force was adopted from Jagannathan et al. (1980) with some modifications. Before nucleation experiments were conducted, seed crystals of potassium alum (KAl(SO4)212H2O) were prepared. Then the seed crystal was used to explore the induction period of supersaturated alum solutions and to investigate the effect of interfacial supersaturation on the number of nuclei generated by fluid shear. 2. Experimental 2.1. Preparation of seed crystals Seed crystals of potassium alum were prepared by dropping a small alum crystal into a flask containing a supersaturated solution, which was 2 8C below the saturation temperature of potassium alum. Then the flask was slightly swirled to induce nuclei, which were then grown for a couple of days. Seed crystals without flaw were produced. The area of the flat face, which would be later subject to injection, is around 25 mm2; however, it might vary from seed to seed by 10%. To determine the saturation temperature, a calibration curve was first constructed by plotting alum concentration against the reading of density meter (Kyoto Electronics DA-210) with an accuracy of 2 105 g/cm3, which is approximately equivalent to 0.05 K in the temperature range studied for the potassium alum–water system. Then the saturation concentration or solubility of various temperatures was determined by the density meter. The solubility can be expressed as a function of temperature as following: ln C ¼ 272:462428 þ
9532:0181 þ 42:667728 ln T T
(5)
where C is the solubility of potassium alum in g hydrate/100 g H2O, and T is temperature in K. Eq. (5) is plotted in Fig. 2.
C.Y. Tai et al. / Journal of the Taiwan Institute of Chemical Engineers 40 (2009) 439–442
441
profile near the crystal/solution interface reach steady state. Then we stopped the agitation and waited for a certain period of time to change the relative velocity between the seed crystal and the swirling solution. After that the 10 mL alum solution already in the syringe with the same concentration as the solution in the stirred tank was injected to the crystal surface. Several minutes later, the seed crystal was pulled up to stay above the liquid level. The number of nuclei generated by injection was counted several hours later and was recounted until the number remained the same. Experiments were conducted for two distances, i.e., 3 and 2 mm, between the jet and the seed crystal. The idea of this experiment came from the hypothesis proposed by Tai et al. (1992). It was intended to explore the nucleation rate as a function of the interfacial supersaturation by changing the stopping time and of the amount of energy imparted to the crystal surface by changing the jet distance. Fig. 2. Solubility diagram of potassium alum.
3. Results and discussion
2.2. Induction period experiment
3.1. Induction period at different operating conditions
A potassium alum solution of desired concentration, which was determined by the density meter, was prepared and poured into an agitated vessel shown in Fig. 3, which was fitted with a jacket for controlling temperature, a thermometer for measuring temperature, an impeller for agitation, a seed holder for holding the seed crystal, and a syringe for injecting solution. The syringe was not used in this experiment but in the nucleation experiment. A seed crystal was glued to the end of the seed holder and was dipped into the stirred vessel with a desired agitation speed. The temperature of solution was set at 1 8C above the saturation temperature to dissolve crystal dusts retained on the crystal faces. This pretreatment of seed crystal was necessary to eliminate initial breeding (Tai et al., 1975). After 30 min the solution temperature was lowered gradually to a desired temperature below saturation temperature, i.e., DTsub (subcooling temperature), and let it stay at that temperature to observe the formation of nuclei. Here the induction period was defined as the time interval between the moment that solution became supersaturated and nuclei formed as detected by naked eyes.
To select a proper over-all supersaturation and agitation speed we encountered a dilemma. The subcooling (Tai et al., 1992) and agitation rate (Jagannathan et al., 1980) should be high in order to give a high interfacial supersaturation and thus to observe secondary nucleation induced by fluid shear. On the other hand, high subcooling and agitation speed would give a short induction period, which would mess up the experimental results, i.e., nuclei could come from primary nucleation as well as secondary nucleation. Thus, various combinations of subcooling and agitation speed were performed; i.e., subcooling temperature varying from 2.5 to 3.5 8C and agitation speed changing from 250 to 350 rpm. The results of the induction experiment are shown in Table 1, in which the induction periods at various subcooling temperatures and agitation speeds are presented. Generally speaking, the induction period decreased as the subcooling temperature and agitation speed increased. For example, when the subcooling increased from 2.5 to 3.0 8C at 350 rpm, the induction period decreased from 4.0 to 3.0 h. Suppose the subcooling was fixed at 3.5 8C, the induction period decreased from 3.0 h to that less than 2.0 h as agitation speed increasing from 200 to 250 rpm or higher. Judging from the experimental procedures of nucleation experiment that the time interval between the stages of lowering the system temperature and making an injection was 1 h and between the injection and counting the number of crystal was at least 2 h, we chose the operating conditions of 3 8C subcooling and 300 rpm with an induction period of 3.6 h for the subsequent secondarynucleation study in order to eliminate primary nucleation, which might occur beyond the induction period.
