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Foams and Foaming
CHAPTER 2.4
Foams and Foaming Kimihisa Ito Department of Applied Mathematics, Waseda University, Tokyo, Japan
2.4.1. FOAMING IN METALLURGICAL PROCESSES Foams are very complex systems consisting of dispersed gas bubbles separated by draining films. In metallurgical processes, slag foaming involves the expansion of slag layer by injected gas or by gas generated by chemical reactions. The precise control of this dynamic phenomenon is crucial for the success of some metallurgical processes.
2.4.1.1. Study of Slag Foaming Observation of slag foaming has been carried out by two different techniques. In the pneumatic method, bubbles are injected into a molten slag through one or more orifices. In the chemical reaction method, gas formation reactions, such as the reduction of iron oxide in slag by carbonaceous materials, are used to supply the bubbles to obtain the foaming slag. The pneumatic method offers the advantage of facilitating the control of the supply rate and mean diameters of the bubbles by varying the experimental conditions like the gas flow rate and orifice diameter. Hence, this method has been widely used for the study of slag foaming. However, the range over which the bubble sizes can be varied is rather limited, especially for small bubbles less than 10 mm in diameter. Figure 2.4.1 shows a typical experimental arrangement used for the study of slag foaming using the pneumatic method [1]. An inert gas is introduced through an orifice into a molten slag placed in a crucible. The surface position of the slag is detected by an electric probe. The foam height is usually defined as the increment in the slag surface level from the original (i.e., when gas flow rate is zero) to that formed after foaming, which is measured at a steady state while the gas is bubbling. The foam life is defined as the time for the foam height decay to some fractions of its initial value after the gas is turned off at the steady state. The bubble formation frequency is determined by a pressure transducer connected to the bubbling nozzle to calculate the mean bubble size from the gas flow rate. Cooper and Kitchener [2] studied the foaming of CaO–SiO2 slag at temperatures ranging from 1748 to 1998 K. They measured the life of a specific volume of foam and found that the foam life increased when the temperature and basicity decreased. It was also observed that the addition of a small amount of P2O5 increased the foam Treatise on Process Metallurgy, Volume 2 http://dx.doi.org/10.1016/B978-0-08-096984-8.00003-3
© 2014 Elsevier Ltd. All rights reserved.
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Kimihisa Ito
Detector
Pressure sensor
Drying column
Electric probe
Recorder
Gas
Foamed slag
Flow meter
Nozzle
Figure 2.4.1 Schematic representation of the typical experimental setup used for generating slag foams by pneumatic method [1].
60
CaO/SiO2=0.64
Foam life (s)
A:Uniform liquid B:Two-liquid regions
40
20 A
0
B 0.4
0.8
1.2
1.6
2.0
Cr2O3 (mol%)
Figure 2.4.2 Variation in the foam life in CaO–SiO2 slag after the addition of Cr2O3 [3].
life. Swisher and McCabe [3] studied the effect of Cr2O3 on the foaming of slags in the temperature range 1853–1913 K by using the technique employed by Cooper and Kitchener. Their studies indicated that Cr2O3 increased the foam life only within the regions of slag compositions that were completely in a single liquid state, but the foam life was decreased in the two-liquid region, as shown in Figure 2.4.2. Hara et al. [4] measured the foam life and foam height in CaO–FeO, SiO2–FeO, and CaO–SiO2–FeO slag systems at 1523 and 1573 K. The foam life was defined in an identical manner as mentioned in the previous studies. Their studies showed that the foam life increased with increasing foam height and decreasing surface tension of the slag.
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Large bubble
Slag
Metal
Time Figure 2.4.3 Slag foaming caused by slag–metal reactions as observed by X-ray fluoroscopic method [6].
The chemical reaction method, on the other hand, is favorable to investigate the dynamic phenomena that occur during the actual metallurgical slag foaming process. Ogawa and Tokumitsu [5,6] observed the slag foaming caused by slag–metal reactions in a graphite crucible with the aid of X-ray fluoroscopic apparatus to clarify the effect of the bubble sizes on the foam height and distribution of bubbles in the slag. X-Ray images of slag foaming caused by the slag–metal reaction are shown in Figure 2.4.3. The foam layer was observed to develop when the diameter of the CO bubbles, evolved at the slag–metal interface, became lesser than around 2 mm. The foam height increased with a decrease in the bubble size for a particular gas evolution rate. The size of the bubbles decreased with an increase in the iron oxide and sulfur contents in the slag. Yokoyama et al. [7] studied slag foaming in CaO–SiO2–Al2O3–MgO systems formed during the reduction of chromite ore by Fe–Csat melts. They assumed the bubble life, the average residence time of CO gas, to be equal to the foam life and calculated it from the CO gas generation rate. The foam life was found to decrease with an increase in the MgO content, and by increasing the ratio of CaO to SiO2 in the slag, the foam life was also strongly affected by the slag viscosity. Kapilashrami et al. [8] analyzed the phenomenon of slag foaming under dynamic conditions on the basis of the results from X-ray image analysis. The mismatch between the gas generation rate and gas escape rate was found to significantly affect the foam height, which was attributed to the rate of the chemical reaction. Khanna et al. [9] have developed novel video-processing software for the sessile drop technique for the rapid and quantitative estimation of slag foaming, which could be used for determining the extent of formation and stability of the foam as a function of time.
