Dissolution Mechanism of Modifying Agent in Fibrotic Process of Steel Slag

Abstract

The kinetic behavior of SiO₂ dissolving in molten steel slag at 1773–1923 K was studied using a combination of high-temperature confocal scanning laser microscopy and a synthetic physical property tester. The experimental results showed that the change in slag electrical conductivity can characterize the homogenization process of the modifying agent in molten steel slag, and the dissolution process of the modifying agent is controlled by solute diffusion in the slag. The concentration difference between the boundary layer and the bulk of the slag is the primary driving force of the dissolution process. By increasing the reaction temperature, the SiO₂ particle dissolution rate in slag can be significantly increased. Moreover, the experimental data and model calculations revealed that the SiO₂ dissolution rate was the fastest when the total Fe (T.Fe) content was 14% and the acidity coefficient (M_k) was 1.5. The dissolution factors were defined to quantitatively evaluate the dissolution mechanism of particle by studying the dissolution process of slag with different components.

1. Introduction

Steel slag, a by-product of steelmaking, is a resource that can be recycled and used as raw material for cement, concrete, and glass ceramics.^1,2,3) At present, the modification of steel slag to prepare fiber materials is regarded as a high value-added utilization method. Molten steel slag is poured directly into the reduction container, and, after complete reduction, is poured in a rotating barrel for slag fiber production by centrifugal force.^4,5) Compared to the conventional fiber-making method, this process is more energy efficient as it removes the need for a raw material melt process, developing a new method for the utilization of steel slag. After reduction, the physical and chemical properties of steel slag should be optimized to improve the shape and quality of the resulting steel slag fibers. Acidic modifying agents (SiO₂-containing materials) are typically added to the steel slag after reduction as such materials can alter its viscosity, acidity coefficient (the mass fraction ratio of all acidic and alkaline substances in the slag), crystallization behavior, and other physical and chemical properties.^6,7,8) However, controlling the dissolution rate and homogenization behavior of the modifying agent remains an issue as it affects the fiber quality as well as the productivity and energy consumption.^9,10) Therefore, in order to optimize the production capacity of steel slag production, it is important to study the dissolution kinetics and mechanism of the modifying agent in the molten slag.

In previous studies, static methods have been used to study homogenization, and some research results have been obtained. Amini et al.¹¹⁾ studied the dissolution behavior of dense lime in CaO–A1₂O₃–SiO₂ slags at 1500°C and 1600°C using a static test method. Maruoka et al.¹²⁾ experimentally confirmed the mechanism of lime dissolution and slagging by adding lime particles to CaO–SiO₂–Fe_tO–P₂O₅. Compared to the static method, the dynamic method can show, to some extent, the interactions between slag components in the furnace. Many studies have used high-temperature confocal scanning laser microscopy (HT-CSLM) to focus on the dissolution kinetics and particle mechanisms (CaO, Al₂O₃, MgO, etc.) in metallurgical slag.^13,14,15) Using the HT-CSLM research method, Feichtinger¹⁶⁾ studied the kinetic process of SiO₂ inclusion adsorption by refining slag in the steelmaking process and established a SiO₂ dissolution kinetics model. Parameters of solute diffusion are presented in this model. However, the diffusion control model overestimated the mass transfer of the solute in the slag and was also affected by the interface reaction rate. To study the dissolution mechanism of lime in the slag, Valdez et al.¹⁷⁾ and Yan et al.¹⁸⁾ suggested that solute dissolution was controlled by mass transfer in the slag, while others argued that it was controlled by mass transfer in the boundary layer of molten slag.^{19,20,21,22,23,24)} Meanwhile, Guo et al.²⁵⁾ implied that the dissolution mechanism would change from reaction control to liquid film diffusion control for CaO, mass transfer in the boundary layer of molten slag for MgO, and mass transfer in the liquid slag for Al₂O₃.

The aforedescribed studies indicate that HT-CSLM is one of the most intuitive, advanced dynamic research and analysis methods. By providing direct observation of the dissolution behavior of micrometer-sized particles in molten slag, it is a superior solution to experimental problems. Therefore, a quantitative evaluation of the dissolution rate was possible by prompt recording of dissolution details from the accumulation stage to the final stage. By combining the HT-CSLM observation with kinetic and thermodynamic calculations, the effects of temperature and slag composition on particle dissolution were systematically interpreted.