2.3. Secondary-nucleation experiment The procedures of seed crystal pretreatment in the nucleation study were the same as that in the induction period experiment. After pretreatment, the solution temperature was lowered and controlled at a desired subcooling for 1 h to let the concentration
3.2. Effect of operating conditions on secondary nucleation A couple of experimental runs were conducted at 3.5 8C subcooling before we started a systematic study at 3.0 8C Table 1 Induction period of potassium alum solution at various subcooling temperatures and agitation speeds. The saturation temperature of solution is 28.0 8C.
Fig. 3. Experimental apparatus.
Subcooling temperature DTsub (8C)
Agitation speed (rpm)
Induction period (h)
2.5 3.0 3.0 3.5 3.5 3.5
350 300 350 200 250 300
4.0 3.6 3.0 3.0 1.5 1.8
442
C.Y. Tai et al. / Journal of the Taiwan Institute of Chemical Engineers 40 (2009) 439–442
by Tai et al. (1992) either. In the experiment the injection was made when the solution was in a quiescence state. The mass-transfer resistance was so high that the interfacial supersaturation was quite low. Under this circumstance the size of clusters gathering on the crystal surface were small. According to Kelvin equation, which states that a large critical radius is required at a low subcooling or low supersaturation, a high subcooling (or supersaturation) was necessary to observe nuclei. Now back to our experiments, nuclei were observed at short stopping time when the subcooling for the nuclei to survive was 3 8C. This is because at short stopping time the stagnant film around seed crystal was not fully developed. However, almost no nuclei was observed when the stopping time was longer than 25 min. At that time probably the solution in the stirred tank became still, a situation similar to the experiment conduced by Jagannathan et al. (1980).
Fig. 4. Effects of jet distance and stopping time on the number of nuclei generated by injection: (~) jet distance 2 mm; (*) jet distance 3 mm.
subcooling. In the two runs the number of nuclei generated was countless at 3 and 10 min of stopping time, which was the time interval between stopping agitation and starting injection. It meant that the injection of solution induced primary nucleation at 3.5 8C subcooling and most of the nuclei came from the bulk solution instead of the crystal/solution interface. For the experiments at 3.0 8C subcooling, the results are shown in Fig. 4, in which the number of nuclei generated by shear force due to injection were plotted against the stopping time for two injection distances, i.e., the distance between the jet and seed crystal. For both distances, 2 and 3 mm, the number of nuclei decreased with increasing stopping time. For the same stopping time, more nuclei were generated at the shorter jet distance. The shear force was not effective for generation of secondary nuclei when the stopping time was longer than 25 min. Our experimental results will be explained by using the hypothesis proposed by Tai et al. (1992). The nucleation rate is a function of interfacial supersaturation and the magnitude of interfacial supersaturation is influenced by Kd under the constraint of constant over-all supersaturation. In a stirred tank the masstransfer coefficient increases with an increase in agitation speed. Thus at a higher agitation rate, the interfacial supersaturation is higher and so is the nucleation rate. In our experiment when we stopped the agitation, the swirling of solution died away gradually. Accordingly, the mass-transfer resistance would increase and the interfacial supersaturation along with the nucleation rate decreased. Fig. 4 shows such a trend. When the stopping time is shorter, the number of nuclei generated by fluid shear is higher. Although the energy transferred to the crystal face might be lower at a shorter stopping time due to the swirling of solution, the number of nuclei generated was still the highest at the