2.4.1.2. Foam Stability The stability of the foam is strongly governed by the resistance forces operating against film thinning. These resistance forces are caused by the surface viscosity of the liquid. The underlying concept is that the viscosity of the inner layer is equal to that of the bulk, but the viscosity of the exterior layers on both sides is much higher than that of the bulk [10]. The surface viscosities of various aqueous solutions and several slag systems have
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been measured [11]. According to the results of experiments conducted on several binary oxide melts carried out by Hara et al., the foaminess of the slags strongly depended on the surface viscosities [12]. In addition, the surface elasticity is also an important contributor to the resistance forces operating against film thinning. Let us assume that the bulk liquid containing the surface active species is initially in equilibrium with the slag surface, and a portion of the surface is locally extended by an external force. In such a system, according to Gibbs [13], the elasticity of the surface E (N m1) is expressed by Equation (2.4.1): E¼
ads ds ¼ da dlna
ð2:4:1Þ
In the above equation, a denotes the surface area (m2) and s (N m1) is the surface tension of the slag. As the diffusion of surface active species from the bulk to the surface requires a definite amount of relaxation time, the surface concentrations of the surface active species in the extended portion will be lower than the equilibrium concentration. Therefore, the surface tension of the extended portion becomes larger than that of the surrounding surface that is in equilibrium with the bulk. This difference in the surface tensions tends to push the adjacent surrounding surface toward the extended region. When such a surface flow is generated, an accompanying bulk flow is produced by the viscous drag on the underlying bulk liquid. This viscoelastic phenomenon, the Marangoni effect, is illustrated in Figure 2.4.4, which is thought to be the major mechanism of slag foam stabilization [1,3,4,14].
2.4.1.3. Foam Drainage Usually, three foam films meet along an edge termed as the “Plateau border,” through which drainage of the liquid from the film occurs due to gravitational force. Although, in sB < sA B
B A Film A
B
B Extension force Marangoni flow A: Locally extended surface B: Unextended surface
Figure 2.4.4 Stabilization of foam by Marangoni effect [10].
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Foams and Foaming
principle, foam drainage and foam collapse are independent, foam drainage does make the films thinner. As the critical film thickness for rupture of slag foams is thought to be much higher than that of aqueous foams, it is reasonable to assume that the collapse of foams can be expressed in terms of the drainage of liquid from the foam. Assuming first-order kinetics for the drainage, the rate of drainage is given by Equation (2.4.2): dv ¼k V0v dt
ð2:4:2Þ
where k (s1) represents the rate constant of foam drainage, V 0 (m3) is the initial volume of liquid in the foam, and v (m3) is the drained liquid volume. By integrating Equation (2.4.2) from t ¼ 0 to t, Equation (2.4.3) is obtained as follows: 0 V v kt ¼ ln ð2:4:3Þ V0 When the container is cylindrical and the void fraction a (), which is the volumetric fraction of gas in the foamed layer, is assumed to be a constant, Equation (2.4.3) can be written as given below: h ð2:4:4Þ kt ¼ ln 0 h In Equation (2.4.4), h (m) is the foam height after a duration of t (s) and h0 (m) is the initial foam height. The average foam life, t (s), can be shown to be equal to 1/k. According to Equation (2.4.4), if the decay of foam height is measured and - ln(h/h0) is plotted against time, the gradient represents the average foam life, which is one of the physical parameters of foaming. On the other hand, the foam life introduced in 2.4.1.1 according to the early studies is only an empirical index and cannot be used for a qualitative analysis. Figure 2.4.5 shows the variation of logarithmic relative foam height with time for CaO–SiO2–FeO slag at 1573K. In this case, the slag foam was prepared by the 0 FeO=30% 1573 K
-ln(h/h0)
0.5
CaO/SiO2=0.43 1.0
2.0
0.67
1.0
1.5
0
2
4
6
t (s)
Figure 2.4.5 Variation of foam height with time [1].
8
10
12
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Kimihisa Ito
pneumatic method, and the bubble diameters ranged from 10 to 15 mm [1]. All the data points showed a good linear relationship, and the foam life increased with decreasing basicity index, i.e., the ratio CaO/SiO2. Mukai et al. [15] directly observed the foaming of CaO–SiO2–Al2O3–FeO slag in reaction with Fe-4.5 wt% C alloy at 1773 K using a X-ray radiographic technique. They measured the decay of foam with time after the formation of CO bubbles ceased and confirmed the validity of Equation (2.4.4) for slag foaming caused by chemical reactions.
2.4.1.4. Physical Model of Slag Foaming Ogawa et al. [16] developed a physical model to describe slag foaming using the results of cold and hot model experiments. The bubble size at the slag–metal interface, the void fraction of the foam, and the film life of a bubble at the top surface of the slag were calculated. These studies confirmed that the bubble size at the slag–metal interface is essentially determined by the static balance between the buoyancy force and the adhesive force at the slag–metal interface. Ito and Fruehan [1] treated slag foaming as a dynamic phenomenon and a special case of one-dimensional two-phase flow, and they measured the foaming index, S (s) [10,17], to make quantitative predictions about foaming in practical operations. A more detailed explanation about the foaming index will be furnished in Section 2.4.2. Ghag et al. [18] proposed a general model to describe foaming, which relates the structure of the foams stabilized by viscoelastic forces to the bubble rupturing processes. In this model, the effective elasticity resulting from the dynamic adsorption of surface active species was considered. Hong et al. [19] investigated the behavior of slag foaming in CaO–Li2O–SiO2–Al2O3 slag systems formed during iron oxide reduction by graphite at 1573 K. To fit their experimental results, they developed a simple model, termed as “drift-flux analysis,” based on the fluid mechanics of a one-dimensional two-phase flow. Gou et al. [20] developed a onedimensional multiphase fluid-dynamics-based model to determine the relationship between superficial gas velocity and void fraction in liquids when gases are injected at high rates. This model can be used to calculate slag heights in bath smelting vessels, as shown Figure 2.4.6. Although nonfoaming aqueous systems and expanded slag show similar tendencies, the foaming regime is different in these systems. Further, Gou et al. pointed out that the behavior of slag foam at high rates of gas injection is markedly different from the foams observed at low flow rates. The advances in the construction of physical models to describe slag foaming in metallurgical processes have been reviewed by Zhu et al. [21].
2.4.2. FOAMING INDEX The dynamic method for measuring the foaminess of aqueous solutions involves the supply of gas bubbles having well-defined diameters at a constant rate. The foaming index S (s) is used as the unit of foaminess [10,17] and is defined by Equation (2.4.5):
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Foams and Foaming
1
Void fraction a (−)
Slag foams
Expanded slags and other liquids
0.1 Nonfoaming aqueous systems
0.01
0.1
1
10
Superficial gas velocity (m s−1)
Figure 2.4.6 Relationship between superficial gas velocity and void fraction in foaming and nonfoaming systems [20].
