Introduction

Al2O3 inclusions formed in the steelmaking process are produced by the Al deoxidizer added for de-oxidation of molten steel. Generally, the non-metallic inclusions create problems in steelmaking process: for example, nozzle clogging, degradation of the mechanical properties of the product, and degradation weldability.[1,2,3] The inclusion content should be minimized by removing inclusions from molten steel to a slag. This process involves (1) transport of the inclusion to the interface, (2) separation of the inclusion to the interface, and (3) removal of the inclusion.[4] The final step involves the dissolution of the inclusion particle in the slag. When an inclusion is not quickly dissolved by the slag, the undissolved inclusion near the interface might be re-entertained in the molten steel. Therefore, the dissolution of inclusions is an important phenomenon to make clean steel.

A number of studies to understand dissolution behavior have been carried out by the rotating cylinder method (RCM),[5,6,7,8,9,10,11] confocal scanning laser microscopy (CSLM),[4,12,13,14,15,16,17,18] and single hot thermocouple technique (SHTT).[19,20,21] Cooper et al.[5] and Choi et al.[6] observed the dissolution of alumina in slag with the RCM. They reported that the dissolution of alumina rods was controlled by mass transfer of alumina into CaO–Al2O3–SiO2 slag. Taira et al.[7] and Bui et al.[10] reported using the RCM in which the dissolution rate of Al2O3 inclusions was controlled by mass transport of alumina into CaO–Al2O3–SiO2 slag. Especially in the study of Bui et al., they observed the formation of intermediate compounds (CaO·2Al2O3, CaO·6Al2O3, 2CaO·Al2O3·SiO2) at the particle/slag which could suppress the diffusion of Al2O3. Sridhar and Cramb[4] researched the dissolution of Al2O3 particles into CaO–Al2O3–SiO2–MgO slag using CSLM. They reported that the dissolution of Al2O3 particles was controlled by boundary layer diffusion of alumina in the Stokes regime. Liu et al.[13] proposed a new approach using a diffusion equation coupled with Lattice Boltzmann modeling. Using mathematical simulations, the dissolution mechanism at the dissolution of spherical Al2O3 particles could be identified as diffusion controlled in CaO–Al2O3–SiO2 slag. Michelic et al.[17] reported that the dissolution studies including the determination of dissolution mechanisms according to the approach proposed by Liu et al.[13] using CSLM is shown for two different slag/inclusion systems. Slag viscosity is a significant factor in both systems, and the shape of the dissolution curve varies with slag viscosity. Generally, the SHTT was used to study the solidification phenomenon in mold slags and crystallization behavior of mold slags.[22,23] However, Kim et al.[19] were the first to begin dissolution studies using the SHTT. They reported that the MgAl2O4 phase was clearly observed at the interface between the MgO particles and CaO–Al2O3–SiO2 slag (containing more than 20 pct Al2O3) through the quenched specimen. Wang et al.[20] investigated the dissolution of Al2O3 inclusions in ladle slags with different CaO/Al2O3 ratios with the SHTT. Chen et al.[21] studied the effect of slag basicity and Li2O content on the dissolution behavior of Al2O3 in mold flux using the SHTT. Compared to other method, the SHTT can be observed the dissolution phenomenon between inclusions and slags in real time. This method can get very clear images through a high-resolution camera. It was also possible to perform various analyses on quenched specimens through rapid quenching. Although previous studies have been conducted, but no study has been focused on Al2O3 activity in the slag. In this study, we were investigating the dissolution phenomenon with the SHTT by changing the alumina activity in the slag at various temperatures.

Experimental Method

Table I shows the composition of the Al2O3 sphere. The Al2O3 particles were 500 ± 25 μm in diameter (GoodFellow Cambridge Limited, Huntingdon, U.K.). The average weight was 0.25 mg, and the purity of Al2O3 was 99.9 pct (3 N).

Table I Composition and Weight of an Al2O3 Sphere Sample
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Table II shows the chemical composition of the slags used in this study. All the slags had a fixed basicity (CaO/SiO2 ratio) of 1. The content of Al2O3 in the slag varied from 5 to 35 pct. The amount of slag used in each experiment was about 10 mg. Chen et al.[21] studied the effect of particle size on the experimental reproducibility, and suggested the mass ratio of the particle to molten slag is to be less than about 2 pct. In this study, Al2O3 content was changed to be about 2.3 to 2.5 pct. The slags were individually mixed with CaCO3 (99.0 pct), Al2O3 (99.5 pct), and SiO2 (99.5 pct) powders. The CaO powder was prepared by calcining CaCO3 in a horizontal furnace at 1200 °C for 3 hours.

