Influence of the Interfacial Tension on the Droplet Formation by Bubble Rupture in Sn(Te) and Salt System

Abstract

Using a molten chloride and Sn system, in-situ observation of the bubble rupture and metal droplet formation can be carried out because the molten chloride phase is transparent. The size distribution of droplets with diameters in the range of 0.1 to 1.0 mm is measured using a high resolution camera, and the influence of the interfacial tension is discussed. The following results were obtained: (1) The addition of Te to the Sn decreased the interfacial tension and increased the number of small droplets, while the total surface area and total volume of droplets in the chloride bath decreased; (2) As the gas flow rate increased, the number of droplets in the Sn system formed by Mode B, where the metal emulsion was generated by the disintegration of the metal column, increased and large droplets were observed. In the Sn–Te system, even at the highest gas flow rate, droplets formed by Mode A, where the metal droplets formed by the rupture of the metal film, were observed in addition to those formed by Mode B; (3) In the Sn system, the size of the bubbles produced in Mode B was larger than that for Mode A. In the Sn–Te system the bubble size was generally smaller than that in the Sn system; (4) The total volume of the droplets formed by a bubble increased with increasing bubble size. In particular, the bubble rupture in Mode B generated a greater volume of droplets than in Mode A, even though the bubble size was the same.

1. Introduction

In order to enhance the reaction rate between the slag and the metal, increasing the interfacial area by efficient emulsion formation is critical. For this purpose, the formation of metal droplets in the slag phase is more effective than the formation of slag droplets in the metal phase because of the relative differences in the viscosities of the bulk phases.¹⁾ Generally, the metal droplets are formed by the impinging gas blown from the top lance and the bubble rupture of the gas injected into the metal phase. For the LD converter process in which most of the oxygen gas is blown from the top lance, the droplets are formed by impinging gas. On the other hand, for the bottom blowing converter and other refining processes including the ladle furnace, the droplets are formed by bubble rupture.

Reiter and Schwerdtfeger^2,3) conducted experiments using the cold model (water/oil, Hg/water, etc.) to observe the formation mechanism of the droplets by bubble rupture, and the effects of the interfacial tension and the density differences were reported. Han and Hollapa^4,5,6) studied the formation of the metal droplets at the interface of the iron/slag system using an X-ray fluoroscopy technique, and the influence of bubble diameter on the total mass of the droplets was established. However, the physical properties of the cold model system are very different from that of a molten steel and slag system. In addition, the size distribution of the metal droplets cannot be measured using this X-ray technique, due to the limitation of its resolving power.

Poggi et al.⁷⁾ invented a unique method to measure the total mass of the emulsified droplets using a Pb and chloride salt system (KCl–LiCl–NaCl). As this chloride salt is water soluble, the metal droplets can be extracted by immersing the sample into water. Using this technique, Song et al.^8,9,10) and Maruoka et al.¹¹⁾ investigated the size distribution of the metal droplets in the chloride phase using various metals (Pb, Al alloy, Sn alloy). They reported the size distribution of the metal droplets with diameters of 100 μm or less as a function of the gas flow rate. In addition, under the bottom blowing condition, they found several modes of bubble rupture by direct observation using a high speed camera, and they analyzed the relationship between the droplet formation rate and the bubble rupture frequency. When using the chloride salt system, most of the sampled droplets were less than 10 μm in diameter; we could not sample larger droplets because of their high sedimentation rate. However, the relative velocities of the small droplets reached zero in a very short time.^11,13) This indicates that the small droplets move with the flow of the bulk liquid and stay in the upper phase for a long time, which causes metal loss. The large droplets that return to the bulk metal after the reaction during the residential time in the upper phase play a more important role in enhancing the reaction rate.