S¼
Vf Q
ð2:4:5Þ
In the above equation, V f (m3) is the volume of the foam layer and Q is the rate of gas flow (m3 s1). The foaming index of molten slags is defined by modifying the definition of foam index used for aqueous foams [10], which will be explained in detail in the subsequent sections.
2.4.2.1. Theory Let us suppose that gas bubbles are continuously generated in the molten slag bath held in a cylindrical container of cross-sectional area A (m2), the foamed slag is in a steady state, and the foam formation and collapse are at equilibrium. The foam height h (m) and foam layer thickness L (m) are defined as shown in Figure 2.4.7. The superficial gas velocity us (m s1) is defined by Equation (2.4.6): us ¼
Q A
ð2:4:6Þ
Ito and Fruehan [1] investigated a system in which gas bubbles with a definite diameter (10–15 mm) were continuously injected at a constant rate into a molten slag bath. Their experimental observations revealed that the foam height increased linearly with increasing superficial gas velocity, and the slope of this linear relation became constant after the flow rate reached a particular value, as shown in Figure 2.4.8. The slope of the line was found to be independent of the crucible diameter, provided the crucible
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Kimihisa Ito
h
Slag
Foam
L
Steady state
Qg=0
Figure 2.4.7 Illustration of foaming that defines foam height and foam layer thickness L (m).
1573 K CaO/SiO2=0.67
Foam height (m)
0.1
FeO=30%
Dcruicible(mm)
28 32 38 50
0.05 S 1
0
0.01
0.02
0.03
Superficial gas velocity (m s-1)
Figure 2.4.8 Relationship between foam height h (m) and superficial gas velocity us (m s1) for various crucible sizes [1].
was large enough to eliminate the wall effects. Consequently, the foaming index S, as defined by Equation (2.4.7), denotes the characteristic foaminess of the slag: S¼
Dh Dus
ð2:4:7Þ
The superficial gas velocity is also correlated to the void fraction and to the actual gas velocity u (m s1) by Equation (2.4.8): us ¼ au
ð2:4:8Þ
The foam height is expressed as a function of the void fraction and foam layer thickness by Equation (2.4.9), if the void fraction is assumed to be independent of the foam height: h ¼ aL
ð2:4:9Þ
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Foams and Foaming
Consequently, S can be expressed in terms of the foam layer thickness and the actual gas velocity as S¼
DL Du
ð2:4:10Þ
From Equation (2.4.10), it is clear that S signifies the average travelling time of the gas through the foamed layer. If the foam formation rate is proportional to the rate of gas flow and the collapse rate of the foam is proportional to its height, the rate equation describing the change in foam height can be represented by Equation (2.4.11): dh ¼ K1 Q K2 h dt
ð2:4:11Þ
where K1 and K2 in the above equation are the formation and collapse rate constants of the foam, respectively. When the system is in steady state, dh ¼0 dt
ð2:4:12Þ
K1 Q ¼ K2 h
ð2:4:13Þ
Therefore,
However, if the gas flow is halted (i.e., Q ¼ 0) when the system is in steady state, Equation (2.4.11) reduces to Equation (2.4.14): dh ¼ K2 h dt
ð2:4:14Þ
Integrating Equation (2.4.14) from t ¼ 0 to t ¼ t and from h ¼ h0 to h ¼ h yields the variation of foam height as a function of time, as shown in Equation (2.4.15): h K2 t ¼ ln 0 ð2:4:15Þ h From Equations (2.4.4) and (2.4.15), it is clear that the collapse rate constant K2 and the drainage rate constant k, are equivalent and are equal to 1/t. In a system where the void fraction can be assumed to be constant, the foaming index can be related to the foam life t. The rate equation that describes foam formation is written as dh dL a V f Q ¼ ¼a ¼ dt dt A dt A
ð2:4:16Þ
From Equations (2.4.11), (2.4.13), and (2.4.16), Equation (2.4.17) is obtained:
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Kimihisa Ito
15 1573 K, FeO=30% CaO–SiO2–FeO CaO–SiO2–FeO–P2O5
S (s)
10
5
0 0
5
10
15
t (s)
Figure 2.4.9 Relationship between the foam life t and foaming index S for CaO–SiO2–FeO slags [1].
t h ¼ A Q
ð2:4:17Þ
From Equations (2.4.6), (2.4.7), and (2.4.17), the foaming index can be related to the average foam life by Equation (2.4.18): t¼
Dh Dh ¼ DðQ=AÞ Dus
ð2:4:18Þ
Therefore, for foams with a uniform void fraction profile, the foaming index S is equal to the average foam life t. Figure 2.4.9 shows a comparison of the foaming index with foam life for CaO–SiO2–FeO slags at 1573 K, and experiments confirmed that the two values are in good agreement with each other [1].
2.4.2.2. Experimental Measurements Experimental measurements of the foaming index have been reported for iron and steelmaking slags under various conditions [1,22–28]. The effect of the concentration of FeO on the foaming index of CaO–SiO2–FeO–MgO slags is shown in Figure 2.4.10 [22–24]. The foaming index decreased when the FeO content increased to up to about 20%. When the FeO concentration was increased further from 20% to 32%, the foaming index nearly remained constant. This is explained on the basis of the viscosity becoming almost constant when the FeO concentration increased above 25%. Figure 2.4.11 shows the effect of slag basicity on the foaming index of CaO–SiO2– FeO–MgO–Al2O3 slags [1,24]. The foaming index decreased with increasing basicity index [(CaO þ MgO)/(SiO2 þ Al2O3)] up to 1.4, at which point the slag was expected to be in the liquidus composition. However, the foaming index increased at higher
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Foams and Foaming
5 CaO–SiO2–FeO–MgOsat [24] (1713 K, CaO/SiO2=0.93–1.1)
4
CaO–SiO2–FeO–Al2O3 [22] (1773 K, CaO/SiO2=1.0) CaO–SiO2–FeO–Al2O3 [22] (1773 K, CaO/SiO2=1.25)
S (s)
3
CaO–SiO2–15Al2O3–10MgO–FeO [22] (1773 K, CaO/SiO2=1.5)
2
1
0
10
20 30 FeO in slag (%)
40
Figure 2.4.10 Variation of foaming index S of the CaO–SiO2–FeO–MgOsat slags with the FeO content in the slag [24]. 10
CaO–SiO2–(18–21%)FeO–MgOsat, 1773 K [24] CaO–SiO2–30FeO–(3–5%)Al2O3, 1573 K [1]
S (s)
8
CaO–SiO2–30FeO–(3–5%)Al2O3, 1673 K [1]
6 4 2
0
0.4
0.8
1.2
1.6
2.0
Basicity index (CaO+MgO)/(SiO2+Al2O3) (-)
Figure 2.4.11 Variation of foaming index S of the CaO–SiO2–FeO–MgOsat slags with the basicity index [(CaO þ MgO)/(SiO2 þ Al2O3)], at 1713 K [24].