Table II Chemical Composition and Viscosity of Slags
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Figure 1 shows that each slag was in the liquid phase at 1550 °C, 1600 °C, and 1650 °C from the CaO–Al2O3–SiO2 ternary phase diagram obtained using Factsage7.3TM. The compositions of the slags before and after are shown in the phase diagram. The amount of the changed composition of Al2O3 in the slag was 2.3 wt pct in slag 1, 2 wt pct in slag 2, and 1.6 wt pct in slag 3 as can be seen in Figure 1.

Fig. 1
figure 1

Phase diagram of the CaO–Al2O3–SiO2 slag a system

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Figure 2 shows a schematic of the apparatus equipped with a high-magnification microscope that can observe the molten slags in real time at experimental temperatures. The SHTT can make a simultaneous measurement of the temperature while a thermocouple is being heated. The +, − poles of the B-type thermocouples were welded to make an oval shape, and the slag powder was mounted on the tip to melt the slag.

Fig. 2
figure 2

Schematic diagram of single hot thermocouple technique apparatus

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Figure 3 shows the procedure of the Al2O3 dissolution experiment. Before proceeding with the dissolution experiment, the slag powder is placed on the thermocouple tip and the temperature of the thermocouple is raised by 8 °C/s to the experiment temperature in the control mode. The experiment temperature was maintained until the slag powder was completely melted and all bubbles in the slags disappeared. After inserting the Al2O3 particles into the transparent molten slag, a dissolution image was taken through a high-magnification microscope within 3 seconds. In this process, with the insertion of Al2O3 particles, a temperature drop could occur, but the temperature is recovered by the power controlling system. We analyzed the images of the dissolution process to obtain the particle diameter with time through image analysis software (Image J). To observe the particle/slag interfacial phenomenon, the samples were quenched at a cooling rate of 30 °C/s. The polished specimen was analyzed by the Scanning Electron Microscope (SEM).

Fig. 3
figure 3

Experimental procedure of Al2O3 dissolution

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Results

To understand the dissolution behavior of Al2O3 particles, we conducted the experiment with SHTT by changing the content of Al2O3 in the slag and by changing the temperature from 1550 °C to 1650 °C.

The Dissolution Rate of Al2O3 as the Activity of Al2O3 in Slag

Figure 4 shows the Al2O3 dissolution optical images over time, and (a), (b), and (c) show the dissolved Al2O3 in slag 1 (5 pct Al2O3), 2 (20 pct Al2O3), and 3 (35 pct Al2O3), respectively. The optical images clearly observed that the radius of the Al2O3 particles decreases as a function of time in all the slags. Table III shows the total dissolution time taken from insertion to dissolution at each slag and the given temperatures. The total Al2O3 dissolution time was 1338 seconds at 1550 °C and 571 seconds at 1650 °C in slag 1. Slag 3 with increased Al2O3 content was 3634 seconds at 1550 °C and 1172 seconds at 1650 °C. Figure 5 shows the change in the radius of the particle with time using Image J analysis. The results show that the higher the Al2O3 content of the slag, the slower the Al2O3 particle dissolution rate. It can be seen that as the temperature increases, the dissolution rate of the Al2O3 particles increases. The dissolution rate on slag 3 rather than either slag 1 or slag 2 was more delayed. In particular, the dissolution rate of slag 3 was slower than the one of slag 1 by about 3 times at 1550 °C.