shortest stopping time. Besides, the shorter jet distance gave a higher number of nuclei because more energy was transmitted to the crystal surface. This result is consistent with that reported by Tai et al. (1992) and Jagannathan et al. (1980). Jagannathan et al. (1980) conducted a fluid-shear experiment which was different from our experiment in two respects. Firstly, the solution was not agitated during a run, and secondly the nuclei generated were transported to a separate chamber where the solution temperature was kept at a high subcooling of 20 8C or more for the nuclei to survive, i.e., to become visible crystals. When the subcooling of generation stage was 3 8C, nuclei could be observed at a subcooling being higher than 20 8C in the observation chamber. This result can be explained by the hypothesis proposed
4. Conclusion An agitated vessel fitted with a jacket, a thermometer, an impeller, a seed crystal holder and a syringe was used to study the effect of interfacial supersaturation on the number of nuclei generated by injecting the solution to the crystal surface. The number of nuclei increased with an increase of interfacial supersaturation and energy imparted to crystal surface. Judging from the results obtained in this experiment together with that reported in the literature, the role played by the interfacial supersaturation did not violate the hypothesis proposed by Tai et al. (1992), i.e., the nucleation rate would be influenced by the interfacial supersaturation. The effect of interfacial supersaturation can be applied to readily soluble and sparingly soluble salts and should not be ignored in the design of an industrial crystallizer. Acknowledgement The authors gratefully acknowledge the support of the National Science Council of the Republic of China. References Clontz, N. A. and W. L. McCabe, ‘‘Contact Nucleation of Magnesium Sulfate Heptahydrate,’’ AIChE Symp. Ser., 110, 6 (1971). Garabedian, H. and R. F. Strickland-Constable, ‘‘Collision Breeding of Crystal Nuclei, Sodium Chlorate—Part 1,’’ J. Cryst. Growth, 13/14, 506 (1972). Jagannathan, R., C. Y. Sung, G. R. Youngquist, and J. Estrin, ‘‘Fluid Shear Secondary Nucleation of Magnesium Sulfate and Potassium Aluminum Sulfate,’’ AIChE Symp. Ser., 193, 90 (1980). Johnson, R. T., R. W. Rousseau, and W. L. McCabe, ‘‘Factors Affecting Contact Nucleation,’’ AIChE Symp. Ser., 121, 31 (1972). Larson, M. A., Secondary Nucleation: An Analysis, p. 50, Jancic, S.J. & E.J. de Jong (Eds.), North-Holland, Amsterdam (1982). Larson, M. A. and J. Garside, ‘‘Solute Clustering in Supersaturated Solutions,’’ Chem. Eng. Sci., 41, 1285 (1986). Larson, M. A., Solute Clustering and Secondary Nucleation, p. 20, Garside, J., R.J. Darvey & A.G. Jones (Eds.), Butterworth Heinemann, Oxford (1991). Mullin, J. W. and C. L. Leci, ‘‘Evidence of Molecular Cluster Formation in Supersaturated Solutions of Citric Acid,’’ Philos. Mag., 19, 1075 (1969). Qian, R. Y. and G. D. Botsaris, ‘‘A New Mechanism for Nuclei Formation in Suspension Crystallizers: The Role of Interparticle Forces,’’ Chem. Eng. Sci., 52, 3429 (1997). Rusli, I. T. and M. A. Larson, Solute Clustering in Supersaturated Solutions, p. 71, Strathdee, G.L., M.O. Klein & L.A. Melis (Eds.), Pergamon, New York, USA (1987). Sung, C. Y., J. Estrin, and G. R. Youngquist, ‘‘Secondary Nucleation of MgSO4 by Fluid Shear,’’ AIChE J., 19, 57 (1973). Tai, C. Y., W. L. McCabe, and R. W. Rousseau, ‘‘Contact Nucleation of Various Crystal Types,’’ AIChE J., 21, 351 (1975). Tai, C. Y., J. F. Wu, and R. W. Rousseau, ‘‘Interfacial Supersaturation, Secondary Nucleation, and Crystal Growth,’’ J. Cryst. Growth, 116, 294 (1992). Tai, C. Y. and C. Y. Shih, ‘‘Analysis of Nucleation and Crystal Growth Data Using the Interfacial Supersaturation,’’ AIChE J., 43, 268 (1997). Tai, C. Y., W. C. Chien, and J. P. Hsu, ‘‘Induction Period of CaCO3 Interpreted by the Smoluchowski’s Coagulation Theory,’’ AIChE J., 51, 480 (2005).
