Measurement of Bubble Size Distribution and Generation Position of Bubbles Generated during Smelting Reduction of Iron Oxide-containing Slag

Abstract

Slag foaming is a phenomenon caused by the generation of CO bubbles due to the reaction between iron oxide in slag and carbon in pig iron. The purpose of this study is to explore the controlling factors of slag foaming by observing the bubble formation behavior caused by the chemical reaction between iron oxide and Fe–C alloy in slag. 0.06 g of Fe–C alloy was charged to the bottom of the BN crucible, and 6.0 g of slag (SiO₂:CaO:Fe₂O₃ = 40:40:30) was charged on top of it. The crucible was placed in an infrared image heating furnace, and the temperature was rapidly raised to 1370°C at a rate of 1000°C/min in a N₂ stream, then held for a predetermined time and rapidly cooled. After rapidly cooling, the internal structure of the sample was observed using a high-resolution X-ray CT device. The spherical equivalent volume is calculated based on the number of bubbles observed and their equivalent circle diameter, and the relationship between the volume ratio of small bubbles in the slag volume and the distance from the bottom of the crucible is calculated, and the bubble density and volume ratio are calculated. It was suggested that the value tends to increase as the distance from the bottom of the crucible increases.

1. Introduction

In research on the steel refining process, how to utilize slag effectively and how to control it have been explored. In particular, since the development of the oxygen steelmaking process, the scattering of slag and molten iron caused by slag foaming are annoying us. Slag foaming is a phenomenon in which gas is blown into low-basic slag, causing the gas to remain in the slag, significantly increasing the volume of the slag and causing it to foam. In recent years, it has been reported that controlling slag foaming is a challenge in recycling processes involving the melting and reduction of slag using electric furnaces.^1,2,3) It has been suggested that slag foaming occurs when slag containing iron oxide is melted and reduced by carbon, and that appropriate selection of the carbon source is important.^2,3) This issue is also being addressed as a challenge⁴⁾ in new iron source production processes such as COREX, which combine fluidized bed reduction and a smelter, and a machine learning estimation model aimed at controlling the slag foaming height has also been reported.⁵⁾

Slag foaming of molten slag in the steel refining process is observed in most refining processes using top-blown oxygen, such as converters, hot metal pretreatment, smelting reduction, and scrap melting using fossil fuels.⁶⁾ In particular, in the case of dephosphorization treatment performed in hot metal pretreatment, silicon present in the hot metal is de-siliconized prior to the dephosphorization reaction, generating low-basicity slag. When dephosphorization treatment is performed in the presence of such low-basicity slag, slag foaming occurs due to the CO gas generated by the decarburization reaction that proceeds in parallel with the dephosphorization reaction and the carrier gas used to inject the dephosphorization agent. The freeboard of the vessels used in the hot metal pretreatment process, such as torpedo cars and ladles, is smaller than that of converters, so when slag foaming occurs, the slag may flow out of the vessel. To calm the foaming, operation must be interrupted, and recovery work on the lower part of the furnace takes time, significantly affecting productivity and workability.⁷⁾ In addition, when the bubbles pass through the interface, they carry the metal layer with them into the slag, causing the iron that should become the product to emulsify in the slag, resulting in a decrease in the iron yield.

Due to these problems, slag foaming has been attracting attention and has been studied since the early stage of BOF steelmaking technology. When considering the foaming mechanism of slag, it is necessary to consider two factors separately: the generation factor, such as the rate of gas generation by reaction and the size of bubbles, and the factor that controls the stability of the generated bubbles. Fundamental research on slag foaming has been conducted from this perspective. In order to examine the factors that stabilize the bubbles, gas is fed into the molten metal at a constant flow rate and the height of the rise of the slag top surface is measured, or the bubble life required for the top surface of the bubbles to fall a certain distance due to the destruction of the bubbles is measured by stopping the gas after foaming the molten metal. In evaluations using a cold model that simulates foaming slag at room temperature, there have been cases where the generation behavior of bubbles was controlled by adding solid fine powder or liquid particles⁸⁾ and the viscosity of the liquid phase, including the gas phase, was measured,⁹⁾ and it has been suggested that the control of the interfacial energy between the solid, gas, and liquid is important. Furthermore, in the cold model, there has been a report on the size and growth behavior of bubbles, which are important for controlling foaming behavior and measuring viscosity.¹⁰⁾ It has been reported that bubbles that rise to the top and remain there become non-spherical.