In this paper, a new experimental research method is proposed, combining HT-CSLM and a synthetic physical property tester to observe the dissolution process of a modifying agent (SiO₂ particle) in molten steel slag in situ. This facilitates the dissolution behavior of the modifying agent to be studied and characterized more accurately. This study is a supplement to the existing theory of slag fiber formation, providing theoretical support for the industrial application of mineral wool prepared using steel slag.

2. Experimental Procedures

2.1. Experimental Materials

Analytically pure chemical reagents (Kenong Chemical Co., Inc.) were used in this study. Eight different slag samples were investigated, and the composition of each is listed in Table 1. The slags were prepared by pre-melting a mixture of SiO₂, CaO, MgO, Al₂O₃, and Fe₂O₃ powders in corundum crucibles at 1873 K for 2 h. The liquid slags were then quenched on a stainless-steel plate floating on water to prevent segregation and crystallization. Subsequently, the glassy solid slag was crushed using an agate mortar. X-ray fluorescence spectroscopy (XRF) was used to analyze the chemical composition of the slag. For the dissolution experiments, the crushed powder was compacted into Pt crucibles (inner diameter of 10 mm and height of 5 mm). Then, to prepare a homogeneous solidified chunk of slag, the filled crucible was melted again in the CSLM furnace and cooled rapidly by turning off power to the furnace. The rapid cooling rate prevented segregation and crystallization during cooling. The modifying agent used in the experiment was SiO₂ particles with analytical pure (Kenong Chemical Co., Inc.). The particle size was 1.0–1.5 mm. In each experiment, a particle with appropriate roundness was selected to be added to the upper surface of the molten steel slag from the feeding tube. Each group of experimental schemes was repeated several times under the same conditions to select the best experimental data.

Table 1. Chemical compositions of steel slags (wt.%).

Slag No.	SiO2	CaO	MgO	Al2O3	T.Fe (Total Fe)	$M_{\mathrm{k}}\left(\frac{W_{Si{O}_2}+W_{A{l}_2{O}_3}}{W_{CaO}+W_{MgO}}\right)$
S 1	36.56	30.43	10.23	8.25	14.00	1.10
S 2	38.55	29.00	10.00	8.00	14.00	1.20
S 3	39.80	26.50	10.60	8.80	14.00	1.30
S 4	40.33	24.86	10.82	9.15	14.00	1.40
S 5	41.20	23.30	10.25	9.36	14.00	1.50
S 6	41.60	23.70	11.30	10.80	10.00	1.50
S 7	43.60	25.30	12.30	12.65	5.00	1.50
S 8	45.67	27.58	10.64	11.62	1.00	1.50

2.2. Experimental Apparatus and Procedure

The experimental device was shown in Fig. 1. An Al₂O₃ disk was placed between the Pt crucible and Pt sample holder to avoid sticking. A synthetic physical property tester (Brookfield DV-II, Brookfield Inc., USA) was used to detect the change in electrical conductivity of the slag when SiO₂ particles were added. The basic method of electrical conductivity measurement was the two-probe method. Two Mo bars (made of Mo with a height of 35 mm and a diameter of 3 mm) were immersed in a liquid slag bath and rotated at the same speed of 10 r/min. Each measurement was performed after the SiO₂ particles were added to the slag, and the electrical conductivity data were collected every 5 s.

Fig. 1.

Schematic diagram of combined experimental apparatus. (Online version in color.)

In the SiO₂ dissolution experiment, the slag chunk was first placed in a Pt crucible and protected by argon gas. It was then heated slowly in a furnace at a heating rate of 200 K/min. After melting, the furnace temperature was adjusted to the required experimental temperature and held for 1 h, making the chemical composition of the molten slag more uniform. Subsequently, the SiO₂ particles were fed to the upper surface of the slag through the conveying pipe of the high temperature feeding unit and slowly dissolved into the slag. Meanwhile, the change in electrical conductivity of the molten slag was recorded, along with a video of the SiO₂ dissolution process. Finally, upon complete dissolution of the SiO₂ particles, the crucible was removed from the furnace. The change in the normalized equivalent diameter (transient equivalent diameter divided by the initial equivalent diameter) with time was used to explain the dissolution mechanism of particles in molten steel slag. In addition, assuming that the particle maintains a spherical shape throughout the dissolution process, the equivalent particle diameter can be calculated by measuring the particle area based on the video image.