basicities, due to the precipitation of solid phases like 2CaOSiO2 or (Fe,Mg)O, which stabilized the foam. The temperature dependence of the foaming index for the CaO–SiO2–FeO–MgO slag system is shown in Figure 2.4.12 [24]. The logarithm of foaming index decreased with increasing temperature. From the data shown in Figure 2.4.9, the dependence of the foaming index on temperature T can be expressed by Equation (2.4.19): log S ¼
6610 3:90 T
ð2:4:19Þ
The apparent activation energy for the foam decay was estimated to be 126.5 kJ mol1 for CaO–SiO2–FeO–MgO slag, and as 160 kJ mol1 for 35%CaO–
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Kimihisa Ito
0.8 0.6
30%CaO–30%SiO2–30%FeO–10%MgO [24] 35%CaO–35%SiO2–30%FeO [1]
Log S (s)
0.4 0.2 0 -0.2 -0.4 -0.6 -0.8
5.6
6.0
6.4
104/T (K-1)
Figure 2.4.12 Dependence of foaming index S on temperature T for CaO–SiO2–FeO–MgO slags [24].
60 50
Slag/metal reaction < 1 mm Nozzle 2 mm Nozzle
S (s)
40 30 20 10 0
400
800
1/db
1200
1600
(m-1)
Figure 2.4.13 Variation of foaming index S as a function of the reciprocal of average bubble diameter [23].
35%SiO2–30%FeO slag [1]. The value reported for 48%CaO–32%SiO2–10% FeO–10%Al2O3 slag at temperatures ranging from 1723 to 1873 K was 139.6 kJ mol1. It can be noted that there was no significant difference in these activation energies. Zhang and Fruehan [23] measured the effect of the bubble size on the foaming index as shown in Figure 2.4.13, in which the foaming index is plotted against the reciprocal of average bubble diameter. In order to vary the sizes of the bubbles widely, foams were generated either by injecting argon gas or by inducing slag–metal reactions. The foaming index was found to be inversely proportional to the bubble diameter for a particular slag system, and therefore, smaller bubbles stabilized slag foaming. The effects of the type of the gas and its pressure on slag foaming were also studied by Zhang and Fruehan [26]. The foaming index was found to depend on the physical
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Foams and Foaming
4 3 mm Spheres 10 mm Disks
S (s)
3
10 mm Spheres Coal char 6 mm Spheres 8 mm Spheres
2
1
0
0.1 0.2 0.3 0.4 0.5 Surface coverage, Aparticle/Acrucible (-)
0.6
Figure 2.4.14 Variation of foaming indexes of slags exhibiting initial foaming indexes of 1.8 and 3.6 s, as a function of the surface coverage by coke [28].
properties of the gas used for foaming. However, the foaming index was not affected by gas pressures ranging from 1 to 2 atm. Zhang and Fruehan also studied the effect of the presence of coke and coal char particles on the foaming index [28]. They used two different slags, 30%CaO–60%SiO2–10% CaF2 and 25.5%CaO–51%SiO2–8.5%CaF2–150%Al2O3, with foaming indexes of 1.8 and 3.6 s, respectively at 1773 K, for their experiments. The foaming indexes of these slags were experimentally measured in the presence of coke spheres or coke disks. The foaming index plotted as a function of the coverage ratio of the slag surface by the carbonaceous materials is shown in Figure 2.4.14. Foaming was drastically suppressed when the coverage by carbonaceous materials increased, in both the slag systems, although the initial foaming indexes of the systems differed from each other by a factor of two.
