A New Experimental Design to Study the Kinetics of Solid Dissolution into Liquids at Elevated Temperature
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A new method was developed to study the dissolution of a solid cylinder in a liquid under forced convection at elevated temperature. In the new design, a rotating cylinder was placed concentrically in a crucible fabricated by boring four holes into a blank material for creating an internal volume with a quatrefoil profile. A strong flow in the radial direction in the liquid was created, which was evidently shown by computational fluid dynamic (CFD) calculations and experiments at both room temperature and elevated temperature. The new setup was able to freeze the sample as it was at experimental temperature, particularly the interface between the solid and the liquid. This freezing was necessary to obtain reliable information for understanding the reaction mechanism. This was exemplified by the study of dissolution of a refractory in liquid slag. The absence of flow in the radial direction in the traditional setup using a symmetrical cylinder was also discussed. The differences in the findings by past investigators using the symmetrical cylinder are most likely due to the extent of misalignment of the cylinder in the containment vessel.
The rotating disk/cylinder (rod) method has been widely applied to study the dissolution of solids in liquids for decades,[1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20] in particular for high-temperature systems such as dissolution of solid metals into liquid metals, and dissolution of ceramic solids into liquid oxides (slags). While valuable information have been gained by these studies, some misconceptions in using this method need to be addressed and analyzed. This is especially true when a cylinder and a small crucible are used. A number of researchers have studied the dissolution rate by rotating a rod concentrically placed in liquid in a small crucible. For example, Matsushima et al. studied the dissolution of solid CaO into liquid slag by using a rotating rod method. A so-called J-factor was introduced to express mass transfer in the liquid. Umakoshi et al. also used this method to investigate the dissolution rate of burnt dolomite in converter slag. They reported that the dissolution rate was not affected by the porosity of the sample. Choi et al. investigated the dissolution of Al2O3 in the CaO-SiO2-Al2O3 slag system. The torque of the rotating alumina rod dipped into liquid slag was found to be related to the dissolution rate.
In fact, the limited applicability of this rotating cylinder method was pointed out clearly by Gregory and Riddiford. They emphasized that this method was only applicable to a disk rotating in a vessel considered to be infinitely large. They also stated that the rotating disk should have a very large ratio between the diameter and thickness. Cooper and Kingery pointed out that the position of the rotating disk played an important role in the dissolution. The constraints of the rotating disk method emphasized by those authors were confirmed in a previous study. Here, the authors reported that the method of a rotating rod in a crucible was unsuitable for the study of dissolution phenomena. CFD calculations were employed to evaluate the velocity distribution of the liquid flow when a rod is rotated concentrically in liquid in a small container. It was found that mass transfer in the liquid could not be enhanced by forced convection since no radial flow would be generated by the rotation of the concentrically placed long rod.
Moreover, the dissolution rate of a cylinder in a liquid greatly depends greatly on the nature of the experimental setup. For example, the cylinder usually is attached to a very long shaft in a high-temperature experiment. When high-speed rotation is employed, the long shaft along with the cylinder is very difficult to be kept exactly in the center of the container. A non-concentric placement would affect the dissolution results, (system dependent).
Unfortunately, many studies using the rotating method have neglected the constraints emphasized by Gregory and Riddiford, mostly because of the inherent limitations of conducting experiments at elevated temperatures. For one, it is very difficult to have sample disk with a diameter very much greater than its thickness in a furnace with very limited volume. What is more, it is also very impractical to have a crucible containing a large amount of liquid in high-temperature experiments.
It should be mentioned that most of studies using rotating rod method found that mass transfer in the liquid slag was the controlling step of dissolution, and the increase of rotation speed could enhance the mass transfer in the liquid resulting in the increase of dissolution rate.[10,16, 17, 18] To determine whether the dependence of the dissolution on rotation rate is actually due to the slightly misaligned rod or the oscillation of the rod would need careful study of the experimental setups. However, some researchers reported that the dissolution rate could also be controlled by other mechanisms. For instance, mechanical peeling is an important mechanism of dissolution. This mechanism is well demonstrated by earlier studies where the peeling off of solid particles led to fast dissolution in liquid slag. An increase of the rotation speed would result in the increase of shear stress and therefore an increase in “dissolution” rate.