Using the chloride and low-melting-point metal (e.g., Sn) system, in situ observation of the bubble rupture and droplet formation can be carried out because the molten chloride phase is transparent. In a previous study,¹²⁾ the frequency and modes of bubble rupture and the behavior of a metal emulsion consisting of large droplets were investigated by direct observation using a high speed camera. Due to limited resolution of the camera, only the size distribution of droplets with diameters of 1 mm or more could be measured. Further, Song et al.¹⁰⁾ measured the size distribution of droplets with diameters of 0.1 mm or less by an extraction method. Therefore, in this work, the size distribution of droplets with diameters in the range of 0.1 to 1.0 mm was measured using a high resolution camera and compared with the previous results.

2. Experimental Techniques

As the experimental method has been described in detail in the previous paper,¹²⁾ only a summary of the procedure is mentioned here. Direct observations of the metal emulsion and the bubble rupture process were carried out using an ultra-high-speed camera with high resolving power (Photron FASTCAM Mini UX100) equipped with a large diameter zoom lens (APO MACRO 180 mm f/2.8 EX DG OS HSM). The macroscopic mode of the bubble rupture was measured using a normal high-speed camera (Nikon 1 V3) equipped with a standard zoom lens (A AF-S DX Zoom-Nikkor 18–70 mm f/3.5–4.5G IF-ED), which was also used in the previous study.¹²⁾ The characteristics of these cameras are summarized in Table 1. The experimental apparatus was the same as used in the previous work¹²⁾ and the experimental conditions used here are shown in Table 2.

Table 1. Characteristics of the high speed cameras used in this study.

Purpose	Droplet behavior	Bubble behavior
Camera	Photron FASTCAM Mini UX100	Nikon 1 V3
Shutter speed [s]	1/10000	1/1000
Frame rate [fps]	4000	120
Resolution	1280×1024	1280×720

Table 2. Experimental conditions used in this study.

Metal	Sn/Sn-0.5 mass%Te
Chloride	50 mass%KCl-42.1 mass%LiCl-7.9 mass%NaCl
Temperature [K]	723
Height of Liquid Phases [mm]	Metal; 60, Chloride; 70
Gas Flow Rate [NmL/min]	50–2000

In this study, pure Sn and a Sn-0.5 mass% Te alloy were used as the metal phase to clarify the influence of interfacial tension. In the previous experiments, the interfacial tension between Sn and the salt decreased from 555 to 463 mN/m with the addition of 0.5 mass% of Te.¹²⁾ Firstly, 386 g of a salt mixture (50 mass% KCl, 42.1 mass% LiCl and 7.9 mass% NaCl) was placed in a square container made of Pyrex glass (inner dimensions: width 60 mm, depth 60 mm, and height 198 mm) and melted at 723 K. Then, 1475 g of Sn (purity: 99.99%) was added to the container. In the case of the Sn-0.5 mass% Te alloy, the prescribed amount of Te (purity: 99.99%) was added to the molten Sn. The heights of the salt phase and the metal phase were set to about 60 mm and 70 mm, respectively. After the metal was melted, Ar-3%H₂ gas was injected from the bottom of the molten metal phase through a Pyrex nozzle. The diameter of the nozzle orifice was 0.5 mm.

In order to measure the bubble rupture behavior using the high-speed camera, several bubbles were observed at each gas flow rate. On the other hand, to observe the macroscopic behavior of the bubble rupture using the normal high-speed camera, three videos were recorded 3 times for 3 s each. These videos were analyzed using image analysis software (Image-Pro Plus 7.0J). Figure 1 shows a snapshot of the recorded video. Figure 1(a) presents the behavior of the bubble rupture and (b) shows a magnified image of the formation of the metal droplets from the bubble surface. The minimum size of the droplets observed in this video was 0.1 mm. From this image, the following parameters were analyzed: (1) the number (N_mb) and the diameter (d_m, mm) of the generated metal droplets for each bubble and (2) the receding velocity of the metal film after its rupture at the bubble surface (ν_f , m/s). In order to calibrate the size of one pixel in the recorded image, a protective tube of a thermocouple with an outer diameter of 6 mm was inserted into the salt bath. The number of droplets was counted carefully using a frame-by-frame advance to avoid counting droplets twice. The location of the metal film edge during its recession on the bubble surface was measured at 1/4000 s or 1/2000 s intervals and the receding velocity was calculated.

