Wetting and Spreading Kinetics between Liquid CaO–SiO₂ Slags and a Solid SiO₂

Abstract

Wetting and spreading phenomena between SiO₂ single crystal and CaO–SiO₂ slags with difference composition; SiO₂ saturated and non-saturated slags at 1600°C were investigated by using the dispensed drop technique (DDT) with a high-speed camera (1000 frames/s). The apparent contact angle and height of non-saturated slag were significantly smaller than those of saturated slag. The apparent radii of saturated and non-saturated slags were significantly different after 0.01 s. The change in the apparent volume of the slags was analyzed by using a spherical cap model. The apparent volume of the saturated slag was constant, but that of the non-saturated slag decreased because of film type spreading. After quenching, the film type spreading was verified, and a dissolution reaction occurred in the non-saturated slag, whereas no such phenomena were observed in the saturated slag. For the saturated slag, the spreading kinetics fit well with the non-reactive viscous model suggested by a previous study. However, non-saturated slag could not be applied to spreading kinetics due to the film type spreading.

1. Introduction

The interfacial properties between liquid metal or slag and solid ceramic are important in the steelmaking process. In particular, wettability between a liquid slag and a solid refractory ceramic is important because they come into contact with each other and cause interfacial reactions at high temperatures.¹⁾

Contact of a refractory with a liquid slag at high temperatures causes the slag to penetrate into the solid refractory and corrosion reaction between the two materials, which results in deterioration and finally shortens the working life of the refractory.^2,3) To evaluate the penetration of a liquid slag into a solid refractory, understanding the contact angle is necessary, as can be seen in Eq. (1), which is known as Lucas-Washburn equation.⁴⁾   

$$\frac{dl}{dt}=\frac{r\gamma cos\theta }{4\eta l},\mathrm{\hspace{0.17em} }{l}^2=\frac{r\gamma }{2\eta }\cdot (cos\theta )\cdot t$$(1)

where l is the slag penetration depth, t is the time during which the slag and refractory are in contact with each other, r is the capillary radius, γ is the surface tension, η is the slag viscosity, and θ is the contact angle. This equation shows that the contact angle influences the penetration depth.

Several researchers have conducted studies on wetting between solid ceramic substrates and liquid slags.^{5,6,7,8,9,10,11,12,13,14,15)} Wetting studies using SiO₂ have also been conducted, but not with liquid slag.^16,17,18) Many factors affect the contact angle, including the solubility of the two materials. Wetting studies based on the dissolution of two materials have been widely carried out regarding the system between liquid metals and solid metals or solid ceramics.^19,20,21,22) However, few studies have been carried out on the solubility difference between slags and solid ceramics. Kim et al.²³⁾ carried out experiments on the system between liquid slags and solid Al₂O₃ with different alumina activities. Yoon et al.²⁴⁾ did a similar study using the MgAl₂O₄ spinel with slags containing showing activity. In this study, the wetting phenomena of a solid SiO₂ were investigated by varying the SiO₂ activity in CaO–SiO₂ slags.

2. Experimental Method

The compositions of CaO–SiO₂ slag were designed from its binary phase diagram by Factsage 7.0^TM, and SiO₂ saturated and non-saturated compositions at 1600°C were prepared as follows, First, pure CaO and SiO₂ powders (≤ 150 μm) were mixed by ball-milling for 8 h, after which they were melted in a graphite crucible by using an induction furnace at temperatures above 1600°C. The obtained slags were cast and crushed into powder. Then the slags were decarburized by heating at 1100°C for 5 h. Decarburization is typically carried out to remove carbon in the slags. The saturated slag was placed into a SiO₂ crucible and held at 1600°C for 10 h to adjust its composition. Finally, the slag compositions were confirmed by X-ray fluorescence (XRF) analysis. The results are shown in Table 1. To reduce the influence of variables on the spreading behavior, β-quartz single crystal (>99.9%) was used as a substrate. The substrate size was 20 × 20 × 0.5 mm, and the orientation was Z-cut. Both sides were polished, and the surface roughness was less than 5A.

Table 1. Chemical compositions of saturated and non-saturated slags.