Fig. 4
figure 4

Al2O3 optical image as a function of time measured by video camera at 1550 °C in (a) slag 1, (b) slag 2, and (c) slag 3

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Table III Dissolution Time of Al2O3 Particles Under Each Condition
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Fig. 5
figure 5

Al2O3 particle dissolution results at 1550 °C, 1600 °C, and 1650 °C and comparison between the calculation dissolution curves through Eqs. [6], [8], and [9] and the experimental data. (a) Slag 1, (b) Slag 2, and (c) Slag 3

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The Particle/Slag Interface Analysis by SEM

To better understand the dissolution behavior of Al2O3 particles in liquid slags, we quenched the liquid slags containing Al2O3 particles. The maximum quenching condition was at a rate of 30 °C/s which acquired for turning off the power of the apparatus. A cross-section of the quenched sample was observed through SEM. Figure 6 shows the SEM images at the given time for each slag. The particle radius at the particle/slag interface during the dissolution of Al2O3 was reduced over time without a reaction layer. Park et al.[24] reported that a reaction product was formed at the particle surface depending on the slag composition. In the slag composition of this study, the SEM images confirmed that no reaction product was formed at the particle surface. Therefore, the dissolution rate was not delayed by the reaction product in this experimental condition.

Fig. 6
figure 6

Al2O3 particles cross-section image by SEM at 1550 °C. (S = Slag). (a) after 4 min in slag 1, (b) after 10 min in slag 1, (c) after 4 min in slag 2, (d) after 10 min in slag 2, (e) after 10 min in slag 3, (f) after 26 min in slag 3

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The Particle Rotation During the Dissolution

The particle rotation has been reported using the CSLM by Valdez[12] and Liu et al.[13]. The particle rotation phenomenon was also observed in the SHTT experiment, which is shown in Figure 7. Figure 7(a) shows the dissolution curve of Al2O3 particles in slag 1 at 1550 °C, and the magnified plot is described in Figure 7(b). The particle rotation was observed during all the experiments. The cycle of a particle rotation was measured for each experiment as shown in Table IV.

Fig. 7
figure 7

Particle rotation during dissolution with a period (a) Dissolution of Al2O3 particle in slag 1 at 1550 °C, (b) rotation frequency of Al2O3 particle

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Table IV Rotating Period of Al2O3 Particles During Dissolution
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The particle rotation affects the dissolution kinetics. According to Yan et al.[25], a kinetic model must be incorporated with a fluid flow due to the rotation and a Peclet number is used. In this study, the kinetic model related to a fluid flow was also needed for clearly understanding the dissolution behavior of particles. It might be due to Marangoni flow and/or natural convection which can be generated by inbalance of alumina concentration at the interface between the slag and particle during dissolution.[16]

Discussion

A Kinetic Model Related to a Fluid Flow

Most researchers used the shrinking core model to predict the particle dissolution curve. During the dissolution process, the mass change of a dissolving sphere can be expressed in Eq. [1] [25]:

$$ {\text{d}}N_{P} = \rho_{p} {\text{d}}V = \rho_{p} 4\pi R^{2} {\text{d}}R $$
(1)

where \({N}_{P}\) and \(V\) are the mass and volume of a dissolving particle; \({\rho }_{p}\) is the densities of the dissolving particle; \(R\) is the radius of the sphere. This mass change with time equals the mass flux across the boundary layer when the mass transfer is the rate-controlling step, and the following equation applies:

$$ - \frac{{4\rho_{p} R^{2} {\text{d}}R}}{{{\text{d}}t}} = 4\pi R^{2} k\Delta C $$
(2)

where \(k\) is the reaction rate constant; \(\Delta C\) is the concentration difference between the dissolving sphere and slag. When a flow condition is flow fluid, it can access via the Pe number and Re number as follows:

$$ {\text{Pe}} = \frac{2RU}{D},\quad {\text{Re}} = \frac{{2R\rho_{s} U}}{\eta } $$
(3)

where U is the fluid flow speed around the particle, \(\eta \) is the viscosity of the liquid slag; \(D\) is the diffusion coefficient of alumina in the slag. A Peclet number is a dimensionless number that can relate the effectiveness of mass transport by advection and the effectiveness of mass transport by diffusion.[26] A Reynolds number is the ratio of inertial force and viscous force, and is a dimensionless number that can determine which behavior is dominant in a given flow condition. If the fluid dynamics falls in the Stokes regime,[27] \({\text{Pe}}\) number \(\ll \) 10, \(Re\) number \(\ll \) 1, mass transfer coefficient \(k\) approximately equals \(D/ R\).[28] Based on the assumption that the fluid flow is the Stokes regime, the previous literature described the dissolution of inclusions using the shrinking core model.