In the hot model at refining temperatures, for example, Cooper et al.¹¹⁾ investigated the slag foaming behavior of CaO–SiO₂–P₂O₅ melts by measuring the time required for foaming slags to collapse from a given height after the foaming slags reached a steady state in a molybdenum crucible at temperatures ranging from 1623 to 1997 K. It was shown that binary CaO–SiO₂ melts did not foam, but the addition of P₂O₅ to melts containing more than 50% SiO₂ caused significant foaming. This showed that the bubble lifetime increased with increasing P₂O₅ and SiO₂ contents. Hara et al.^12,13) measured bubble lifetime and bubble height by gas injection into CaO–SiO₂–FeO and Na₂O–SiO₂ melts and reported that the bubble lifetime was well correlated with the surface tension, and that the bubble lifetime increased rapidly with decreasing surface tension. Ito and Fruehan¹⁴⁾ gave the foaming index, which corresponds to the bubble life, as a function of the viscosity and surface tension of the melt from an experiment in which Ar gas was pumped into a FeO–CaO–SiO₂ melt through a capillary tube. The foaming index proposed by Ito and Fruehan is shown below.

  

$$\sum =\text{570}\frac{\mu }{\rho \sigma }$$(1)

Here, Σ is the bubble life (s), μ is the viscosity of the slag (Pa s), ρ is the density of the slag (kg/m³), and σ is the surface tension (N/m). This makes it possible to explain that the bubble life increases with increasing viscosity and decreasing surface tension. However, in these studies, the inner diameter of the injection nozzle used was large at 2.1 mm and 2.5 mm, and the bubble diameter formed was also large, so there is a question as to whether the characteristics of the bubbles in the actual process were well reproduced. In addition, Mukai⁷⁾ pointed out that bubbles created by gas injection through a capillary tube differ from bubbles created by gaseous products of chemical reactions in the actual process in terms of gas flow rate, vessel volume, and bubble size and dispersion. In the actual process, slag foaming occurs when iron oxide in the slag floating on the molten iron reacts with the carbon in the molten iron at the bottom of the vessel due to the specific gravity relationship, as shown in Fig. 1. Therefore, it is necessary to investigate the bubbles that arise from the chemical reaction between FeO and Fe–C alloys.

Fig. 1. Slag foaming formation image illustration between molten slag and pig iron.

Most of the previous studies have investigated the relationship between the physical properties of slag and the stability of bubbles, but there have been few studies that have investigated the physical aspects such as the internal structure of foamed slag and the generation and distribution behavior of CO bubbles, which are the direct cause of foaming. Therefore, in the 1980s, slag foaming caused by gas generated by reactions similar to actual operating conditions was investigated by direct observation using transmission X-rays.^15,16,17,18) In observations of the reaction between molten slag containing iron oxide and carbon-saturated iron,¹⁵⁾ it was reported that the foaming height of the slag is related to the change in bubble diameter, and that when fine bubbles are generated, foaming is intense, and as the bubble diameter increases, foaming decreases rapidly, suggesting that the process in which fine bubbles are formed, grow while merging, and are destroyed is related to the bubble life. In addition, the importance of slag viscosity control has been suggested in evaluating the decarburization and dephosphorization reactions caused by emulsions dispersed in the slag.¹⁶⁾ However, due to the resolution problem in the X-ray transmission method, it is difficult to approach the generation process of fine bubbles of less than 1 mm in size, and it is desired to clarify the formation mechanism of fine bubbles, which are considered to be the main operating factor in slag foaming.