2.4.2.3. Dimensional Analysis and Empirical Equations It is expected that the foaming index can be related to the physical properties of the slag. Hence, dimensional analysis was applied to derive a relationship which describes the foaming index as a function of slag properties [22,23,29]. It can be assumed that foaming index, as described in Equation (2.4.20), is based on the information obtained from pneumatic experiments, in which the injected bubble diameters were varied within a specific range: S ¼ f ðr,m,s,gÞ
ð2:4:20Þ
In the above equation, r is the density (kg m3) of the liquid slag, m is the slag viscosity (N s m2), s is the slag surface tension (N m1), and g is gravitational acceleration (m s2). With five variables and three fundamental dimensions, two dimensionless
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Kimihisa Ito
numbers, NS and Mo (expressed in Equations 2.4.21 and 2.4.22), were obtained by Jiang and Fruehan [22]: Sgm s gm4 Mo ¼ 3 rs
NS ¼
ð2:4:21Þ ð2:4:22Þ
Mo is the Morton number, which is generally used to describe the motion of bubbles in a liquid. The relationship between the two dimensionless numbers was calculated from the experimentally measured foaming indexes and the physical properties of the slag, and consequently, Equation (2.4.23) was derived: log Mo ¼ 2log NS þ 5:11
ð2:4:23Þ
The final equation derived that related the foaming index with slag viscosity, density, and surface tension is shown in Equation (2.4.24). The units used in this equation are SI units as used in Equation (2.4.20): m S ¼ 115 pffiffiffiffiffiffi rs
ð2:4:24Þ
Kim et al. [27] proposed similar relationships (such as those shown in Equations 2.4.25 and 2.4.26), based on the foaming index measurements they carried out on CaO–SiO2– FeO–MgOsat–X systems (X was Al2O3, MnO, P2O5, and CaF2): m S ¼ 214 pffiffiffiffiffiffi ðfor CaO based slagsÞ rs m S ¼ 999 pffiffiffiffiffiffi ðfor MgO saturated slagsÞ rs
ð2:4:25Þ ð2:4:26Þ
Skupien and Gaskell [30] repeated Jiang and Fruehan’s [22] dimensional analysis and correlated NS and Mo by using experimentally obtained surface tensions and viscosities to derive Equation (2.4.27): S¼
100m0:54 r0:39 s0:15
ð2:4:27Þ
Since equations from (2.4.24) to (2.4.27) are obtained from the data of pneumatic foaming experiments with similar geometries, in which the bubble diameters in the foam are estimated to be around 10 mm. It should be noted that above four equations are applicable only for the slag foam containing bubbles with diameters about 10 mm. Based on the experimental data shown in Figure 2.4.13, Zhang and Fruehan [23] reconsidered the dimensional analysis to include the average bubble diameter db(m) as
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Foams and Foaming
a new independent variable. Now, with six independent variables, another dimensionless number Ar was obtained, in addition to NS and Mo. Ar, the Archimedes number, signifies the ratio of the buoyancy force to the viscous force and is related to the slag properties by Equation (2.4.28): Ar ¼
gdb3 r2 m2
ð2:4:28Þ
Subsequently, Equation (2.4.29) was obtained by regression analysis: NS ¼ 900Mo0:39 Ar0:28
ð2:4:29Þ
The final mathematical description of the foaming index is represented in Equation (2.4.30): S ¼ 115
m1:2 s0:2 rdb 0:9
ð2:4:30Þ
The viscosity used in these correlations should be the bulk viscosity including the effect of second phase particles. If the particles are small compared to the bubble size, they will increase the bulk viscosity, decreasing the drainage rate, and hence increase the foam index. This was discussed in detail by Ito and Fruehan [1] and Zhu et al. [21]. Ghag et al. [18] proposed a different type of relationship based on a foaming model in which the structure of the foam is stabilized by viscoelastic forces. The final relationship that included the effective elasticity Eeff (N m1), resulting from the dynamic adsorption of surface active species, was derived from the data of cold model studies using water– glycerol–SDBS solutions at 293 K; however, there is no direct evidence for the applicability of their model to the foaming of metallurgical slags.
2.4.2.4. Mass-Limited Foaming When the foam index and the gas flow rate are high enough to foam all of the available slag, the foam height will no longer increase with the gas flow rate but will be relatively constant with increasing flow rate. This is discussed by Zhu et al. [21] in more detail. Depending on a number of slag properties and the gas flow rate, the gas fraction cannot exceed 80–90% of the foam. This means the foam volume cannot exceed 4–10 times the static slag volume.
2.4.3. SLAG FOAMING IN INDUSTRIAL PROCESSES If the void fraction a is kept constant in the foamed slag and the flow regime is maintained unchanged with the gas velocity, the foam height h in practical metallurgical
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Kimihisa Ito
processes can be estimated using the foaming index of the slag from Equation (2.4.31), which can be derived by integrating Equation (2.4.7): Dh S¼ Dus h ¼ S us us þ h
ð2:4:7Þ ð2:4:31Þ
1 where u* s (m s ) is the superficial gas velocity and h* (m) is the foam height when the foaming begins. Both u* s and h* are usually expected to be negligibly small in real processes, and consequently, the foam height in the furnace, Hf (m), is given by Equation (2.4.32):
Hf ¼ Sus
ð2:4:32Þ
If the cross-sectional area of the furnace A (m2) is known, Hf (m) can be estimated from the total gas flow rate in the furnace and the foaming index of the slag, by using Equations (2.4.6) and (2.4.32): us ¼
Q A
ð2:4:6Þ
2.4.3.1. Electric Arc Furnace The control of slag foaming is important in an electric arc furnace (EAF) operation, as the slag foam protects the refractory from the high intensity arc, allowing for high power input and productivity. Carbon is injected into the slag to make slag foam by the generation of CO bubbles, which are formed by the reaction of the carbon with FeO in the slag. The CO bubbles used for slag foaming can also be produced by the decarburization of the metal. The foam height can be estimated by substituting the values of the generation rate of CO and foaming index in Equations (2.4.6) and (2.4.32). Matsuura and Fruehan [31] examined slag foaming in a steelmaking EAF aimed at achieving high productivities with a mathematical model of the EAF, to compute the CO generation rate and slag chemistry for evaluating Equation (2.4.32). They calculated the effects of the amounts of pig iron, carbon, oxygen, and slag on the foam height and concluded that the foam was usually essentially limited by the amount of slag in the furnace. When the amount of total carbon (pig iron, coke, and coal) and oxygen was reduced, the foam height, limited by the CO generation rate, decreased. Oosthuizen et al. [32] estimated the slag foam depth using a dynamic EAF model describing the time evolution of the EAF and the off-gas system variables. Industrial data on foaming of basic slags in an EAF were used to estimate the relationship between the foam index and FeO content in the slag.
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As discussed in Section 4.2.4 and by Zhu et al. [21] and Matsuura and Fruehan [31], when the gas rate is high, the foam is simply limited by the volume of slag available. For the EAF, it was assumed the volume fraction of gas in the foam cannot exceed 80% so the foam volume cannot be greater than four times the slag volume. This restriction applies to much of the EAF process when high pig iron and oxygen amounts are used. At lower CO rates, the foam index can be used to calculate the foam volume.