Fig. 1.

An example of the bubble rupture and the formation of droplets showing (a) the behavior of the bubble rupture and (b) the magnified image of the formation of metal droplets from bubble surface.

The frequency of the bubble rupture in the salt phase (F, s⁻¹), and the modes of the bubble rupture were obtained using the normal high-speed camera. In our previous work¹²⁾ the emulsion formation mode by bubble detachment was categorized into two modes. In Mode A, the metal droplets formed by the rupture of the metal film covering the bubble before the bubble detachment from the interface. In Mode B, a metal column was formed under the detached bubble from the interface and then, the metal emulsion was generated by the rupture of the metal film and the disintegration of the metal column. In both modes, the bubble was almost spherical at the moment when the metal film ruptured. Therefore, the maximum horizontal length of the bubble was assumed to be the diameter of the bubble.

3. Results

Figure 2 shows the number of droplets formed by the rupture of a single bubble at each gas flow rate. In Figs. 2(a) and 2(b), the results for pure Sn and Sn-0.5 mass% Te are shown, respectively. As the droplet formation behavior was largely different in each bubble, the observed vales scattered widely. Therefore, it is difficult to explain the dependence on the gas flow rate clearly. However, in the Sn/chloride system, the number of droplets, especially formed by Mode B, tended to increase with increasing gas flow rate below 800 NmL/min. The droplets formed by Mode A was not observed at 800 and 2000 NmL/min by the limitation of the observation time. With the addition of Te, the number of droplets did not significantly increase with increasing gas flow rates below 2000 NmL/min. On the other hand, at 2000 NmL/min, the number of droplets formed by Mode B was same as that of the Sn system. In both systems, the total number of droplets was predominantly controlled by those formed by Mode B.

Fig. 2.

Influence of the gas flow rate on the number of droplets formed by the rupture of a single bubble in each mode in (a) Sn/chloride and (b) Sn–Te/chloride.

Figures 3(a) and 3(b) show the influence of the gas flow rate on the bubble rupture frequency of the Sn and Sn–Te systems, respectively. In both cases, the bubble rupture frequency of Mode A increased with the gas flow rate up to 500 NmL/min, where a local maximum was observed, and then gradually decreased for higher gas flow rates. The bubble rupture frequency in Mode B gradually increased in each case. Comparing the Sn and the Sn–Te systems, the bubble rupture frequency in Mode A increased significantly with the addition of Te, whereas no significant difference was observed for Mode B.

Fig. 3.

Influence of the gas flow rate on the frequency of bubble rupture in each mode in (a) Sn/chloride and (b) Sn–Te/chloride.

Combining the results from Figs. 2 and 3, the influence of the gas flow rate on the number of droplets formed per second for the Sn and Sn–Te systems are shown in Figs. 4(a) and 4(b), respectively. When the gas flow rate was less than 1500 NmL/min, the total number of droplets was slightly greater in the Sn system, but at 2000 NmL/min the number of droplets increased greatly with the addition of Te because of the increase in the droplet formation by Mode B.

Fig. 4.

Influence of the gas flow rate on the number of droplets formed per second in each mode in (a) Sn/chloride and (b) Sn–Te/chloride.

Figures 5(a) and 5(b) show the droplet size distribution and its dependence on the gas flow rate. In the Sn system, droplets of 0.4 mm or larger were observed when the gas flow rate increased to ≥800 NmL/min, while smaller droplets were measured in the Sn–Te system. Compared with the Sn system, the number of small diameter droplets (0.1–0.4 μm) increased remarkably when the gas flow rate increased to 2000 NmL/min, with the addition of Te.