This study aimed to clarify the controlling factors of slag foaming from the internal structure by examining the physical aspects of slag foaming that occurs from the chemical reaction between FeO and Fe–C alloy in slag, such as the size and distribution behavior of CO bubbles that compose the foam, which have not been approached much so far. In particular, we focused on the size and distribution of bubbles, and conducted research with an emphasis on exploring the controlling factors from a new perspective by investigating the generation and distribution of fine bubbles with a diameter of 1 mm or less, which is currently an issue.

2. Experimental

In this study, in order to conduct experiments simulating slag foaming that occurs from the reaction between slag and pig iron during molten iron pretreatment, we focused on fine bubbles that are generated by the reduction reaction between iron oxide in the molten slag and carbon in the Fe–C alloy, and observed the distribution behavior of bubbles in the foaming slag using the following method.

2.1. Experimental Sample

The basic system of slag generated in hot metal pretreatment is a CaO–SiO₂–Fe_xO ternary system, so in this study, the components of the slag were CaO, SiO₂, and Fe₂O₃. The CaO/SiO₂ basicity ratio was adopted as the simplest, 1. As for iron oxide, Fe₂O₃ was adopted in this study for simplicity, considering the difficulty of handling during slag preparation and experimentation due to the change in iron valence. As for the iron oxide concentration in the slag, a preliminary study was conducted on the cases of Fe₂O₃ concentrations of 20 mass% and 40 mass%, and it was found that in the case of 20 mass%, the slag viscosity was high and large cavities were formed in the foamed slag, making it difficult to observe bubbles smaller than 1 mm, which is the focus of this study. Therefore, in this study, a slag with a Fe₂O₃ concentration of 40 mass%, which has a lower viscosity than the slag with a 20 mass% slag, was adopted. Table 1 shows the composition of the slag samples used in this study. The experiments used special-grade reagents SiO₂, CaCO₃ (all manufactured by Sigma-Aldrich Japan Co., Ltd., purity: ≥99.0) and Fe₂O₃ (99.8%-Fe manufactured by Strem Chemicals). Taking into account the thermal decomposition of CaCO₃, each sample was weighed to obtain the specified composition and thoroughly mixed using an Al₂O₃ mortar. The mixed powder was then filled into a platinum crucible and melted for 1 hour in an air atmosphere at 1500°C. It was then poured onto a copper plate and quenched, and the resulting glass-like slag sample was ground to a particle size of −600 μm.

Table 1. Chemical composition of Fe–C alloy (mass%).

C	Si	Mn	P	S	Cu	Al	N
0.63	0.24	0.48	0.0058	0.0027	0.008	0.03	0.0028

The carbon concentration of the iron-carbon alloy sample used in this study was 0.63 mass% because a preliminary study had confirmed that when the carbon concentration was high, large cavities would occur in the foaming slag, making it difficult to observe fine bubbles smaller than 1 mm. This iron-carbon alloy sample was a standard sample (manufactured by the Japan Iron and Steel Federation) with the composition shown in Table 1. The iron sample was crushed to a particle size of about 1 to 2 mm before use.

2.2. Experimental Method

The purpose of this experiment is to observe slag foaming, which is a problem in molten iron pretreatment, and it is necessary to observe slag foaming at around 1400°C. In order to minimize reactions during the temperature increase and decrease process and observe the state in which slag foaming is occurring, it is necessary to suppress the reactions before slag foaming and rapidly cool the slag while maintaining the foaming state. From these reasons, this experiment was conducted using an infrared image heating device that allows for rapid heating and cooling.

This equipment is composed of an infrared image heating furnace in the middle, a furnace tube, a lifting mechanism for the sample crucible in the lower stage, and a cooling chamber, as shown in Fig. 2. Rapid heating and cooling are possible through the use of various ingenious features, such as the infrared image heating furnace for rapid heating, the lifting and lowering type sample crucible, the cooling chamber, and the air-cooled quartz reaction tube that is highly resistant to thermal shock.