Contents lists available at ScienceDirect
Journal of the Taiwan Institute of Chemical Engineers journal homepage: www.elsevier.com/locate/jtice
Effect of interfacial supersaturation on secondary nucleation Clifford Y. Tai *, Chia-Der Tai, Ming-Hui Chang Department of Chemical Engineering, National Taiwan University, Taipei 10617, Taiwan
A R T I C L E I N F O
A B S T R A C T
Article history: Received 29 February 2008 Received in revised form 23 January 2009 Accepted 31 January 2009
A stirred tank was used to study the effect of interfacial supersaturation on secondary nucleation. The experiment was performed by the injection of solution to a seed crystal surface and thus to induce secondary nuclei. The distance between the jet and the seed crystal and the stopping time, which was the time interval between starting injection and stopping agitation, were varied to show the difference in the number of crystals generated by secondary nucleation. From the two-step crystal growth model, the interfacial supersaturation decreases with an increase in stopping time, thus the secondary nucleation is influenced by the interfacial supersaturation. ß 2009 Taiwan Institute of Chemical Engineers. Published by Elsevier B.V. All rights reserved.
Keywords: Interfacial supersaturation Secondary nucleation Fluid shear Injection induction period
1. Introduction Nucleation is generally defined as the formation of nuclei from a homogeneous phase under supersaturation. There are two types of nucleation, i.e., primary nucleation and secondary nucleation, depending on the absence or presence of solute crystals in the system. In the former system, a shower of nuclei bursts out at high supersaturation, then the supersaturation decreases and the magma density increases drastically on a sudden. On the other hand, when secondary nucleation dominates at low supersaturation, nuclei are generated gradually and the changes in supersaturation and magma density are rather slow. Thus, the control of supersaturation in the solution is possible for the secondary-nucleation system. As a result, large single crystals with different morphology can be prepared as required by chemical industries. The effect of supersaturation on the secondary nucleation thus attracts great attention in the crystallization community. The state of supersaturation is a necessary but not sufficient condition for the generation of particles within a homogeneous phase. A supersaturated solution may last forever without disturbance or seeding. Such a solution is under metastable condition. The secondary nucleation will occur in the metastable region. A key to understand secondary nucleation is the identification of the source of secondary nuclei or clusters. Experimental evidences showing the existence of clusters in supersaturated solutions were reported in the literature over a long period of years (Larson and Garside, 1986; Mullin and Leci, 1969; Rusli and Larson, 1987). The results were summarized and
explained by Larson (1991) for a variety of common inorganic and organic solutes in aqueous supersaturated solutions; the clusters might exist as large as 100 A˚ containing molecules of an order of hundreds. Meanwhile, hypothesis concerning the source of secondary nuclei was proposed. Clontz and McCabe (1971) suggested that the adsorption layer existing between the stagnant film and crystal surface consisted of clusters entity from which crystals were generated. Larson (1982) re-emphasized the possibility of the solution/crystal interface as a source of secondary nuclei as proposed earlier by Clontz and McCabe (1971). The dual role of supersaturation in the determination of secondarynucleation rate was proposed by Garabedian and StricklandConstable (1972), i.e., the supersaturation will affect the number of nuclei or clusters forming at the solution/crystal interface, and the fraction of nuclei surviving in the bulk solution after being detached from the interface. However, no differentiation was made between the two supersaturations. Building on the perspective of these researchers, Tai et al. (1992) postulated a hypothesis that clusters queued up to incorporate into the growing crystal formed the adsorption layer, where the interfacial supersaturation acted as a key variable in the formation of secondary nuclei. The actual role of interfacial supersaturation is unclear, but it might determine the cluster size or concentration at crystal surface. The interfacial supersaturation is referred to that appeared in the two-step model of crystal growth, which can be described mathematically by the following equations: G ¼ K d ðs s i Þ
diffusion
(1)
and * Corresponding author. Tel.: +886 2 23620832; fax: +886 2 23623040. E-mail address: [email protected] (C.Y. Tai).