However, the rotation of particles was observed during the dissolution in the SHTT, and the dissolution of particles was affected by the fluid flow at the particle/slag boundary. The flow speed around the particles is not zero, which means that the fluid flow will not be a Stokes regime. Yan et al.[25] studied the change of \({\text{Pe}}\) and \({\text{Re}}\) as a function of particle radius with the diffusion coefficient and viscosity. It clearly shows that the condition for \({\text{Pe}}\) << 10 is not satisfied, especially for larger particles. Thus, \(k\ne D/R\) would not hold. Instead, the mass transfer has to be directly linked with actual particle size and the fluid dynamics at the particle/slag boundary with Eqs. [4] and [5], to calculate the true dependence of \(k\) on particle size:

$$ k_{s} = \frac{{D_{s} \left( {4.0 + 1.21{\text{Pe}}^{2/3} } \right)^{1/2} }}{2R}, \quad {\text{Pe}} \le 10,000 $$
(4)
$$ k_{s} = \frac{{1.1D_{s} {\text{Pe}}^{1/3} }}{2R},\quad {\text{Pe}} \ge 10,000 $$
(5)

Figure 8 compares the calculated dissolution curves using Eqs. [2], [4], and [5] in each slag with the experimental data. The calculated dissolution curve and the experimental data are fitted well, but there was an initial deviation at 1550 °C for slag 2 for slag 3. This may have been due to the acceleration of dissolution when the temperature recovered after insertion of the particle.

Fig. 8
figure 8

Determination of activation energy for the diffusion coefficient

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The diffusion coefficient can be obtained by calculating the mass transfer coefficient through Eqs. [2], [4], and [5] in Table V. Detailed calculation parameters are listed in Table V. The range of the diffusion coefficient calculated in this study was within the range of 10−12 to 10−10 m2/s as suggested by Yan et al.[25] However, the diffusion coefficient on slag 3 at 1550 °C decreased to 4.55 × 10−13 m2/s. The reason may be because the viscosity of slag 3 was higher than other slags. It must be the high viscosity as shown in Table V.

Table V Calculated Diffusion Coefficients and Activation Energy in Present Study and Literature Available for Alumina Dissolution
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Activation Energy

We conducted experiments at various temperature conditions to determine the activation energy of Al2O3 dissolution. Figure 5 shows that the dissolution rate of the particle increases as the temperature increases. The effect of temperature on the diffusion coefficient can be using the Arrhenius relation represented by Eq. [6]:

$$ D = D_{0} \cdot \exp \left( { - \frac{{E_{D} }}{RT}} \right) $$
(6)

where ED is the activation energy, R is the gas constant, T is temperature, and D0 is a constant. Figure 8 shows the natural logarithm of the diffusion coefficient vs. 1/T (K). Based on the Arrhenius relation, the slope obtained from this figure is indicative of the activation energy for the diffusion. The calculated activation energy is 323 kJ/mole in slag 1, 343 kJ/mole in slag 2, and 486 kJ/mole in slag 3. As the Al2O3 activity in the slag increased, the activation energy of diffusion increased due to the dissolution of the driving force.

Conclusion

We studied the dissolution behavior of Al2O3 by changing Al2O3 activity in CaO–Al2O3–SiO2 slag using a single hot thermocouple technique. The following conclusions can be drawn as below.

  1. 1.

    The dissolution rate of Al2O3 decreased with increasing Al2O3 activity in slag. The driving force for Al2O3 dissolution was the concentration difference of Al2O3 between the particle/slag interface and the bulk slag. Decreasing the concentration of Al2O3 in slags increased in the dissolution rate.

  2. 2.

    The particle rotation was observed during the dissolution experiment. The dissolution of Al2O3 was controlled by mass transfer with a fluid flow. The diffusion coefficient of Al2O3 was calculated from 10−12 to 10−10 m2/s in a way similar to a previous study. However, we obtained 4.55 × 10−13 m2/s for 35 pct Al2O3 at 1550 °C. It must be the low viscosity.

  3. 3.

    The activation energy of the diffusion was 323 kJ/mole at 5 wt pct Al2O3, 343 kJ/mole at 20 wt pct Al2O3, and to 486 kJ/mole at 35 wt pct Al2O3. It increased with increasing Al2O3 activity in slags due to the lower driving force of alumina content.