Fig. 2. Schematic illustration of infrared image heating device and quenching chamber.

The temperature of the sample was measured and controlled by using an R-type thermocouple, which was placed inside the graphite rod as shown in Fig. 3(a). In addition, since the height of the slag increases due to slag foaming, it is necessary to prevent the slag from touching the graphite rod. In addition, to prevent the temperature difference between the inside of the furnace and the thermocouple from becoming too large, the position of the graphite rod was set that the bottom end of the graphite rod was at the top end of the BN crucible as shown in Fig. 3(b). For the sample crucible, a graphite crucible (outer diameter 36 mm, inner diameter 30 mm, height 40 mm) and a BN crucible (outer diameter 25 mm, inner diameter 20 mm, height 32.5 mm) were used to prevent slag foaming due to the reaction between the graphite crucible and the slag. The sample was placed in the BN crucible in the order of Fe–C alloy and slag as shown in Fig. 3(c). Preliminary studies confirmed that when the amount of Fe–C alloy was large, large cavities would form due to violent forming. The weights were adjusted to 0.06 g of Fe–C alloy and 6.0 g of slag. After loading the sample, the crucible was placed in an infrared image heating furnace and rapidly heated to 1370°C at 1000°C/min in an inert atmosphere of N₂ gas flow at a flow rate of 2 NL/min, and then held for a specified time and rapidly cooled at 1000°C/min using a rapid cooling chamber.

Fig. 3. Schematic illustration of sample holder part and sample setting. (Online version in color.)

2.3. 3D X-ray CT Imaging

In this study, a high-resolution three-dimensional X-ray CT scanner (BRUKER SKYSCAN 1172) was used to observe the distribution of bubbles from the cross-section of foaming slag. CT (Computed Tomography) scanners can investigate the internal structure and materials of objects by utilizing the differences in the “ease of transmission (X-ray transmittance)” and “ease of absorption (X-ray absorption coefficient)” of X-rays when they pass through the object. Not only in the case of objects composed of different materials, but even in the same object, the X-ray absorption coefficient varies depending on the density, so it is possible to estimate the shape by measuring the difference. When X-rays are irradiated to an object from a certain direction, the detector recognizes the decrease in the intensity of the shadow of the projection due to the absorption of X-rays. By placing the object on a rotating pedestal and irradiating X-rays while rotating, it is possible to identify the positions of strong absorption in the object, calculate the X-ray absorption rate at specific positions on the object’s cross-section, and construct a cross-section by aggregating these data. The measurement conditions were: Camera Pixel Size 9.00 μm, Image Pixel Size 20.00 μm, Source Voltage 80 kV, Source Current 100 μA, Exposure time 2000 ms, and Rotation Step 1.2 degrees.

3. Results and Discussion

After the experiment, cross-sections of each sample were observed using a CT scanner. Figure 4 shows an example of an observation of a quenched sample after 2 min of holding. CT imaging provided a horizontal cross-section of the crucible as shown in Fig. 4(a) and a vertical cross-section of the crucible as shown in Fig. 4(b), allowing for the distinction between slag, iron, bubbles, and voids. In the figure, the gray parts are slag, and the white lumps are iron. The small black circular parts in the slag are bubbles, and the black parts with larger areas are voids.

Fig. 4. Cross-sectioning photographs of quenched sample in BN crucible in (a) Radial section, and (b) Vertical section (Hold for 2.0 minutes).

3.1. Evaluation of Foaming Slag Height

In this study, it was assumed that the slag foam height of the quenched sample was the same as the foam height during the high-temperature melting test, and the measurement results of the foamed slag height under each experimental condition are summarized in Fig. 5. From this figure, it can be seen that the foamed slag height increases linearly with time.

Fig. 5. Relationship between slag forming height and holding time at 1370°C. (Online version in color.)