G ¼ K r s ni
surface reaction
1876-1070/$ – see front matter ß 2009 Taiwan Institute of Chemical Engineers. Published by Elsevier B.V. All rights reserved. doi:10.1016/j.jtice.2009.01.006
(2)
C.Y. Tai et al. / Journal of the Taiwan Institute of Chemical Engineers 40 (2009) 439–442
440
Fig. 1. Schematic diagram of two-step model for crystal growth (after Tai et al., 1992).
where Kd and Kr are mass-transfer and surface-reaction coefficient, respectively, n is the surface-reaction order, s (=c/c* 1) is the over-all supersaturation and si (=ci/c* 1) is the interfacial supersaturation as shown in Fig. 1. The magnitude of interfacial supersaturation, which cannot be measured by any instrumentation at the present time, was influenced by Kd, Kr and n under the constraint of constant s as postulated by Tai et al. (1992). Accordingly, operation variables, such as temperature, agitation rate, and impurity concentration, which affected Kd, Kr and n, would influence the interfacial supersaturation and thus the nucleation rate and crystal growth rate. Based on the postulation they were able to rationalize experimental data, some of which appeared to be conflicting, reported in the literature in a qualitatively manner. In addition, after a long argument they reached a conclusion that fluid shear (Jagannathan et al., 1980; Sung et al., 1973) acted as the same manner as a contacting rod (Clontz and McCabe, 1971; Johnson et al., 1972; Tai et al., 1975) to induce the secondary nucleation, i.e., for both cases energy was transmitted to a crystal surface for detaching clusters that queued up in the solution/crystal interface. Nevertheless contacting rod was more effective than fluid shear in producing secondary nuclei, because the impact force caused by contact would give a more rigorous disturbance to the adsorption layer (Tai et al., 1992). To demonstrate the role played by interfacial supersaturation, Tai and Shih (1997) conducted a fluidized-bed experiment to measure the crystal growth and secondary-nucleation rates under the same supersaturation. The crystal growth rate data were analyzed by the two-step growth model to determine the interfacial supersaturation. Then the secondary-nucleation rate data were correlated with the following two forms, i.e., with or without the interfacial supersaturation. B0 ¼ 9:55 104 Re2:4 s i 1:4 s 1:0
(3)
and B0 ¼ 4:8 104 Re2:5 s 2:1 0
(4)
where B is the nucleation rate and Re is the Reynolds number. Eq. (3) fits experimental data much better than Eq. (4) does, with an error of 15.9% and 34.2%, respectively, defined as
{S{[B0(exp) B0(cal)]/B0(cal)}2}1/2. Viewing that the Re has a similar effect on B0, the interfacial supersaturation, si, should play a role in the process of secondary nucleation. It implies that the number of nuclei generated by contact, which comes from solution/crystal interface, is influenced by the interfacial supersaturation; however, the fraction of nuclei which survives in development stage is determined by the over-all supersaturation. The system they worked with was potassium alum, which is a readily soluble salt. Another experimental evidence to show the importance of interfacial supersaturation was presented by Qian and Botsaris (1997). They proposed a nucleation model, so called embryos coagulation secondary nucleation, to provide an explanation for an experimentally observed type of secondary nucleation, which is termed catastrophic secondary nucleation. This type of secondary nucleation has a kinetic characteristic of a primary nucleation; at a certain critical supersaturation a shower of nuclei appears suddenly from the solution/crystal interface. The system they worked with was potassium chloride, which is a readily soluble salt. For a sparingly soluble system, Tai et al. (2005) found that addition of seed crystal of CaCO3 to a supersaturated solution has the effect of reducing the induction period. They postulated that nuclei was induced by an increase in the concentration of clusters in the vicinity of seed crystal surface, due to the van der Waals attractive force existing between the clusters and seed crystals. It means that the supersaturation at the crystal/solution interface becomes higher to induce nucleation due to the presence of seed crystals. In this report experiments were further conducted in a stirred tank to examine the number of crystal generated by fluid shear at various interfacial supersaturations. The interfacial supersaturation was varied by changing Kd but keeping the same size of seed crystals or constant Kr. The idea of generating nuclei by shear force was adopted from Jagannathan et al. (1980) with some modifications. Before nucleation experiments were conducted, seed crystals of potassium alum (KAl(SO4)212H2O) were prepared. Then the seed crystal was used to explore the induction period of supersaturated alum solutions and to investigate the effect of interfacial supersaturation on the number of nuclei generated by fluid shear. 2. Experimental 2.1. Preparation of seed crystals Seed crystals of potassium alum were prepared by dropping a small alum crystal into a flask containing a supersaturated solution, which was 2 8C below the saturation temperature of potassium alum. Then the flask was slightly swirled to induce nuclei, which were then grown for a couple of days. Seed crystals without flaw were produced. The area of the flat face, which would be later subject to injection, is around 25 mm2; however, it might vary from seed to seed by 10%. To determine the saturation temperature, a calibration curve was first constructed by plotting alum concentration against the reading of density meter (Kyoto Electronics DA-210) with an accuracy of 2 105 g/cm3, which is approximately equivalent to 0.05 K in the temperature range studied for the potassium alum–water system. Then the saturation concentration or solubility of various temperatures was determined by the density meter. The solubility can be expressed as a function of temperature as following: ln C ¼ 272:462428 þ
9532:0181 þ 42:667728 ln T T
(5)
where C is the solubility of potassium alum in g hydrate/100 g H2O, and T is temperature in K. Eq. (5) is plotted in Fig. 2.