Fig. 5.

Influence of the gas flow rate on the number of droplets formed per second in each size range in (a) Sn/chloride and (b) Sn–Te/chloride.

Figures 6(a) and 6(b) show the influence of the gas flow rate on the total surface area of the droplets (S; mm²/s) for the Sn and Sn–Te systems. Figures 7(a) and 7(b) show the influence of the gas flow rate on the total volume of the droplets (V; mm³/s) for the Sn and Sn–Te systems. These values were calculated using the following equations.   

$$S=4\pi \sum _{i=1}^n(D_i/2{)}^2\times F$$(1)

  

$$V=\frac{4}{3}\pi \sum _{i=1}^n(D_i/2{)}^3\times F$$(2)

where D_i is the measured diameters of the droplets (mm), n is the observed number of droplets by the rupture of a single bubble and F is the bubble rupture frequency (s⁻¹).

Fig. 6.

Influence of the gas flow rate on the total surface area of droplets formed per second for (a) Sn/chloride and (b) Sn–Te/chloride systems.

Fig. 7.

Influence of the gas flow rate on the total volume of the droplet formed per second for (a) Sn/chloride and (b) Sn–Te/chloride systems.

Although the observed values varied widely, the total surface area and the total volume in the Sn system was greater than that of the Sn–Te system until the gas flow rate reached 2000 NmL/min, although the total number of droplets in the Sn–Te system was greater than that of the Sn system. At 2000 NmL/min, although the number of droplets in the Sn–Te system was about two times that of the Sn system, the total surface area and the total volume did not show large differences. These results show that the formation of the larger droplets is very effective in increasing the surface area and the volume of droplets emulsified in the upper phase.

Figure 8 shows the size distribution of the droplets as a function of gas flow rate. In the Sn system, with the increase in the gas flow rate, the droplets formed by Mode B increased and at 2000 NmL/min, those formed by Mode A disappeared. The large droplets were mainly formed by Mode B. In the Sn–Te system, even at the highest gas flow rate, droplets formed by Mode A were observed and the number of small droplets was dominant. Figure 9 shows the average size of the bubbles for each gas flow rate. In the Sn system, the average bubble size from Mode B was larger than that from Mode A. In Mode A, the bubble size increased with increasing gas flow rate. In the Sn–Te system, the bubble size was generally smaller than that of the Sn system and the difference between Mode A and B was small.

Fig. 8.

The size distribution of the droplets for the Sn/chloride and the Sn–Te/chloride systems at each gas flow rate.

Fig. 9.

The average bubble diameter for the Sn/chloride and the Sn–Te/chloride systems for each bubble rupture mode.

In Figs. 10 and 11, the receding velocities of the ruptured film that covered the bubble are shown as a function of time. The influences of the gas flow rate and the bubble diameter are shown in Figs. 10 and 11, respectively. In each case, the receding velocity decreased drastically with time and it showed a relatively small value in the Sn–Te system compared to the Sn system for the same gas flow rate. Considering the bubble size (Fig. 11), when the bubble diameter was smaller than 16 mm, the receding velocity showed a smaller value in the Sn system than the Sn–Te system. In the Sn–Te system, as the most of the bubbles were smaller than 16 mm, the receding velocity was small.

Fig. 10.

Changes in the receding velocity of the metal film with time after bubble rupture at each gas flow rate.

Fig. 11.

Changes in the receding velocity of the metal film with time after bubble rupture for each bubble size.