In addition, the dissolution behavior of refractory in molten slag is an important issue in steelmaking for the reason that the lifetime of ladle lining mainly depends on the dissolution mechanism and the steel cleanliness depends greatly on the surface condition of the refractory lining.[23,24] An in-depth understanding of the dissolution of refractory into slag demands a reliable experimental technique at extremely high temperatures (> 1873 K (1600 °C)).
In view of the aforementioned constraints of the rotating rod technique and the limitations of high-temperature experiment, a new experimental design was developed to improve the rotating rod method. The new experimental setup should not only meet the constraints of the rotation method, but also enable to rapidly quench the sample to preserve the condition of the interface between the refractory and the liquid phase. The design of a new and relevant setup is the main focus of the present study.
As mentioned in the introduction, the new experimental design to study the dissolution should be able (1) to generate flow in the radial direction of the crucible; and (2) to have quenching capability so that the rod along with the slag can be rapidly solidified to preserve the state as at high temperature.
In a previous work, both experimental measurements at room temperature and CFD calculations were carried out to evaluate the traditional rotating rod method. The result of CFD calculation reveals that rotating a cylinder concentrically in a small circular container is ineffective in generating radial velocity in the liquid. The results of CFD calculation were later confirmed by the experimental results.
The upper surface of the liquid is a free surface. The shear stress is zero between the gas and liquid. No mass transfer takes place between the gas and the liquid.
Wall function can be applied to all solid boundaries.
Heat transfer has no effect on the flow. Energy conservation is not considered.
The liquid is water at 298 K (25 °C).
The equations of continuity and momentum are solved simultaneously with the k-ε turbulence model. In order to compare the calculation with the previous work, (wherein a simple cylindrical container is employed) the liquid height in the container is 95 mm. A rod with diameter of 8 mm has the length of 45 mm immersed in the water centrically.
It must be mentioned that the present model is only intended to examine whether the radial flow would be generated by rotating a cylinder in a baffled container. Therefore, no attempt was made to describe the velocity of flow in an accurately quantitative manner.
These results clearly indicate that the radial flow could be introduced efficiently by the new rotating method with the use of a baffled container with a quatrefoil profile.
To study the mechanism and rate of dissolution of a refractory cylinder in liquid slag, to freeze the condition of the interface between the solid and liquid as it was at experimental temperature is essential. In addition, to obtain the phases present at the interface at high temperature can provide information regarding the mechanism of the dissolution process. For example, it can reveal whether the dissolution rate is controlled by chemical reaction at the interface along with mass transfer, or by chemical reaction along with mechanical peeling of the reaction layer. In view of the difficulties to rapidly quench the sample outside the furnace, the experimental setup should be able to quench the sample in a chamber internally connected to the reaction tube. If the slag can be frozen in a few seconds, the solid–liquid reaction can be stopped. A rapid solidification can also maintain the phases in the sample in their states as they were at high temperature. To freeze the sample in seconds, a quenching chamber with sufficient water cooling is essential. Impinging of helium gas or argon gas of high flow rate directly on the sample holder can further increase the efficiency of quenching.
In view that experiments at room temperature generally yield better control and accuracy than that at high temperature, a cold physical model was employed.
Setup at Room Temperature
Sugar rods were used as the solid rods. They were carefully chosen, so that each rod was straight. All the selected rods had a diameter of 8 mm and a height of 90 mm. The upper part of the sugar rod was mounted to a steel shaft using a steel connector. To minimize wobbling, the shaft was made as short as possible.
Before the experiment, the diameter of each sugar rod was carefully measured. For each run, the sugar rod was placed above the water in order to avoid pre-dissolving. As the sugar rod was pushed down into the water, the timer was set as the zero reaction time. The immersed length of the sugar rod into the water was 45 mm. The partially dissolved sugar rod was immediately taken out from the water, after a predetermined time. The diameter of the sugar rod after the reaction was measured carefully along its length (every 5 mm), and an average value was obtained.