C.Y. Tai et al. / Journal of the Taiwan Institute of Chemical Engineers 40 (2009) 439–442
441
profile near the crystal/solution interface reach steady state. Then we stopped the agitation and waited for a certain period of time to change the relative velocity between the seed crystal and the swirling solution. After that the 10 mL alum solution already in the syringe with the same concentration as the solution in the stirred tank was injected to the crystal surface. Several minutes later, the seed crystal was pulled up to stay above the liquid level. The number of nuclei generated by injection was counted several hours later and was recounted until the number remained the same. Experiments were conducted for two distances, i.e., 3 and 2 mm, between the jet and the seed crystal. The idea of this experiment came from the hypothesis proposed by Tai et al. (1992). It was intended to explore the nucleation rate as a function of the interfacial supersaturation by changing the stopping time and of the amount of energy imparted to the crystal surface by changing the jet distance. Fig. 2. Solubility diagram of potassium alum.
3. Results and discussion
2.2. Induction period experiment
3.1. Induction period at different operating conditions
A potassium alum solution of desired concentration, which was determined by the density meter, was prepared and poured into an agitated vessel shown in Fig. 3, which was fitted with a jacket for controlling temperature, a thermometer for measuring temperature, an impeller for agitation, a seed holder for holding the seed crystal, and a syringe for injecting solution. The syringe was not used in this experiment but in the nucleation experiment. A seed crystal was glued to the end of the seed holder and was dipped into the stirred vessel with a desired agitation speed. The temperature of solution was set at 1 8C above the saturation temperature to dissolve crystal dusts retained on the crystal faces. This pretreatment of seed crystal was necessary to eliminate initial breeding (Tai et al., 1975). After 30 min the solution temperature was lowered gradually to a desired temperature below saturation temperature, i.e., DTsub (subcooling temperature), and let it stay at that temperature to observe the formation of nuclei. Here the induction period was defined as the time interval between the moment that solution became supersaturated and nuclei formed as detected by naked eyes.
To select a proper over-all supersaturation and agitation speed we encountered a dilemma. The subcooling (Tai et al., 1992) and agitation rate (Jagannathan et al., 1980) should be high in order to give a high interfacial supersaturation and thus to observe secondary nucleation induced by fluid shear. On the other hand, high subcooling and agitation speed would give a short induction period, which would mess up the experimental results, i.e., nuclei could come from primary nucleation as well as secondary nucleation. Thus, various combinations of subcooling and agitation speed were performed; i.e., subcooling temperature varying from 2.5 to 3.5 8C and agitation speed changing from 250 to 350 rpm. The results of the induction experiment are shown in Table 1, in which the induction periods at various subcooling temperatures and agitation speeds are presented. Generally speaking, the induction period decreased as the subcooling temperature and agitation speed increased. For example, when the subcooling increased from 2.5 to 3.0 8C at 350 rpm, the induction period decreased from 4.0 to 3.0 h. Suppose the subcooling was fixed at 3.5 8C, the induction period decreased from 3.0 h to that less than 2.0 h as agitation speed increasing from 200 to 250 rpm or higher. Judging from the experimental procedures of nucleation experiment that the time interval between the stages of lowering the system temperature and making an injection was 1 h and between the injection and counting the number of crystal was at least 2 h, we chose the operating conditions of 3 8C subcooling and 300 rpm with an induction period of 3.6 h for the subsequent secondarynucleation study in order to eliminate primary nucleation, which might occur beyond the induction period.