2.4.3.2. Bath Smelting Furnace During bath smelting (a smelting process that reduces thick layered slags), it is important to stably maintain the slag height and avoid any abnormal slag foaming. Therefore, the prediction and the control of slag foaming is one of the key requirements of this process. Jiang and Fruehan [22] calculated the foam height in a bath smelting furnace using Equation (2.4.32) and compared their results with real pilot trials [33]. The results obtained from the calculations are summarized in Figure 2.4.15. In Figure 2.4.15, PRD and PCR denote the prereduction degree of the iron ore and the postcombustion ratio, respectively. The calculated foam height increased with increasing T. Fe content in the slag. The predicted foam height was in good agreement with the observed values, when PRD ¼ 0% and PCR ¼ 40%, which were close to the real conditions. The dotted curve shows the calculated foam heights when excess coke was present. These values were obtained by using the observation that the presence of carbonaceous materials reduced the foaming index by a factor of 2 (Figure 2.4.14). The calculated values also agreed well with the observations obtained from real slag foaming trials. Ogawa et al. [34] experimentally investigated the mechanism of controlling slag foaming by the use of carbonaceous materials using a 1-ton bath smelting furnace. 3.0 1: PRD = 0, PCR = 60 2: PRD = 0, PCR = 40
Foam height (m)
2.5
3: PRD = 30, PCR = 40
3 2
2.0
Slag foaming without coke
1
1.5 1.0 0.5
Real slag foaming with coke in slag
0
2
4 T. Fe in slag (%)
6
8
Figure 2.4.15 Comparison of the estimated and real foaming heights in a bath smelting process that uses a 5-ton converter [22].
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Kimihisa Ito
5
Slag foaming ratio (-)
Overflow
4
3
5.0 6.0
2
3.4 3.1
1 Ore feed rate = 2.3 (kg/min)
0
0.1 0.2 0.3 0.4 0.5 Mass ratio of coke/slag (-)
0.6
Figure 2.4.16 Effect of coke to slag mass ratio on the slag foaming ratio [34].
Figure 2.4.16 shows the relationship between the coke to slag mass ratio in the furnace and the slag foaming ratio which is defined by Equation (2.4.33), for various iron ore feed rates: slag foaming ratio ¼
Vs þVg Vg
ð2:4:33Þ
In the above equation, V s (m3) is the volume of slag and V g (m3) is the volume of gas in the foamed slag. The slag foaming ratio increased with increasing iron ore feed rate and decreasing amount of coke, which suggested that the presence of coke exerted a suppression effect on slag foaming. It was experimentally confirmed that the stable operation of bath smelting in a 100-ton scale furnace was possible, as far as sufficient carbonaceous material was present in the slag.
2.4.3.3. Basic Oxygen Furnace In hot metal pretreatment processes, slag foaming has been a key challenge both in desiliconization and dephosphorization processes. Kitamura and Okohira [35] investigated the slag foaming caused by the reaction between the FeO-containing slag and hot metal in the CaO–SiO2–Al2O3–P2O5–TiO2–MnO–MgO–CaF2 system. The maximum slag foam height was observed when the basicity index [CaO/SiO2] was around 1.2, which slightly increased with increasing temperature and CaF2 concentration. The achievement of maximum values can be attributed to the combination of decreasing foaming index and increasing CO generation rate that accompany the increase in slag basicity. In the high basicity region, the slag foaming height increased with the increase in temperature and CaF2 concentration.
215
Foams and Foaming
Foam height (m)
8
6
200-ton converter Dconverter = 6.0 m
Stage 1 (1633 K) CaO/SiO2 = 0.8 35%FeO, 2%MgO
4 Stage 2 (1693 K) CaO/SiO2 = 1.2 32%FeO, 4%MgO
2
0
Stage 3 (1753 K) CaO/SiO2 = 1.5 23%FeO, 6%MgO
0.002 Decarburization rate
0.004
0.006
([mass%C] s−1)
Figure 2.4.17 Variation of calculated foam heights during the first half of the blowing process in the BOF, as a function of the decarburization rate [24].
Jung and Fruehan [24] estimated the foam height of slags during the first half of the blowing process in the basic oxygen furnace (BOF). The superficial gas velocity of a 200-ton converter (6.0 m in diameter) was assumed to be dominated by the decarburization reaction of steel. The results of the calculations using Equation (2.4.32) are shown in Figure 2.4.17. The foam height linearly increased with increasing decarburization rate and decreased with the progress of the stages. Bramming et al. [36] developed a vessel vibration measurement technique that employed a triaxial accelerometer mounted on a trunnion. The transfer of kinetic energy from the foaming slag to the vessel resulted in vibration excitation at the vessel walls. Consequently, the frequency band with the best correlation to the foam level was determined by FFT analysis. The results showed a correlation between vessel vibrations and foam heights, which can be used for the control of dynamic foam levels and slopping.
2.4.3.4. Suppression of Foaming Zhang and Fruehan [28] found that coke and coal char have the same strong antifoam effect on the liquid slag. The foaming index of the slag was drastically decreased when the coverage of liquid slag surface by carbonaceous materials increased. In the case of slag foams generated by the reaction of FeO with coke, X-ray characterization revealed that small bubbles coalesced on the interface between the carbonaceous materials such as coke and the slag [34] because of the poor wettability between them. The large bubbles formed by the coalescence of the small bubbles can rise through the foaming slag layer at relatively high speeds, leading to lower foam heights.
REFERENCES [1] K. Ito, R.J. Fruehan, Metall. Trans. B 20B (1989) 509. [2] C.F. Cooper, J.A. Kitchener, JISI 230 (1959) 48.