3. Results and Discussion

3.1. Influence of SiO₂ Particle Dissolution Process on Electrical Conductivity of Liquid Slag

The variation of slag electrical conductivity with time can be observed in Fig. 2. Five groups of slag with SiO₂ particles at a temperature of 1923 K, the same total Fe (T.Fe) content, and different acidity coefficients were used. The increase in SiO₂ and Al₂O₃ content of the slag promotes the formation of many polymerization anion groups, such as (SiO₄)⁴⁻, causing slag electrical conductivity to decrease as acidity coefficient increases. This further strengthens the slag mesh structure making electromigration difficult in the dissolution process and leading to a decrease in the slag electrical conductivity. At the same acidity coefficient, the slag electrical conductivity first decreases then increases with time at constant temperature, eventually stabilizing. From a dynamic perspective, this is because the dissolution process is unbalanced when SiO₂ particles are first added to molten steel slag. As (SiO₄)⁴⁻ anion groups are polymerized in local slag, the intermolecular cohesion is strengthened, increasing the viscosity of local modified slag, and decreasing the electrical conductivity. At this point, the melting of SiO₂ particle in the dissolution process is a restrictive link. As melting progresses, SiO₂ particles continuously dissolve and diffuse into the slag causing the local SiO₂ content of the slag to become consistent. As a result, the intermolecular cohesion in the slag decreases gradually, reducing the viscosity of the slag and increasing the electrical conductivity. With more time at constant temperature, the electrical conductivity of the modified slag fluctuates and gradually tends to stabilize, with a range of electrical conductivity fluctuation less than 0.01 S/cm. This stabilization indicates the slag has reached a state of complete homogenization. When the electrical conductivity stabilizes, the five groups of slag are removed and put into water for quenching and solidification. The SiO₂ content in the modified slag was analyzed by cutting sampling, as shown in Fig. 3. The figure shows that within a given slag sample, the SiO₂ content is consistent throughout. This indicates that the SiO₂ particles were completely dissolved, the composition of the slag was uniform, and the modified slag was in a homogenized state. Therefore, the change in slag electrical conductivity can be used as a means of verifying homogenization of modifying agents within molten steel slag. This provides a new characterization method and theoretical basis for the industrial application of mineral fibers prepared by the modification of molten steel slag.

Fig. 2.

Curves of slag electrical conductivity under different acidity coefficient. (Online version in color.)

Fig. 3.

w(SiO₂) in different positions of modified slag. (Online version in color.)

3.2. Effect of Temperature, T.Fe Content, and M_k on SiO₂ Particle Dissolution Process

The changes of temperature, T.Fe content, and M_k on the dissolution of SiO₂ in molten steel slag with time were depicted in Fig. 4 with t_f as the total dissolution time, r as the SiO₂ particle equivalent radius at time t, and r₀ as the initial equivalent radius of the SiO₂ particle. For simplification, the average SiO₂ dissolution rate was used to characterize the dissolution of SiO₂ particles under three different conditions. The average dissolution rate (v = 2r₀/t_f, where r₀ is the initial equivalent radius, and t_f is the total dissolution time of the SiO₂ particle) was calculated by dividing the initial equivalent diameter by the total dissolution time, as shown in Table 2. Faster dissolution of SiO₂ particles is indicated by a larger average dissolution rate. The Fig. 3(a) shows the average dissolution rate of SiO₂ particle in S 2 slag is 2.35, 2.96, 3.08, and 3.15 μm/s for the experiments with different temperatures of 1773, 1823, 1873, and 1923 K, respectively. This indicate that the SiO₂ particle observed average dissolution rate increases with an increase in temperature. The Fig. 3(b) shows the average SiO₂ dissolution rate at 1923 K is 6.01, 4.53, 4.88, and 5.75 μm/s for the experiments of the slags with different T.Fe contents of 14.0, 10.0, 5.0, and 1.0 pct, respectively. This implied that the observed average SiO₂ dissolution rate was highest for slag with 14.0% T.Fe. The Fig. 3(c) shows the average SiO₂ dissolution rate at 1923 K is 6.01, 4.93, 3.40, 3.15, and 2.93 μm/s for the experiments of the slags with different M_k of 1.5, 1.4, 1.3, 1.2, and 1.1, respectively. Therefore, indicates that the average SiO₂ dissolution rate reaches its maximum value when the M_k of slag is 1.5.