	Chemical composition (wt%)		C/S
	CaO	SiO2
Saturated slag	32.5	67.5	0.5
Non-saturated slag	54.0	46.0	1.2

Wetting and spreading phenomena were investigated by using the dispensed drop technique (DDT). Figure 1 shows a schematic of the apparatus. The chamber was sealed and evacuated by a rotary pump and filled with 99.999 wt% pure Ar gas to control the partial pressure of oxygen. This was repeated three times, and the furnace temperature was elevated to 1600°C at a rate of 10°C/min. When it reached the target temperature, liquid slag was pushed by a graphite bar and dropped onto the substrate. To avoid the effect of gravity, the distance between the substrate and the graphite crucible was maintained at only 10 mm. The sample weight of each droplet was about 5 mg for saturated slag, and about 1 mg for non-saturated slag. Images of the slag droplet ware captured by a high-speed camera at 1000 frames/s (Image size: 1280*720 pixel). After the experiment, each sample was immediately quenched to room temperature by turning off the electric power. The contact angle and spreading behavior were measured by using image analysis software (Image J software). After quenching, the cross-sections of the samples were analyzed by scanning electron microscopy (SEM) and an energy dispersive X-ray spectrometery (EDS).

Fig. 1.

Dispensed Drop Technique (DDT) apparatus. (Online version in color.)

3. Results and Discussion

3.1. Wetting and Spreading Behaviors

The wetting and spreading behaviors of the liquid slag droplets on SiO₂ substrate were studied by observation of the droplets as a function of time. Figure 2 shows droplet images of saturated and non-saturated slags from 1 ms to 1000 ms taken from the high-speed camera. When the liquid drops touched the substrate, it was determined to be 0 s. The apparent contact angle, height and spreading radius of the droplets were measured.

Fig. 2.

Images of droplets as a function of time. (Online version in color.)

Figure 3(a) shows variation of the apparent contact angle of the saturated and non-saturated slags on solid SiO₂ for 3 s. The contact angle of the saturated slag rapidly decreased from 140° to 66° within 0.4 s, and it reached 46.9° at 3 s. However, that of the non-saturated slag rapidly decreased to 38° within 0.2 s and it reached 15.4° at 3 s.

Fig. 3.

Experimental values of saturated and non-saturated slags droplet (a) Apparent contact angle (b) Apparent droplet radius (c) Apparent droplet height for 3 seconds. (Online version in color.)

Figure 3(b) shows variation of the apparent droplet radius ratio of saturated and non-saturated slags. Because the droplets were different in size, they were calculated as the ratio of the apparent radius at the time measurement to the apparent radius at 0 s. The apparent droplet radius ratio of the non-saturated slag exceeded 1 as soon as it touched, and that of the saturated slag exceeded 1 after 0.1 s. It was interesting that the apparent radius of the non-saturated slag increased rapidly up to the first 0.01 s and remained unchanged, whereas that of the saturated slag increased gradually.

Figure 3(c) shows variation of the apparent droplet height ratio of the saturated and non-saturated slags. The distance between the substrate and the maximum height of the droplet was measured. Because the droplets were different in size, they were also calculated as the ratio of the apparent height at the time measurement to the apparent height at 0 s. The apparent height of both slags decreased rapidly initially but then decreased slowly. The apparent height of the saturated slag decreased to 0.7 but that of non-saturated slag decreased more severely to 0.3 within 0.1 s. After that, those values gradually decreased to 0.43 and 0.13 at 3 s, respectively. The difference in the apparent droplet height ratio was much larger than that of the apparent contact angle.

In the case of the non-saturated slag, the apparent droplet radius increased rapidly for 0.01 s and was almost constant. However, the apparent contact angle and the apparent droplet height slowly decreased after 0.01 s as can be seen in Figs. 3(a) and 3(c), respectively. Considering with previous results, the mass of the slag seemed to be disappearing.