In this study, Stokes’ equation¹⁹⁾ was used. Equation (2) shows Stokes’ equation. u (m/s) is the terminal velocity of the bubbles in the slag, d_p (m) is the bubble diameter, ρ_P (1.14 kg/m³) is the density of the CO bubbles, ρ_f (3.17×103 kg/m³) is the density of the slag,²⁰⁾ g (9.80 m/s²) is the acceleration of gravity, and μ (1.60 Pa·s) is the viscosity of the slag.⁹⁾

  

$$\text{u}=\frac{{{\text{d}}_{\text{p}}}^2\text{(}{\rho }_{\text{p}}-{\rho }_{\text{f}}\text{)g}}{\text{18}\mu }$$(2)

Since the speed of the bubble that has reached terminal velocity is constant, the travel distance L (m) of the bubble can be expressed as in Eq. (3).

  

$$\text{L}=\text{ut}=\frac{{\text{d}}_{\text{p}}{}^{\text{2}}\text{(}{\rho }_{\text{p}}-{\rho }_{\text{f}}\text{)g}}{\text{18}\mu }\text{t}$$(3)

The bubble floating distance was calculated by substituting the necessary slag properties⁹⁾ and the bubble diameter (100 μm to 1 mm) into formula (3). In this calculation, it was assumed that it takes 60 s for the rising bubbles to reach the terminal velocity after the holding temperature is reached, and the time t was calculated by subtracting 60 s from the holding temperature. The results are shown in Fig. 6(a). Figure 6(b) shows an enlarged view of the area with small bubble diameters. From these results, it is estimated that the calculated bubble floating distance is much higher than the experimental value of the foamed slag height, except for bubbles of about 100 to 200 μm, and bubbles of 200 μm or more are constantly detached from the slag foam layer.

Fig. 6. Calculated bubble floating distances of each bubble diameter cases. (Online version in color.)

3.2. Evaluation by Circle Equivalent Diameter Distribution

Circle equivalent diameter distribution was used to evaluate slag foaming. The circle equivalent diameter distribution is defined as the distribution of the diameter of a circle equivalent to a specified area of a cross section. After photographing the cross section of the crucible using CT photography, the images were colored and organized according to the range of circle equivalent diameters. With the full-field analysis of the cross-section direction of the crucible in mind, the resolution and number of pixels of the CT images that can be obtained were taken into consideration, and the minimum circle equivalent diameter was set to 200 to 300 μm. In addition, the black parts in the crucible that do not show the circle equivalent diameter range represent slag. Using this method, the size, number, and positional relationship of the bubbles were organized as follows. Figure 7 shows the horizontal cross section of the crucible photographed using a CT device for the samples after each experiment. Since there were almost no bubbles larger than 2 mm in size, the cross section of the crucible was observed in 2 mm increments.

Fig. 7. Radial section photograph of quenched sample in BN crucible using micro-CT observation. (Online version in color.)

Based on these images as like as Fig. 7, the relationship between the number of bubbles and the range of equivalent circle diameters is shown in Fig. 8. From this figure, it can be seen that there are many bubbles with equivalent circle diameters of 200 to 300 μm, regardless of the reaction time or the distance from the bottom of the crucible. This is because, according to Stokes’ equation (2), the smaller the bubble, the smaller the terminal velocity at the same viscosity. The residence time of small bubbles is longer, and the number of small bubbles in the slag increases. Focusing on bubbles with equivalent circle diameters of 200 to 300 μm in Fig. 8, the number of bubbles tends to increase in the experiment with a short reaction time of 1.5 min. It is thought to be because the size of bubbles generated at the slag/metal interface increases over time, decreasing the amount of small bubbles generated.

Fig. 8. Relationships between the diameter range equivalent to a circle and the number of bubbles at each level from bottom. (Online version in color.)