Fig. 4.

Dissolution of SiO₂ particle in the molten steel slag (a) Temperature (S 2 slag); (b) T.Fe content (1923 K); (c) M_k (1923 K). (Online version in color.)

Table 2. Experimental data and calculation results of SiO₂ particle dissolution process.

Trial	value	2×r0, mm	tf, s	v, μm/s	C0, wt%	Csat, wt%	Csat − C0, wt%	k	viscosity η, Pa.s	$\frac{C_{sat}-C_0}{\eta }$	D×10−11, m2/s
Temp., K	1773	0.98	418	2.35	38.55	66.82	28.27	1.68	0.623	45.38	4.47
	1823	1.07	362	2.96	38.55	69.15	30.60	1.94	0.385	79.48	4.52
	1873	1.00	325	3.08	38.55	71.26	32.71	2.23	0.266	122.97	4.63
	1923	0.96	306	3.15	38.55	72.62	34.07	3.36	0.138	246.88	4.91
T.Fe, wt%	14	0.98	163	6.01	41.20	67.55	26.35	2.42	0.289	91.18	3.86
	10	0.96	212	4.53	41.60	66.23	24.63	2.26	0.257	95.84	4.42
	5	1.05	215	4.88	43.60	65.71	22.11	2.11	0.243	100.52	4.57
	1	0.99	172	5.75	45.67	65.38	19.71	1.93	0.162	121.67	4.73
Mk	1.5	0.98	163	6.01	41.20	67.55	26.35	2.42	0.289	91.18	3.34
	1.4	1.10	223	4.93	40.33	69.21	28.88	2.68	0.251	115.06	4.27
	1.3	0.98	288	3.40	39.80	70.86	31.06	3.05	0.206	150.77	4.66
	1.2	0.96	306	3.15	38.55	72.62	34.07	3.36	0.138	246.88	4.91
	1.1	0.98	335	2.93	36.56	73.08	36.52	3.42	0.125	292.16	5.22

3.3. Dissolution Kinetics Model of SiO₂ Particle in Molten Steel Slag

As shown in Fig. 5, the classical shrinkage nuclear reaction model can be used to study the dissolution mechanism of SiO₂ particles in molten steel slag. In Fig. 5(a), a concentration boundary layer with thickness θ forms on the surface of the solid SiO₂ particle, where C_p is the SiO₂ concentration on the boundary layer, and C_p’ is the SiO₂ concentration of the dissolving particle. Because the concentration of the pure SiO₂ particle is much higher than that of SiO₂ in the slag, the thickness of the SiO₂ concentration boundary layer on the surface of solid particle can be ignored. Thus, C_p’ equals C_p (ΔC_SiO2=0). The particle radius gradually decreases as the particle dissolves, and the mass flux (J, kg/m² s) from the surface of the dissolved particle can be expressed as:   

$$J=-\left(C_p-C_i\right)\frac{dr}{dt}$$(1)

where C_i is the SiO₂ concentration of the slag at the particle-slag interface, r is the radius of the particle, t is the dissolution time, and C_SiO2 is the product of ρ and w with units in kg/m³, where ρ and w are the density and weight percentage of SiO₂ particles, respectively.

Fig. 5.

Concentration profile for SiO₂ particle dissolution in molten steel slag with developing concentration boundary layer (a) fixed SiO₂ concentration of molten steel slag; (b) varied SiO₂ concentration of molten steel slag at the particle surface. (Online version in color.)