Setup at High Temperature
As discussed above, the new experimental setup should meet two additional requirements in comparison with the traditionally used technique; namely (1) the generation of flow in radial direction, and (2) maintaining the system as it is at experimental temperature by quenching. To meet the first requirement, a graphite crucible of the shape shown in Figure 1 was employed. The quenching facility is described along with the experimental setup below.
For each test, a graphite working crucible along with 100 g of pre-melted slag was placed into a holding crucible made of graphite. The pre-melted slag had the initial composition of 53 to 54 mass pct CaO, 31 to 33 mass pct Al2O3, 8 to 9 mass pct MgO, and 6 to 7 mass pct SiO2 after melting. Two types of ceramic rods were prepared, viz dense MgO·Al2O3 spinel and porous MgO. The choice of the porosity of the rod in this study was considered mostly on its resistance to slag penetration based on a previous studies. The dense spinel rod was produced by using high-purity Al2O3 and MgO powders in the mole ratio of Al2O3:MgO = 1:1. Porous MgO rod was prepared by industrial dead-burnt MgO (DBM) powders (purity 96.6 pct, particle size range 0 to 1 mm). Both types of ceramic rods were sintered at the temperature of 1873 K for 10 hours in a muffle furnace. After sintering, the spinel rod had a density of 3.2 g/cm3 (apparent porosity < 5.0 pct) and the porous MgO had a density of 2.6 g/cm3 (apparent porosity = 28.0 pct). The ceramic rods had 8 mm (± 0.5 mm) in diameter. While the spinel samples were used to examine the applicability of the new setup in the study of dissolution controlled by mass transfer, the porous MgO samples were used mainly to examine the applicability of the setup in the study of reaction mechanism.
The bottom of the ceramic rod was placed above the slag surface. After assembling all the parts, the assembly was fastened onto the end of the steel tube and placed in the quenching chamber. The whole system was sealed, evacuated, and flushed with argon gas. A constant argon flow of 0.05 L/minute was supplied during the experiment. As the hot zone of the furnace was heated up to the temperature of 1873 K (1600 °C), the sample was first lowered to the resting position of the furnace at a speed of 26 mm/minute. The resting position was at the temperature zone of 1673 K (1400 °C). The purpose for resting was to avoid thermal shock of the alumina tube and the same time to limit the reaction between the liquid oxides and graphite when the slag was melting. The resting was 20 minutes for each run, and thereafter the sample was pushed down all the way into the even temperature zone in seconds. Preliminary experiments had shown that the slag would need 3 minutes to become completely molten. After the melting of slag, the ceramic rod was immersed into the liquid (about 20 mm in the liquid). The height of liquid slag was around 40 mm. Thereafter, the rotation was started and the reaction time was counted. At the end of experiment, the sample was quickly lifted up to the quenching chamber in a few seconds, and meanwhile a high flow of argon gas was impinged onto the sample holder. The diameter of the ceramic rod was measured before and after the experiment.
After quenching, the slag along with the ceramic rod was cross-sectioned for SEM/EDS analysis (Hitachi TM3000, Japan).
Cold Model Experiments
Dissolution in Liquid at High Temperature
In order to examine the applicability of the new design in high-temperature experiments, graphite crucibles with the quatrefoil profiles were used. As mentioned above, the focus of this examination is two-fold, viz (1) getting reliable information regarding the effect of rotation rate on mass transfer; (2) obtaining the morphologies of the sample especially the sold–liquid interface area for mechanism study.
In the region of the remaining rod, liquid slag penetrates throughout the whole MgO-porous rod through the large open pores. The slag-penetrated layer is formed on the MgO-porous rod, since the composition of the liquid inside this layer is nearly the same as the outer slag. The shear stress introduced by the rotation of the rod would remove the slag-penetrated layer when the liquid fraction is high enough.
Necessity of Quenching
Many works suggest that the dissolution process in high temperature is controlled by the mass transfer in the liquid. On the other hand, some investigations report that mechanical peeling off of small solid particles or islands from the rod into the liquid can be another determinate step in the dissolution process.