4. Discussion

Figures 12 and 13 compare data from this study for the Sn system (size distribution of the droplets as a function of gas flow rate and the total surface area of the droplets, respectively) to the results of our previous study.¹²⁾ In the previous study, only droplets larger than 1 mm in diameter were observed as we used the normal high speed camera. The number of droplets larger than 1 mm in diameter was much smaller than that observed in the present study, but the total surface area was much larger. Song¹⁰⁾ conducted an experiment using the Sn-7.5% Sb alloy and the emulsified droplets were evaluated. In this study, the droplets in the chloride were extracted by immersing the sample into water. By this method, the observed size distribution is dependent not only on the droplet formation rate by the bubble rupture but also on the sedimentation rate of the droplets. In order to evaluate the formation rate of the droplets, Song et al.⁹⁾ measured the total mass of the droplets in 1 g of the sampled salt phase with time after the start of the bubble formation. Assuming that the formation rate is a constant, independent of time, and the sedimentation rate is proportional to the total mass of the droplets in the salt phase at any time, the formation rate (v_f; s⁻¹) was calculated from the increasing rate of total mass with time and the total mass after it reached the steady state. In the present study, the formation rate of the total volume of droplets (V; mm³/s) was calculated and the results are shown in Fig. 7. Assuming the uniform distribution of droplets in the salt phase, the formation rate of the total mass of droplets in 1 g of salt phase was calculated using Eq. (3).   

$$v_f=V\times {10}^{-9}\times \rho /W$$(3)

where, ρ is the density of the droplet (kg/m³) and W is the total mass of the salt phase in the container (kg).

Fig. 12.

Comparison of the size distribution data of the droplets with the results of the previous study.¹²⁾

Fig. 13.

Influence of the gas flow rate on the total surface area of the droplets and comparison with the previous paper.¹²⁾

Figure 14 compares the droplet formation rate (the total mass of the droplets formed per second divided by the mass of the bulk salt phase) obtained by Song¹⁰⁾ and Yoshida¹²⁾ with the results from the present study. From these figures, it is clear that the total mass of the emulsified droplets is mainly controlled by the large droplets, even though the number of small droplets is much higher. On the other hand, the descending velocity of the large droplets is high and the residence time is limited. In previous studies,^10,13) the descending velocity was calculated by the force balance on the droplet and the following equations were proposed. At the initial conditions, i.e., at t = 0, u_dr,0 = 0 (i.e. the initial velocity of the descending droplet is zero), the influence of the droplet size on the descending velocity can be calculated.   

$$\begin{array}{l}{u}_{dr}=\frac{e^{2t\sqrt{AB}}\left[A+\sqrt{AB}\cdot u_{dr,0}\right]+\sqrt{AB}\cdot u_{dr,0}-A}{e^{2t\sqrt{AB}}\left[\sqrt{AB}+B{u}_{dr,0}\right]+\sqrt{AB}-B{u}_{dr,0}}\\ A=\frac{2g\left({\rho }_d-{\rho }_s\right)}{\left(2{\rho }_d-{\rho }_s\right)},\mathrm{\hspace{0.17em} }B=\frac{3{\rho }_s{C}_D}{4r_d\left(2{\rho }_d-{\rho }_s\right)}\end{array}$$(4)

where, t is the time (s), u_dr is the descending velocity of the droplet (m/s), g is the acceleration due to gravity, C_D is the drag coefficient, and subscripts d and s indicate metal and chloride, respectively. The calculated values are shown in Fig. 15, for the Sn/chloride system and the steel/slag system. In the steel/slag system, the terminal velocity of the descending droplet is about 10 mm/s, if the droplet diameter is assumed to be in the range 1.0–10.0 mm. In the previous work, droplets of diameter 1 mm or larger were measured, but it is clear that their terminal velocity was too large and it was difficult for these droplets to form a stable emulsion and they easily settled to the metal phase after a very short residence time. In the case of the study by Song et al., the terminal velocity of the droplets around 10 μm in diameter was too small and all droplets moved with the macroscopic flow of the bulk liquid and it was difficult for them to return to the metal bath. Therefore, the droplet behavior shown in this study has important implications when considering the behavior in the steel/slag system.

Fig. 14.

Relationship between the droplet formation rate and the gas flow rate for various size ranges of the measured droplets.