If the mass flux from the dissolving particle surface is equal to the rate of loss of solute from the particle by the reaction, J = J_r. For a first-order chemical reaction at the particle-liquid slag interface, the rate equation for SiO₂ dissolution can be expressed as   

$$J_r=k_r\rho \left(w_p-\frac{w_i}{K}\right),\mathrm{\hspace{0.17em} } k_r=k_{0}exp\left(-\frac{E_r}{RT}\right)$$(2)

  

$$\mathrm{W}\mathrm{h}\mathrm{e}\mathrm{n}\mathrm{\hspace{0.17em} } w_{(Si{O}_2)s}=w_{(Si{O}_2)l},\mathrm{\hspace{0.17em} } K=w_{sat}$$(3)

  

$$\mathrm{t}\mathrm{h}\mathrm{e}\mathrm{n},\mathrm{\hspace{0.17em} } J_r=k_r\rho \left(w_p-\frac{w_i}{w_{sat}}\right)$$(4)

K is the chemical equilibrium constant of SiO₂ particle dissolution reaction in molten steel slag, k_r is the reaction rate constant, k₀ is constant, E_r is activation energy, R is the gas constant, and T is the temperature. The weight percentages of SiO₂ in the particle, the particle-slag interface, and SiO₂ saturated slag are w_p, w_i, and w_sat, respectively.

By setting J = J_r, the reaction rate control model of SiO₂ particles in the slag is   

$$\frac{r}{r_0}=1-\frac{t}{t_f},\mathrm{\hspace{0.17em} } t_f=\frac{r_0\left(C_p-C_i\right)}{k_r\rho \left(w_p-\frac{w_i}{w_{sat}}\right)}$$(5)

where r₀ is the initial radius of the particle, and t_f is the total dissolution time in steel slag.

When J_r > J_i, the interfacial concentration gradient of SiO₂ is the driving force for diffusion between the particles and slag. The dissolution rate of the particles in the slag bath can be expressed as   

$$J_i={-D\frac{\partial c}{\partial x}|}_{x=r}$$(6)

where D is the diffusion coefficient of SiO₂ particles in molten steel slag, which is a function of the slag temperature and viscosity according to the Stokes‐Einstein relation:^15,18,21)   

$$D=\frac{k_{B}T}{6\pi \eta r_{eff}}$$(7)

where k_B is the Boltzmann constant, η is the viscosity of the slag, and r_eff is the effective hydrodynamic radius of a molecule obtained from the Stokes‐Einstein‐Debye relation.²⁶⁾

During the entire dissolution process, if the thickness of the diffusion layer for mass transfer at the interface between the particles and slag is sufficiently developed, the right side of Eq. (6) is a constant value, and the dissolution process of the particle is controlled by the diffusion boundary layer. Assuming that the velocity of a moving particle in molten steel slag is in the limit of Stokes flow, the mass transfer coefficient (β) is related to the particle radius (r) and diffusion coefficient (D). At this point, the mass flux through the concentration boundary layer can be calculated using the following formula:   

$$J_{\beta }=\beta \left(C_i-C_0\right),\mathrm{\hspace{0.17em} } \beta \approx \frac{D}{r}$$(8)

where C₀ is the SiO₂ concentration in the slag bath, and J_r > J_i, C_i = C_sat.

By setting J = J_β, for the diffusion boundary layer model, the following relationship exists between the dissolution time (t) and the measured radius (r) of the particle:   

$${\left(\frac{r}{r_0}\right)}^2=1-\frac{t}{t_f},\hspace{1em}{t}_f=\frac{r_0^2\left(C_p-C_{sat}\right)}{2D\left(C_{sat}-C_0\right)}$$(9)

During the particle dissolution process, if the thickness of the SiO₂ concentration diffusion boundary layer continues to develop, the dissolution process is controlled by diffusion. This means that the SiO₂ concentration gradient in the boundary layer between the particle and slag is a function of time, so the right side of Eq. (6) is not a constant value.