As shown in Figure 10, an abrupt increase of dissolution on the rod was found after 40 seconds of rotation in slag. As discussed earlier, the composition of slag around the rod is very close to the initial slag composition. This indicates that the diameter change of porous MgO rod is not due to chemical dissolution followed by mass transfer in the bulk slag, but by detachment of the slag-penetrated layer. In a previous work, the impact of the formation of a slag-penetrated layer on the dissolution of refractory was systemically studied. When forced convection is applied in the system, the constant removal of the slag-penetrated layer due to the shear stress between the liquid and the refractory would result in faster dissolution. The SEM microphotograph shown in Figure 11 is a further confirmation of the reported peeling mechanism. Even though the experimental method in the present work was somewhat different from the previous publication, the peeling mechanism is well brought out by the reacted MgO refractory along with the slag.
The decrease of the diameter of the solid rod could be either by (1) chemical dissolution followed by mass transfer, or (2) by the formation of a slag-penetrated layer followed by detachment. In fact, (1) and (2) could both be important, and jointly contribute to the decrease of the diameter of the rod. Since different studies employ different experiment setups, the mechanism is system dependent. This would explain varied findings by different researchers, even though the refractory and slag were similar. In the present setup, quenching is facilitated. This facility allows maintaining the morphology of the interface as it was at experimental temperature. The example of MgO rod illustrated evidently that any mathematical treatment based on assumption of mass transfer control would lead to spurious conclusions in such case.
Necessity of Creating Radial Flow and Uncertainties of the New Rotating Method
The traditional rotating rod method cannot create effective forced convection if the rod is placed exactly in the center, because there is no flow of the liquid in the radial direction. This is further confirmed by present results as shown in Figure 8(b). However, most dissolution studies at high temperature found that a higher rotation speed made the dissolution faster. Note that it is very difficult to keep the rod exactly in the center of the vessel in the experiments at high temperatures. Even a slightly non-concentrically placed rod would result in a certain degree of convection, which would depend on the rotation speed. Unfortunately, the degree of non-concentricity varies from one experimental setup to another, and even varies from one experiment to another in the same setup. Since the convection is mainly introduced by the non-concentricity, the experimental uncertainty would therefore be substantial, which could even lead to erroneous conclusions.
In the present experimental design, convection is created by the baffles, leading to the formation of radial flow. This aspect is clearly brought out by the velocity distributions shown in Figures 2 and 3. The enhancement of mass transfer in the case of spinel rod and sugar rod shown in Figures 9 and 8(a) further confirms the function of the baffles.
It should be mentioned that even in the new setup, misalignment of the rod in the crucible is inevitable. The slight dependence of the dissolution on the rotation speed shown in both Figures 8(b) and 9 is evidence of the non-concentricity of the rod. Note that even the vibration of the rod during stirring could also introduce experimental uncertainties. However, convection is generated by both the baffles and the misalignment of the rod. It would be valuable to compare the uncertainty with the velocity of the flow generated only by the baffles.
It should be mentioned that the main focus of present work was to present a new rotating rod method. No attempt is made to study the kinetics of the dissolution of ceramic rod specifically. While the systems experimentally studied at high temperature involve slag and refractories, this design could be employed for any solid–liquid reactions.
A new method was developed to study the dissolution of solid in liquid. In this method, a cylinder was rotated in a container fabricated by boring four 18-mm-diameter holes into a blank material in order to create an internal volume with a quatrefoil profile. The quatrefoil profile created efficient flow in the radial direction, which resulted in mass transfer in the same direction. The radial velocity generated by the baffles was found to be substantially larger than the uncertainties due to the slight misalignment of the rod from center. Experiments at both room temperature and steelmaking temperature along with CFD calculation showed evidently the applicability of the new experimental design. The experimental setup also facilitated the quenching of the sample. The quenching enables the preservation of the morphology of the sample as it was at high temperature. This function was proved to be very valuable to provide reliable information for a mechanism study. For example, in the case of porous MgO rod, the main mechanism of dissolution in slag was the peeling off of a slag-penetrated layer.
Huijun Wang is thankful for the financial support of China Scholarship Council in the form of scholarship. This work was supported by the European Union’s Research Fund for Coal and Steel (RFCS) research program [Grant Agreement No RFSR-CT-2015-00005].
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