3.2. Interfacial Reaction Observation from Quenched Samples

Figure 4 shows cross-section SEM images between two slags and the SiO₂ substrate after quenching from 1600°C. A pseudo triple line with the assumption that there was no reaction was applied over the image. The interface between the saturated slag and the SiO₂ substrate was flat, as shown in Fig. 4(a), indicating that no dissolution reaction occurred during spreading. On the other hand, the interface between the non-saturated slag and the SiO₂ substrate was not flat as shown in Fig. 4(b). It is clear that the substrate dissolved into the slag, and the apparent contact angle measured was not the same as the actual contact angle during spreading. The actual angle was larger than the apparent one. As seen in the EDS mapping image of Fig. 4(b), Si ions are presented in yellow and Ca ions are presented in gray. It appeared that SiO₂ only dissolved into the slag, but there was no diffusion of Ca ions from the slag to the SiO₂ substrate.

Fig. 4.

Cross-section images between slags and SiO₂ substrate by SEM and dashed line is estimated original interface of substrate (a) Saturated slag (b) Non-saturated slag. (Online version in color.)

Figure 5 shows the whole image of the cross-section between the non-saturated slag and the SiO₂ substrate. It can be clearly seen that a dissolution reaction occurred, and it created a crater during spreading. The volume of the crater could be calculated by comparing the volumes of the spreading droplets. The calculated crater volume was approximately 22% of the droplet volume, indicating that the composition of SiO₂ in the slag varied from 46.0 wt% to 50.3 wt% during spreading.

Fig. 5.

Cross-section image of the non-saturated slag by optical microscope. (Online version in color.)

3.3. Volume Calculation Based on Spherical Cap Model

To clearly understand the phenomenon described in the last section A, the volume of the liquid slags could be calculated from the captured images by adopting a spherical cap model. Figure 6(a) shows the geometry of the spherical cap model. It can be used by assuming that a single droplet changes in a spherical cap shape. Then, the volume from the model can be obtained as.^23,24)   

$$V=\frac{1}{3}\pi \left\{2R^3(1-cos\theta )-r^2(R-h)\right\}$$(2)

where r is the apparent droplet radius, and h is the apparent droplet height, which are experimentally obtained values. Here, $R\left(=\frac{r^2+h^2}{2h}\right)$ and $\theta \left(={sin}^{-1}\frac{2hr}{r^2+h^2}\right)$ are functions of r and h, respectively.

Fig. 6.

Volume calculation based on spherical cap model (a) Geometry of the spherical cap model (b) The ratio of the slag apparent droplets volume calculated by spherical cap model (c) Spreading behavior of non-saturated slag droplet after quenching. (Online version in color.)

Figure 6(b) presents the ratio of V/V_i (V = the apparent volume at the time of measurement, V_i = the initial droplet volume). As seen in Fig. 6(b), the volume of the saturated slag remained unchanged over 3 s. On the other hand, that of the non-saturated slag significantly decreased in volume. After quenching of the non-saturated slag, it was found that a very thin film (area 2) spread out from the main droplet (area 1) as seen in Fig. 6(c). The apparent radius (area 1) of the droplet after quenching was 2 mm, and the larger radius (contained area 2) was 2.85 mm. It turned out that the non-saturated slag wetted to the SiO₂ substrate within 0.01 s, and a film-type spreading, which was invisible from the photos, occurred afterward. Therefore, the apparent radius appeared to be constant, whereas the apparent contact angle and the height gradually decreased as seen in Fig. 3.

Figure 7 shows a schematic of the spreading behavior of liquid slags based on the study above. The droplet of saturated slag spread as if it fit well the spherical cap model. However, the spreading of non-saturated slag presented a new phenomenon - a film type of spreading while it reacts with the substrate.

Fig. 7.

Spreading behaviors of saturated and non-saturated slag droplets.

3.4. Driving Force for Spreading and Spreading Kinetic Model

The driving force of a spreading droplet can be divided into inertial and viscous forces. Inertial spreading typically occurs in a low viscosity liquid, and local equilibrium is rapidly established at the triple line. The contact angle at the initial time is not far from that at equilibrium. Viscous spreading is controlled by viscous friction inside the droplet. The dissipation of energy mainly occurs close to the triple line of the droplet. The driving force, if θ ≤ 90°, can be expressed as.²⁵⁾   

$$\frac{f_{in}}{f_v}=0.0024\frac{\rho {\sigma }_{LV}}{{\eta }^2}{\theta }^{5}R$$(3)

where f_in is the inertial force, f_v is the viscous force, ρ is the density (kg/m³), σ_LV is the surface tension (J/m²), η is the viscosity (Pa∙s), θ is the contact angle (rad), and R is the droplet radius (10⁻³ m). To know the driving force, it is necessary to know the physical properties of the slag. Physical properties, such as the viscosity, surface tension, and density of the saturated slag, are shown in Table 2.