A simple calculation method can be used to obtain the time-dependent value of the right-hand side of Eq. (6). As shown in Fig. 5(a), the initial SiO₂ concentration in the slag bath is C₀, and the concentration boundary at infinity is C_i. Meanwhile, it is assumed that the boundary concentration at the particle surface (x = r) is a constant of the saturation concentration, C_sat. The aforedescribed boundary conditions are applied to Fick’s second law of diffusion in spherical coordinates, and the slag concentration field (x≥r) can be obtained using the Laplace integral transformation:   

$$\frac{C-C_0}{C_{sat}-C_0}=\frac{r}{x}erfc\left(\frac{x-r}{2\sqrt{Dt}}\right),\hspace{1em}x\ge r$$(10)

The mass flux (J_D) at the interface (r) between the particle and slag can be calculated by substituting the above equations into Eq. (6).   

$$J_D=-\left(C_{sat}-C_0\right)\left(\frac{D}{r}+\sqrt{\frac{D}{\pi t}}\right)$$(11)

Then, by setting J = J_D, the relationship between the particle measured radius (r) and solution time (t) in the approximately invariant interfacial concentration diffusion control model can be obtained:   

$$\frac{dr}{dt}=-\frac{kD}{r}-k\sqrt{\frac{D}{\pi t}},\hspace{1em}k=\frac{C_{sat}-C_0}{C_p-C_{sat}}$$(12)

Equation (12) is the invariant interfacial concentration approximation for SiO₂ dissolution. The first term on the right of Eq. (12) is the geometric dissolution rate, whose value increases with a decrease in the particle radius (r), and the second term is the initial interfacial concentration-induced dissolution rate, which decays gradually over time owing to the diffusion of solute in the liquid slag. When the effect of the initial interfacial concentration on the particle dissolution rate decreases gradually over time, the predicted results of Eq. (12) at the end of dissolution are close to those of the diffusion boundary layer control model (Eq. (9)). However, the Eq. (12) is not highly accurate in the early stage of particle dissolution, and it cannot accurately reflect the instantaneous state of the early dissolution process of particles. As shown in Fig. 5(b), when J_r > J_i, it takes time for the SiO₂ concentration (C_i) in the liquid slag to increase from the initial C₀ to C_sat. Therefore, at the initial stage of particle dissolution, the dissolution rate predicted by the diffusion control model was greater than the actual slag dissolution rate.

3.4. Application of Kinetics Model

To further analyze the accuracy and reliability of the aforedescribed dissolution dynamics model, C_sat and C₀ for each experiment in the CaO–SiO₂–MgO–Al₂O₃–Fe₂O₃ molten steel slag systems were calculated using the phase diagram calculation module in the software Fact-Sage 7.2 software. All experimental data and calculation results are shown in Table 2. The added weight of SiO₂ particles was considered negligible compared to the total content of liquid slag.

The influence of different temperatures on the normalized r/r₀ and t/t_f curves of SiO₂ dissolution in S 2 slag was shown in Fig. 6. Each symbol in the figure represents a fifth-order polynomial fit to the experimental data. To show the dissolution mechanism of particles in liquid slag more conveniently, the original experimental data were not used in this study, but a polynomial fitting method was adopted. The figure indicates that the reaction control model Eq. (5) and the diffusion boundary layer control model Eq. (9) cannot fully fit the data in the experiment. The Eq. (12) describes the dissolution rate of the particle overestimates at the beginning of dissolution, which may be because of the assumption that the SiO₂ concentration at the particle-slag interface was a fixed value. As the reaction proceeded, the calculated control model showed a good fit with the experimental values. Therefore, it can be considered that the diffusion control model can adequately explain the dissolution process of SiO₂ particles in the slag. Further analysis and discussion are as follows:

Fig. 6.

The normalized r/r₀ and t/t_f curves for the dissolution of SiO₂ in S 2 slag with different temperature. (Online version in color.)

When J_r < J_i (=J_β or J_D), dissolution is reaction rate controlled. As the reaction progressed, the SiO₂ particle radius continued to decrease. According to Eq. (4), the SiO₂ concentration at the particle-slag interface remains less than the SiO₂ saturation concentration, that is, C_i < C_sat.

When J_r > J_i (=J_β or J_D), the concentration gradient of SiO₂ at the particle-slag interface is the driving force for particle dissolution, and C_i gradually approaches the saturation concentration C_sat (Fig. 5(b)). When C_i at the interface increased from C₀ to C_sat, over time t_i, the rate of change of the particle radius (r) was controlled by the interface reaction and was unrelated to the mass transfer rate of liquid slag at the particle-slag interface. If J_r > J_i remains unchanged, when the concentration at the interface C_i is equal to the saturation concentration C_sat, the dissolution mechanism changes from interface reaction controlled to mass transfer controlled within the slag. In particular, the remaining conditions remain unchanged, the mass transfer thickness of the interfacial diffusion layer is fully developed, and the dissolution mechanism changes from interfacial reaction controlled to diffusion boundary layer controlled (Eq. (9)). In addition, when the mass transfer thickness of the particle-slag interfacial diffusion layer increases continuously and J_r > J_i and C_i = C_sat are maintained, the dissolution mechanism changes from interfacial reaction controlled to diffusion controlled under the invariant interfacial concentration approximation (Eq. (12)).