2.3. Secondary-nucleation experiment The procedures of seed crystal pretreatment in the nucleation study were the same as that in the induction period experiment. After pretreatment, the solution temperature was lowered and controlled at a desired subcooling for 1 h to let the concentration
3.2. Effect of operating conditions on secondary nucleation A couple of experimental runs were conducted at 3.5 8C subcooling before we started a systematic study at 3.0 8C Table 1 Induction period of potassium alum solution at various subcooling temperatures and agitation speeds. The saturation temperature of solution is 28.0 8C.
Fig. 3. Experimental apparatus.
Subcooling temperature DTsub (8C)
Agitation speed (rpm)
Induction period (h)
2.5 3.0 3.0 3.5 3.5 3.5
350 300 350 200 250 300
4.0 3.6 3.0 3.0 1.5 1.8
442
C.Y. Tai et al. / Journal of the Taiwan Institute of Chemical Engineers 40 (2009) 439–442
by Tai et al. (1992) either. In the experiment the injection was made when the solution was in a quiescence state. The mass-transfer resistance was so high that the interfacial supersaturation was quite low. Under this circumstance the size of clusters gathering on the crystal surface were small. According to Kelvin equation, which states that a large critical radius is required at a low subcooling or low supersaturation, a high subcooling (or supersaturation) was necessary to observe nuclei. Now back to our experiments, nuclei were observed at short stopping time when the subcooling for the nuclei to survive was 3 8C. This is because at short stopping time the stagnant film around seed crystal was not fully developed. However, almost no nuclei was observed when the stopping time was longer than 25 min. At that time probably the solution in the stirred tank became still, a situation similar to the experiment conduced by Jagannathan et al. (1980).
Fig. 4. Effects of jet distance and stopping time on the number of nuclei generated by injection: (~) jet distance 2 mm; (*) jet distance 3 mm.
subcooling. In the two runs the number of nuclei generated was countless at 3 and 10 min of stopping time, which was the time interval between stopping agitation and starting injection. It meant that the injection of solution induced primary nucleation at 3.5 8C subcooling and most of the nuclei came from the bulk solution instead of the crystal/solution interface. For the experiments at 3.0 8C subcooling, the results are shown in Fig. 4, in which the number of nuclei generated by shear force due to injection were plotted against the stopping time for two injection distances, i.e., the distance between the jet and seed crystal. For both distances, 2 and 3 mm, the number of nuclei decreased with increasing stopping time. For the same stopping time, more nuclei were generated at the shorter jet distance. The shear force was not effective for generation of secondary nuclei when the stopping time was longer than 25 min. Our experimental results will be explained by using the hypothesis proposed by Tai et al. (1992). The nucleation rate is a function of interfacial supersaturation and the magnitude of interfacial supersaturation is influenced by Kd under the constraint of constant over-all supersaturation. In a stirred tank the masstransfer coefficient increases with an increase in agitation speed. Thus at a higher agitation rate, the interfacial supersaturation is higher and so is the nucleation rate. In our experiment when we stopped the agitation, the swirling of solution died away gradually. Accordingly, the mass-transfer resistance would increase and the interfacial supersaturation along with the nucleation rate decreased. Fig. 4 shows such a trend. When the stopping time is shorter, the number of nuclei generated by fluid shear is higher. Although the energy transferred to the crystal face might be lower at a shorter stopping time due to the swirling of solution, the number of nuclei generated was still the highest at the