Table 2. Physical properties of saturated slag (at 1600°C).

	Density (g/cm3) (ref 26, 27)	Viscosity (Pa·s) (ref 26, 28)	Surface tension (mN/m) (ref 26, 29)
Saturated slag	2.50	1.86	380

Figure 8 shows the ratio of spreading driving forces as a function of time. If the result value (f_in/f_v) is greater than 1, the inertial force is dominant; if it is less than 1, the viscous force is dominant. For saturated slag, the viscous force prevails from the moment when the droplet touched the substrate. For non-saturated slag, however, the result cannot be applied because of film type spreading after 0.01 s and dissolution reaction.

Fig. 8.

The ratio of inertial force to viscous force of saturated slag. (Online version in color.)

For the saturated slag, the viscous force was dominant for the spreading kinetics. And, as seen in Fig. 6(a), there was no dissolution during spreading. In this case, a non-reactive viscous model can be applied as expressed by the following equations.^30,31) Equations (4) and (5) are valid for θ < 90° and θ < 45°, respectively:   

$$\text{U}=\frac{{\sigma }_{LV}}{3K\eta }tan\theta (cos{\theta }_F-cos\theta )$$(4)

  

$$\text{U}=\frac{{\sigma }_{LV}}{6K\eta }\theta ({\theta }^2-{\theta }_F^2)$$(5)

where U is the spreading rate (m/s), σ_LV is the surface tension (J/m²), η is the viscosity (Pa∙s), θ is the contact angle, θ_F is the final contact angle after quenching, and K is $\text{ln}\left|\frac{X_{max}}{X_{min}}\right|$, (X ≈ radius of droplet). Figure 9 shows a comparison of the theoretical and experimental values of the spreading rate in the case of saturated slag. As seen in Fig. 9, the experimental values fit well with the theoretical values for saturated slag. For the saturated slag, it can be said that the spreading behavior fit to the non-reactive viscous model.

Fig. 9.

Spreading rate of saturated slags at 1600°C. (Online version in color.)

4. Conclusions

The wetting and spreading phenomena of liquid CaO–SiO₂ slags on a solid SiO₂ single crystal substrate were studied at 1600°C by using a dispensed drop technique with a high-speed camera. The results were summarized as follows.

(1) The apparent contact angle and apparent height of the non-saturated slag were significantly smaller than those of the saturated slag. In the case of the saturated slag, the apparent droplet radius increased over 3 s. However, the apparent droplet radius of the non-saturated slag increased rapidly within 0.01 s and was almost constant thereafter.

(2) With the spherical cap model calculation, the apparent volumes were calculated. The volume of the saturated slag was nearly constant, but that of the non-saturated slag significantly decreased over time. This is mainly attributed a film type spreading within 0.01 s and this phenomenon was observed for a quenched sample.

(3) For the saturated slag, the quenched interface was flat, and dissolution was not found, indicating that the apparent and actual contact angles were the same. For the non-saturated slag, a dissolution reaction occurred, and the apparent and actual contact angles were not the same. Based on the quenched sample, SiO₂ diffused into the slag, and the dissolution volume was calculated as 22%, indicating that the composition of SiO₂ varied from 46.0 wt% to 50.3 wt% during spreading.

(4) For the saturated slag, the viscous force was dominant for the spreading kinetics. In the non-reactive viscous model, the experimental values fit well with the theoretical values. For the non-saturated slag, data could not be applied to the model due to the film type spreading.

Acknowledgements

This paper was partly supported by Korea Institute for Advancement of Technology (KIAT) grant (P0008425, The Competency Development Program for Industry Specialist) and by Korea Institute of Energy Technology Evaluation and Planning (KETEP) grant (20172010106310), funded by the Ministry of Trade Industry & Energy (MOTIE), Korea.

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