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[3] J.H. Swisher, C.L. McCabe, TMS-AIME 230 (1964) 1669. [4] S. Hara, M. Ikuta, M. Kitamura, K. Ogino, Tetsu-to-Hagane 69 (1983) 1152. [5] Y. Ogawa, N. Tokumitsu, in: Proceedings of 6th International Iron and Steel Congress, ISIJ, Nagoya, 1990, p. 147. [6] Y. Ogawa, N. Tokumitsu, Tetsu-to-Hagane 87 (2001) 14. [7] S. Yokoyama, M. Takeda, K. Ito, M. Kawakami, Tetsu-to-Hagane 78 (1992) 223. [8] A. Kapilashrami, A.K. Lahiri, M. Gornerup, S. Seetharaman, Metall. Mater. Trans. B 37B (2006) 145. [9] R. Khanna, M. Rahman, R. Leow, V. Sahajwalla, Metall. Mater. Trans. B 38B (2007) 719. [10] J.J. Bikerman, Foams, Springer-Verlag, New York, NY, 1973. [11] S. Hara, M. Kitamura, K. Ogino, Tetsu-to-Hagane 75 (1994) 2174. [12] S. Hara, T. Yunoki, K. Ogino, Tetsu-to-Hagane 75 (1989) 2182. [13] J.W. Gibbs, The Scientific Papers of J. Willard Gibbs, Longmans, London, 1906. [14] P. Kozakevitch, J. Metals 21 (1969) 57. [15] K. Mukai, T. Nakamura, H. Terashima, Tetsu-to-Hagane 78 (1992) 1682. [16] Y. Ogawa, D. Huin, H. Gaye, N. Tokumitsu, ISIJ Int. 33 (1993) 224. [17] B.J. Akers, Foams, Academic Press, London, 1976, p. 1. [18] S.S. Ghag, P.C. Hayes, H.-G. Lee, ISIJ Int. 38 (1998) 1208. [19] L. Hong, M. Hirasawa, M. Sano, ISIJ Int. 38 (1998) 1339. [20] H. Gou, G.A. Irons, W.-K. Lu, Metall. Mater. Trans. B 27B (1996) 195. [21] T.X. Zhu, K.S. Coley, G.A. Irons, Metall. Mater. Trans. B 43B (2012) 751. [22] R. Jiang, R.J. Fruehan, Metall. Trans. B 22B (1991) 481. [23] Y. Zhang, R.J. Fruehan, Metall. Mater. Trans. B 26B (1995) 803. [24] S.-M. Jung, R.J. Fruehan, ISIJ Int. 40 (2000) 348. [25] B. Ozturk, R.J. Fruehan, Metall. Mater. Trans. B 26B (1995) 1086. [26] Y. Zhang, R.J. Fruehan, Metall. Mater. Trans. B 26B (1995) 1088. [27] H.S. Kim, D.J. Min, J.H. Park, ISIJ Int. 41 (2001) 317. [28] Y. Zhang, R.J. Fruehan, Metall. Mater. Trans. B 26B (1995) 813. [29] K. Ito, R.J. Fruehan, Metall. Trans. B 20B (1989) 515. [30] D. Skupien, D.R. Gaskell, Metall. Mater. Trans. B 31B (2000) 921. [31] H. Matsuura, R.J. Fruehan, ISIJ Int. 49 (2009) 1530. [32] D.J. Oosthuizen, J.H. Viljoen, I.K. Craig, P.C. Pistorius, ISIJ Int. 41 (2001) 339. [33] N. Tokumitsu, M. Matsuo, K. Hatayama, H. Ishikawa, Y. Yamamoto, Y. Hayashi, in: Process Technol. Conf. Proc., Toronto, ISS of AIME, vol. 7, 1988, p. 99. [34] Y. Ogawa, H. Katayama, H. Hirata, N. Tokumitsu, M. Yamauchi, ISIJ Int. 32 (1992) 87. [35] S. Kitamura, K. Okohira, ISIJ Int. 32 (1992) 741. [36] M. Bramming, S. Millman, A. Overbosch, A. Kapilashrami, D. Malmberg, B. Bjorkman, ISIJ Int. 51 (2011) 71. [37] D. Lotun, L. Pilon, ISIJ Int. 45 (2005) 835.
Foams and Foaming Kimihisa Ito Department of Applied Mathematics, Waseda University, Tokyo, Japan
2.4.1. FOAMING IN METALLURGICAL PROCESSES Foams are very complex systems consisting of dispersed gas bubbles separated by draining films. In metallurgical processes, slag foaming involves the expansion of slag layer by injected gas or by gas generated by chemical reactions. The precise control of this dynamic phenomenon is crucial for the success of some metallurgical processes.
2.4.1.1. Study of Slag Foaming Observation of slag foaming has been carried out by two different techniques. In the pneumatic method, bubbles are injected into a molten slag through one or more orifices. In the chemical reaction method, gas formation reactions, such as the reduction of iron oxide in slag by carbonaceous materials, are used to supply the bubbles to obtain the foaming slag. The pneumatic method offers the advantage of facilitating the control of the supply rate and mean diameters of the bubbles by varying the experimental conditions like the gas flow rate and orifice diameter. Hence, this method has been widely used for the study of slag foaming. However, the range over which the bubble sizes can be varied is rather limited, especially for small bubbles less than 10 mm in diameter. Figure 2.4.1 shows a typical experimental arrangement used for the study of slag foaming using the pneumatic method [1]. An inert gas is introduced through an orifice into a molten slag placed in a crucible. The surface position of the slag is detected by an electric probe. The foam height is usually defined as the increment in the slag surface level from the original (i.e., when gas flow rate is zero) to that formed after foaming, which is measured at a steady state while the gas is bubbling. The foam life is defined as the time for the foam height decay to some fractions of its initial value after the gas is turned off at the steady state. The bubble formation frequency is determined by a pressure transducer connected to the bubbling nozzle to calculate the mean bubble size from the gas flow rate. Cooper and Kitchener [2] studied the foaming of CaO–SiO2 slag at temperatures ranging from 1748 to 1998 K. They measured the life of a specific volume of foam and found that the foam life increased when the temperature and basicity decreased. It was also observed that the addition of a small amount of P2O5 increased the foam Treatise on Process Metallurgy, Volume 2 http://dx.doi.org/10.1016/B978-0-08-096984-8.00003-3
© 2014 Elsevier Ltd. All rights reserved.
197
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Kimihisa Ito
Detector
Pressure sensor
Drying column
Electric probe
Recorder
Gas
Foamed slag
Flow meter
Nozzle
Figure 2.4.1 Schematic representation of the typical experimental setup used for generating slag foams by pneumatic method [1].