In evaluating slag foaming, bubbles with a circle equivalent diameter of 1 mm or less were defined as small bubbles, and more detailed analysis was performed focusing on small bubbles in the foamed slag. The foamed slags at each experimental time were observed in cross-section at 1 mm intervals up to the maximum height, and the total number of bubbles at all heights for each circle equivalent diameter range is shown in Fig. 9. It can be seen that the number of bubbles contained in the slag increases as the holding time increases. It is thought to be because the reaction time between the slag and the Fe–C alloy is longer, which generates more bubbles. In addition, the number of bubbles contained decreases as the bubble diameter increases. It is thought to be because the larger the bubble, the fewer the number of bubbles generated, and even if they do generate, they do not easily remain in the slag due to their fast-rising speed.

Fig. 9. Relationships between the diameter range equivalent to a circle and the number of bubbles in whole part. (Online version in color.)

3.3. Three-dimensional Evaluation of Slag Foaming

Two-dimensional evaluation was performed using the distribution of equivalent circle diameters, but to understand the internal structure of slag foaming in more detail, three-dimensional evaluation is necessary. Therefore, as shown in Fig. 10, the foaming slag was divided into 1 mm height intervals, and the volume of bubbles and cavities present in a 1 mm tall cylinder was calculated from the two-dimensional cross-sectional view and analyzed.

Fig. 10. 3D image of forming slag and 3D evaluation method (Hold for 2 min). (Online version in color.)

It was assumed that bubbles with a circle equivalent diameter of 1 mm or less in each cross section exist as spheres in a 1 mm tall cylinder, and calculated the sphere equivalent volume from the circle equivalent diameter. In addition, as shown in Fig. 11, for parts with a circle equivalent diameter larger than 1 mm, it was calculated the volume by assuming that the state of the cross-sectional view continues for 1 mm in the height direction.

Fig. 11. Schematic illustration of small air bubbles evaluation method. (Online version in color.)

To verify the validity of this method for estimating bubble volume, we assumed that the volume of the slag did not change before and after the experiment in all experiments, and calculated the volume of the foamed slag from the height of the foamed slag in each experiment. The theoretical value of the total volume of bubbles and cavities was calculated by subtracting the volume of the foamed slag from the volume of the slag, and the experimental value was the total volume of bubbles and cavities calculated from cross sections every 1 mm in height. Figure 12 shows the relationship between the theoretical and experimental values. It can be seen from this graph that there is no large discrepancy between the theoretical and experimental values, confirming the validity of this evaluation method.

Fig. 12. Ideal and experimental values of total volume of bubbles and voids for each height of forming slag. (Online version in color.)

It was assumed that all bubbles with a circle equivalent diameter of 1 mm or less that were generated under each experimental condition were spherical, and calculated the spherical equivalent volume of bubbles for each circle equivalent diameter. Figure 13 shows the relationship between the total volume of bubbles with a circle equivalent diameter of 1 mm or less in each cross section and the distance from the bottom of the crucible. Comparing Figs. 12 and 13, it is considered that the volume of small bubbles is considerably smaller than the total volume of the foamed slag. Therefore, it is considered that the dominant factor determining the foaming height and volume of the foamed slag in this experiment is not small bubbles, but large bubbles and cavities, but this is a topic for future study.

Fig. 13. Relationship between the volume of small bubbles and the distance from the bottom of the crucible for each reaction time. (Online version in color.)

Since the main purpose of this study is to evaluate the distribution behavior of bubbles contained in the slag, it was evaluated the small bubbles contained in the slag, excluding the large cavities that exist in each cross section. As shown in Figure, the volume of the region excluding the part with a circle equivalent diameter of 1 mm or more in a 1 mm thick cylinder is V (mm³), the number of small bubbles in each cross section is n (−), and the bubble density N (/mm³) in the slag is defined as follows.