When the dissolution rate is much faster than the mass transfer in the slag (J_r >> J_i), it takes a very short time for SiO₂ to reach the saturation concentration (t_i → 0), which leads to an extremely steep concentration gradient of SiO₂ at the particle-slag interface (J_i → +∞), and the total dissolution process can be regarded as the Eq. (12). Therefore, as shown in Fig. 7, in the early dissolution stage of the particle, the normalized dissolution curve is located between the diffusion control model and the diffusion boundary layer model. When using the Eq. (12) for analysis, special attention should be paid, and appropriate corrections made, to its tendency to overestimate the dissolution rate of particles. In addition, the normalized dissolution curve of the experiment at 1773 K fits the reaction model well at the initial stage of dissolution, which may correspond to the increase in C_i from C₀ to C_sat. Therefore, the initial dissolution of SiO₂ may be controlled by an interfacial reaction. With an increase in the experimental temperature, the time t_i for the interface concentration C_i to increase from C₀ to C_sat decreases gradually as temperature accelerates the reaction process. The results show that at the initial stage of dissolution, the degree of fit of the experimental curve and reaction model is worse, with the interface reaction-controlled dissolution time being shorter. Subsequently, as the initial interface concentration-induced dissolution rate (the second term on the right of Eq. (12)) attenuates with time, the dissolution rate observed in the experiment decreases. At the end of dissolution, the geometric dissolution rate (the first term on the right-hand side of Eq. (12)) increases with decreasing particle size, resulting in the experimental dissolution curve approaching both the diffusion boundary layer control model and the diffusion control model of invariant interfacial concentration approximation.

Fig. 7.

Normalized dissolution curves for SiO₂ particle (a) T.Fe content (1923 K); (b) M_k (1923 K). (Online version in color.)

Figure 7 shows the normalized dissolution pattern of SiO₂ particles in liquid slag at different T.Fe contents and M_k. Similar to the experimental temperature variation, the experimental data showed that the dissolution mechanism of the particle was controlled by diffusion. According to the Eq. (12), when r₀, t_f, and k are known, the effective binary diffusion coefficient of SiO₂ particles can be calculated. The calculated effective binary diffusion coefficients of SiO₂ particle with different conditions is 3.34–5.22×10⁻¹¹ m²/s (as shown in Table 2). These values are the same order of magnitude as those obtained by Feichtinger¹⁶⁾ (3.79–8.49×10⁻¹¹ m²/s) and Samaddar²⁷⁾ (4.5×10⁻¹¹ m²/s).

4. Conclusions

In this study, the dissolution behavior of a modifying agent (SiO₂ particle) in slag during the steel slag fibrosis process was studied using a combination of HT-CSLM and a synthetic physical property tester. The influence of temperature, T.Fe content, and M_k on the dissolution rate of SiO₂ particles were analyzed. The following conclusions were drawn:

(1) Changes in molten steel slag electrical conductivity can be used to characterize the homogenization process of modifying agent in the slag. This provides a new characterization method and theoretical basis for the industrial application of mineral fibers prepared by modification of molten steel slag.

(2) A more complex diffusion control model was determined for the actual concentration boundary layer at the particle-slag interface with the dissolution of SiO₂ particles in molten steel slag controlled by solute diffusion.

(3) By increasing the reaction temperature, SiO₂ particle dissolution rate in the slag can be increased significantly. The SiO₂ dissolution rate was the fastest when the T.Fe content was 14%, and the acidity coefficient was 1.5.

Acknowledgements

The authors would like to express their appreciation to the National Natural Science Foundation of China (No. 51471002); University Natural Science Research Project of Anhui Province (KJ2020ZD25). In addition, the authors would like to thank Editage (www.editage.cn), for editing the English text of a draft of this manuscript.

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