shortest stopping time. Besides, the shorter jet distance gave a higher number of nuclei because more energy was transmitted to the crystal surface. This result is consistent with that reported by Tai et al. (1992) and Jagannathan et al. (1980). Jagannathan et al. (1980) conducted a fluid-shear experiment which was different from our experiment in two respects. Firstly, the solution was not agitated during a run, and secondly the nuclei generated were transported to a separate chamber where the solution temperature was kept at a high subcooling of 20 8C or more for the nuclei to survive, i.e., to become visible crystals. When the subcooling of generation stage was 3 8C, nuclei could be observed at a subcooling being higher than 20 8C in the observation chamber. This result can be explained by the hypothesis proposed
4. Conclusion An agitated vessel fitted with a jacket, a thermometer, an impeller, a seed crystal holder and a syringe was used to study the effect of interfacial supersaturation on the number of nuclei generated by injecting the solution to the crystal surface. The number of nuclei increased with an increase of interfacial supersaturation and energy imparted to crystal surface. Judging from the results obtained in this experiment together with that reported in the literature, the role played by the interfacial supersaturation did not violate the hypothesis proposed by Tai et al. (1992), i.e., the nucleation rate would be influenced by the interfacial supersaturation. The effect of interfacial supersaturation can be applied to readily soluble and sparingly soluble salts and should not be ignored in the design of an industrial crystallizer. Acknowledgement The authors gratefully acknowledge the support of the National Science Council of the Republic of China. References Clontz, N. A. and W. L. McCabe, ‘‘Contact Nucleation of Magnesium Sulfate Heptahydrate,’’ AIChE Symp. Ser., 110, 6 (1971). Garabedian, H. and R. F. Strickland-Constable, ‘‘Collision Breeding of Crystal Nuclei, Sodium Chlorate—Part 1,’’ J. Cryst. Growth, 13/14, 506 (1972). Jagannathan, R., C. Y. Sung, G. R. Youngquist, and J. Estrin, ‘‘Fluid Shear Secondary Nucleation of Magnesium Sulfate and Potassium Aluminum Sulfate,’’ AIChE Symp. Ser., 193, 90 (1980). Johnson, R. T., R. W. Rousseau, and W. L. McCabe, ‘‘Factors Affecting Contact Nucleation,’’ AIChE Symp. Ser., 121, 31 (1972). Larson, M. A., Secondary Nucleation: An Analysis, p. 50, Jancic, S.J. & E.J. de Jong (Eds.), North-Holland, Amsterdam (1982). Larson, M. A. and J. Garside, ‘‘Solute Clustering in Supersaturated Solutions,’’ Chem. Eng. Sci., 41, 1285 (1986). Larson, M. A., Solute Clustering and Secondary Nucleation, p. 20, Garside, J., R.J. Darvey & A.G. Jones (Eds.), Butterworth Heinemann, Oxford (1991). Mullin, J. W. and C. L. Leci, ‘‘Evidence of Molecular Cluster Formation in Supersaturated Solutions of Citric Acid,’’ Philos. Mag., 19, 1075 (1969). Qian, R. Y. and G. D. Botsaris, ‘‘A New Mechanism for Nuclei Formation in Suspension Crystallizers: The Role of Interparticle Forces,’’ Chem. Eng. Sci., 52, 3429 (1997). Rusli, I. T. and M. A. Larson, Solute Clustering in Supersaturated Solutions, p. 71, Strathdee, G.L., M.O. Klein & L.A. Melis (Eds.), Pergamon, New York, USA (1987). Sung, C. Y., J. Estrin, and G. R. Youngquist, ‘‘Secondary Nucleation of MgSO4 by Fluid Shear,’’ AIChE J., 19, 57 (1973). Tai, C. Y., W. L. McCabe, and R. W. Rousseau, ‘‘Contact Nucleation of Various Crystal Types,’’ AIChE J., 21, 351 (1975). Tai, C. Y., J. F. Wu, and R. W. Rousseau, ‘‘Interfacial Supersaturation, Secondary Nucleation, and Crystal Growth,’’ J. Cryst. Growth, 116, 294 (1992). Tai, C. Y. and C. Y. Shih, ‘‘Analysis of Nucleation and Crystal Growth Data Using the Interfacial Supersaturation,’’ AIChE J., 43, 268 (1997). Tai, C. Y., W. C. Chien, and J. P. Hsu, ‘‘Induction Period of CaCO3 Interpreted by the Smoluchowski’s Coagulation Theory,’’ AIChE J., 51, 480 (2005).