  

$$\mathrm{N}=\mathrm{n}/\mathrm{V}\mathrm{\hspace{0.17em} }(/{\mathrm{m}\mathrm{m}}^3)$$(4)

Figure 14 shows the relationship between the distance from the bottom of the crucible and bubble density N. It can be seen that bubble density N tends to increase the farther the distance from the bottom of the crucible is, regardless of the holding time. Considering that the bubbles at the top of the crucible are bubbles that were generated at an earlier stage, it is thought that many small bubbles are generated in the early stages of the slag foaming reaction, and the number of small bubbles that are generated gradually decreases as time passes.

Fig. 14. Relationship between the distance from the bottom of the crucible and the bubble density for each reaction time. (Online version in color.)

Figure 15 shows the relationship between bubble density and distance from the bottom of the crucible for each bubble size. From this figure, it can be seen that the smaller the equivalent circle diameter of the bubble, the higher the bubble density. According to formula (2), for the same viscosity, the smaller the bubble, the lower the terminal velocity. The residence time of small bubbles is longer, while large bubbles rise to the surface and escape from the slag immediately. In addition, it can be seen that under all experimental conditions, the bubble density of bubbles with an equivalent circle diameter of 200 to 500 μm increases with the distance from the bottom of the crucible, while bubbles with an equivalent circle diameter of 500 to 1000 μm tend to have a lower bubble density regardless of height.

Fig. 15. Relationship between the distance from the bottom of the crucible and the bubble density for each bubble size (Hold for 2.0 min). (Online version in color.)

Since it is believed that the volume of bubbles affects the height of the foamed slag, the evaluation was performed using the volume ratio of small bubbles (−). The sphere-equivalent volume of bubbles with a circle-equivalent diameter of 1 mm or less was defined as V’ (mm³), and the volume ratio of bubbles with a circle-equivalent diameter of 1 mm or less in the slag was defined as follows using the bubble density N (/mm³).

  

$$\mathrm{V}\mathrm{o}\mathrm{l}\mathrm{u}\mathrm{m}\mathrm{e}\mathrm{\hspace{0.17em} }\mathrm{r}\mathrm{a}\mathrm{t}\mathrm{i}\mathrm{o}\mathrm{\hspace{0.17em} }\mathrm{o}\mathrm{f}\mathrm{\hspace{0.17em} }\mathrm{s}\mathrm{m}\mathrm{a}\mathrm{l}\mathrm{l}\mathrm{\hspace{0.17em} }\mathrm{b}\mathrm{u}\mathrm{b}\mathrm{b}\mathrm{l}\mathrm{e}\mathrm{s}=\mathrm{N}\cdot \mathrm{V}’\mathrm{\hspace{0.17em} }\mathrm{\hspace{0.17em} }(-)$$(5)

Figure 16 shows the relationship between the volume fraction of bubbles with a circle equivalent diameter of 1 mm or less in the slag calculated based on formula (5) and the distance from the bottom of the crucible.

Fig. 16. Relationship between the distance from the bottom of the crucible and the volume ratio of small bubbles for each holding time. (Online version in color.)

Compared to Figs. 12 and 13, these results show a correlation between the distance from the bottom of the crucible and the volume of small bubbles, and regardless of the experimental conditions, the volume fraction of small bubbles in the slag tends to increase as the distance from the bottom of the crucible increases. To confirm the size and distribution of bubbles in more detail, the relationship between the sphere equivalent volume for each circle equivalent diameter and the distance from the bottom of the crucible was calculated. The results are shown in Figs. 17 and 18.

Fig. 17. Relationship between the distance from the bottom of the crucible and the volume ratio of small bubbles for each bubble size smaller than 500 μm (Hold for 2.0 min). (Online version in color.)

Fig. 18. Relationship between the distance from the bottom of the crucible and the volume ratio of small bubbles for each bubble size bigger than 500 μm (Hold for 2.0 min). (Online version in color.)