Fig. 15.

Change in the terminal velocity of the descending droplet as a function of droplet size in the oxide and chloride bath.

Figure 16 shows the relationship between the bubble diameter and the total volume of the droplets formed by a bubble, for the Sn (a) and Sn–Te (b) systems. It can be seen that in the case of bubble diameter of 17.5 mm or larger, the frequency to show the larger volume of droplets increased. In particular, the bubble rupture in Mode B generated a greater volume of droplets even though the bubble sizes were the same. As shown in Fig. 1, the droplets were formed by the ripple caused by the metal film receding after bubble rupture. A similar phenomenon was reported by Uemura et al.¹⁴⁾ in an oil/water system. If most of the droplets were formed by a ripple, the receding velocity would be important. As shown in Figs. 10 and 11, the receding velocity of the film is low for small bubbles and it can be considered that a large bubble would form droplets efficiently. In addition, in Mode B, the droplets were also formed by the disintegration of the metal column. Ueda et al.¹⁵⁾ considered the mechanism of the breakup of this column using numerical calculations and concluded that it is caused by the Plateau-Rayleigh instability. In this case, as the instability of the liquid column is related to the interfacial tension, a decrease in the interfacial tension can increase the stable column length.

Fig. 16.

Relation between the bubble size and the total volume of the droplets formed by a bubble in (a) Sn/chloride and (b) Sn–Te/chloride.

Figure 17 shows the column rupture height at each gas flow rate for the Sn and the Sn–Te systems. Although the data varied widely, the average column height of the Sn–Te system was relatively higher than that of the Sn system and this result can be qualitatively explained by the above mechanism. Therefore, the increase in the bubble size and the bubble rupture frequency (instability of the column) in Mode B are the critical factors affecting the formation of the large surface area and large volume of emulsified droplets. In this context, the decrease in the interfacial tension by the addition of Te has a negative effect, because it causes the decrease in the bubble size, enhances the bubble rupture in Mode A, and stabilizes the metal column in Mode B.

Fig. 17.

The column rupture height at each gas flow rate for (a) Sn/chloride and (b) Sn–Te/chloride.

5. Conclusions

In order to enhance the reaction rate between the slag and the metal, increasing the interfacial area by forming a metal emulsion is important. Using a molten chloride and Sn system, in-situ observation of the bubble rupture and droplet formation can be carried out since the molten chloride phase is transparent. The size distribution of droplets with diameters in the range of 0.1–1.0 mm was measured using a high resolution camera. The influence of the interfacial tension on the formation of droplet and bubble was investigated and the following results were obtained.

(1) The addition of Te to the Sn decreased the interfacial tension resulting in an increase in the number of small metal droplets, but the total surface area and the total volume of droplets in the chloride bath decreased. Comparing the previous results to this study, it is clear that the total mass of the emulsified droplets is mainly controlled by the large droplets, even though the number of small droplets is much higher.

(2) The size of bubbles produced by Mode B was larger than that of Mode A, and the bubble size in the Sn–Te system was smaller than that in the Sn system. When the bubble size increased, the total volume of the droplets formed by a bubble increased; in particular, the bubble rupture in Mode B generated a greater volume of droplets even though the bubble size was the same.

(3) The receding rupture velocity of the film that covered the bubble decreased drastically with time and it was relatively small for the Sn–Te system under the same gas flow rate as the pure Sn system. When the bubble diameter was smaller than 16 mm the receding velocity was smaller for both the Sn and the Sn–Te systems compared to larger bubble diameters.

The above results indicate that the increase in the bubble size and the bubble rupture frequency in Mode B are important factors for the formation of a large surface area and large volume of emulsified droplets. In this context, the decrease in the interfacial tension by the addition of Te had a negative effect, as it caused the average bubble size to decrease, enhanced the bubble rupture in Mode A, and stabilized the metal column in Mode B.

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