From Fig. 17, the volume fraction of bubbles with a circle equivalent diameter of 200–500 μm increases as the distance from the bottom of the crucible increases. It is thought to be due to the fact that the bubble density increases as the distance from the bottom of the crucible increases. From Fig. 18, the volume fraction distribution in the height direction of bubbles with a circle equivalent diameter of 500–1000 μm is more irregular and variable than that of bubbles with a circle equivalent diameter of 200–500 μm. It is thought to be because bubbles with a circle equivalent diameter of 500–1000 μm are generated in smaller quantities than bubbles with a circle equivalent diameter of 200–500 μm, and the effect of the volume per bubble is greater.

3.4. Mechanism of Bubble Generation and Distribution

Based on the experimental results, how bubbles are generated and distributed was discussed as follows. Figure 19 shows the transition illustrations of bubble generation and distribution.

Fig. 19. Schematic illustration of bubble distribution and formation mechanism. (Online version in color.)

When the reaction starts, small bubbles are generated as shown in ①, which causes the liquid level to rise. It is thought that the iron oxide concentration in the slag decreases as the reaction progresses. Ogawa et al.¹⁵⁾ reported that the bubbles generated at the slag/metal interface become larger as the iron oxide concentration decreases. Terashima et al.²¹⁾ reported that the size of the bubbles generated at the interface between the slag and the carbon rod, which is difficult to wet, is large, but the size of the bubbles generated at the interface between the slag and the molten iron, which is easily wetted, is small, and it is thought that the size of the bubbles generated changes depending on the difference in wettability. In addition, Mukai et al.²²⁾ measured the contact angle between the slag and the molten iron and reported that the wettability of the slag and the molten iron improves as the iron oxide concentration in the slag increases. From these reports, it is thought that when the iron oxide concentration in the slag decreases and the slag and the molten iron become less wettable, the bubbles grow larger, and when the iron oxide concentration in the slag increases and the slag and the iron become more wettable, the bubbles remain small and detach from the interface and rise to the surface. Therefore, as the iron oxide concentration decreases over time, it is thought that large bubbles start to form at the slag/metal interface as shown in ②. Since small bubbles do not form at the slag/metal interface where large bubbles are formed, it is thought that the number of small bubbles formed decreases compared to the early stage of the reaction. This explains why the bubble density of small bubbles with a circle equivalent diameter of 200 to 500 μm decreases as the distance from the bottom of the crucible increases. In addition, as time passes from the state in ② and the reaction progresses, the number of large bubbles generated increases as shown in ③. However, since large bubbles rise quickly, it is thought that the time they remain in the slag is shorter and the number of bubbles contained within them decreases. It is thought that this is why the bubble density decreases regardless of the height.

4. Conclusions

In this study, simulated slag was prepared using CaO, SiO₂, and Fe₂O₃, and the size and distribution behavior of bubbles generated by the chemical reaction between Fe–C alloy and iron oxide in the molten slag was observed after quenching using an infrared image heating device. The following findings were obtained by observing the cross-sections of the samples after quenching at 1370°C. Regardless of the experimental conditions, many bubbles with a circle equivalent diameter of 200 to 300 μm were observed. It is thought to be because, according to Stokes’ equation, when the viscosity of the slag is the same, the smaller the bubble, the smaller the terminal velocity, resulting in a longer residence time. The bubble density and volume fraction of bubbles with a circle equivalent diameter of 200 to 500 μm tended to increase with the distance from the bottom of the crucible. It is thought to be because larger bubbles begin to generate over time, and the number of small bubbles generated at the same time decreases. Bubbles with a circle equivalent diameter of 500 μm or more tended to have a smaller bubble density regardless of height. As the reaction progresses, the iron oxide concentration in the slag decreases, generating large bubbles. However, because the bubbles rise quickly, they remain in the slag for a short time and the number of bubbles contained therein is small.

Statement for Conflict of Interest

The authors have no conflicts of interest related to the conduct of this study.

Acknowledgments

The authors would like to thank the research group “Visualization and Sensing of Slag for a Better Understanding of Multi-Phase Melts Flow” established by the Iron and Steel Institute of Japan for financial support and scientific advice.

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