60
CaO/SiO2=0.64
Foam life (s)
A:Uniform liquid B:Two-liquid regions
40
20 A
0
B 0.4
0.8
1.2
1.6
2.0
Cr2O3 (mol%)
Figure 2.4.2 Variation in the foam life in CaO–SiO2 slag after the addition of Cr2O3 [3].
life. Swisher and McCabe [3] studied the effect of Cr2O3 on the foaming of slags in the temperature range 1853–1913 K by using the technique employed by Cooper and Kitchener. Their studies indicated that Cr2O3 increased the foam life only within the regions of slag compositions that were completely in a single liquid state, but the foam life was decreased in the two-liquid region, as shown in Figure 2.4.2. Hara et al. [4] measured the foam life and foam height in CaO–FeO, SiO2–FeO, and CaO–SiO2–FeO slag systems at 1523 and 1573 K. The foam life was defined in an identical manner as mentioned in the previous studies. Their studies showed that the foam life increased with increasing foam height and decreasing surface tension of the slag.
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Foams and Foaming
Large bubble
Slag
Metal
Time Figure 2.4.3 Slag foaming caused by slag–metal reactions as observed by X-ray fluoroscopic method [6].
The chemical reaction method, on the other hand, is favorable to investigate the dynamic phenomena that occur during the actual metallurgical slag foaming process. Ogawa and Tokumitsu [5,6] observed the slag foaming caused by slag–metal reactions in a graphite crucible with the aid of X-ray fluoroscopic apparatus to clarify the effect of the bubble sizes on the foam height and distribution of bubbles in the slag. X-Ray images of slag foaming caused by the slag–metal reaction are shown in Figure 2.4.3. The foam layer was observed to develop when the diameter of the CO bubbles, evolved at the slag–metal interface, became lesser than around 2 mm. The foam height increased with a decrease in the bubble size for a particular gas evolution rate. The size of the bubbles decreased with an increase in the iron oxide and sulfur contents in the slag. Yokoyama et al. [7] studied slag foaming in CaO–SiO2–Al2O3–MgO systems formed during the reduction of chromite ore by Fe–Csat melts. They assumed the bubble life, the average residence time of CO gas, to be equal to the foam life and calculated it from the CO gas generation rate. The foam life was found to decrease with an increase in the MgO content, and by increasing the ratio of CaO to SiO2 in the slag, the foam life was also strongly affected by the slag viscosity. Kapilashrami et al. [8] analyzed the phenomenon of slag foaming under dynamic conditions on the basis of the results from X-ray image analysis. The mismatch between the gas generation rate and gas escape rate was found to significantly affect the foam height, which was attributed to the rate of the chemical reaction. Khanna et al. [9] have developed novel video-processing software for the sessile drop technique for the rapid and quantitative estimation of slag foaming, which could be used for determining the extent of formation and stability of the foam as a function of time.
2.4.1.2. Foam Stability The stability of the foam is strongly governed by the resistance forces operating against film thinning. These resistance forces are caused by the surface viscosity of the liquid. The underlying concept is that the viscosity of the inner layer is equal to that of the bulk, but the viscosity of the exterior layers on both sides is much higher than that of the bulk [10]. The surface viscosities of various aqueous solutions and several slag systems have
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Kimihisa Ito
been measured [11]. According to the results of experiments conducted on several binary oxide melts carried out by Hara et al., the foaminess of the slags strongly depended on the surface viscosities [12]. In addition, the surface elasticity is also an important contributor to the resistance forces operating against film thinning. Let us assume that the bulk liquid containing the surface active species is initially in equilibrium with the slag surface, and a portion of the surface is locally extended by an external force. In such a system, according to Gibbs [13], the elasticity of the surface E (N m1) is expressed by Equation (2.4.1): E¼
ads ds ¼ da dlna
ð2:4:1Þ
In the above equation, a denotes the surface area (m2) and s (N m1) is the surface tension of the slag. As the diffusion of surface active species from the bulk to the surface requires a definite amount of relaxation time, the surface concentrations of the surface active species in the extended portion will be lower than the equilibrium concentration. Therefore, the surface tension of the extended portion becomes larger than that of the surrounding surface that is in equilibrium with the bulk. This difference in the surface tensions tends to push the adjacent surrounding surface toward the extended region. When such a surface flow is generated, an accompanying bulk flow is produced by the viscous drag on the underlying bulk liquid. This viscoelastic phenomenon, the Marangoni effect, is illustrated in Figure 2.4.4, which is thought to be the major mechanism of slag foam stabilization [1,3,4,14].
2.4.1.3. Foam Drainage Usually, three foam films meet along an edge termed as the “Plateau border,” through which drainage of the liquid from the film occurs due to gravitational force. Although, in sB < sA B
B A Film A
B
B Extension force Marangoni flow A: Locally extended surface B: Unextended surface
Figure 2.4.4 Stabilization of foam by Marangoni effect [10].
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Foams and Foaming
principle, foam drainage and foam collapse are independent, foam drainage does make the films thinner. As the critical film thickness for rupture of slag foams is thought to be much higher than that of aqueous foams, it is reasonable to assume that the collapse of foams can be expressed in terms of the drainage of liquid from the foam. Assuming first-order kinetics for the drainage, the rate of drainage is given by Equation (2.4.2): dv ¼k V0v dt
ð2:4:2Þ
where k (s1) represents the rate constant of foam drainage, V 0 (m3) is the initial volume of liquid in the foam, and v (m3) is the drained liquid volume. By integrating Equation (2.4.2) from t ¼ 0 to t, Equation (2.4.3) is obtained as follows: 0 V v kt ¼ ln ð2:4:3Þ V0 When the container is cylindrical and the void fraction a (), which is the volumetric fraction of gas in the foamed layer, is assumed to be a constant, Equation (2.4.3) can be written as given below: h ð2:4:4Þ kt ¼ ln 0 h In Equation (2.4.4), h (m) is the foam height after a duration of t (s) and h0 (m) is the initial foam height. The average foam life, t (s), can be shown to be equal to 1/k. According to Equation (2.4.4), if the decay of foam height is measured and - ln(h/h0) is plotted against time, the gradient represents the average foam life, which is one of the physical parameters of foaming. On the other hand, the foam life introduced in 2.4.1.1 according to the early studies is only an empirical index and cannot be used for a qualitative analysis. Figure 2.4.5 shows the variation of logarithmic relative foam height with time for CaO–SiO2–FeO slag at 1573K. In this case, the slag foam was prepared by the 0 FeO=30% 1573 K
-ln(h/h0)
0.5
CaO/SiO2=0.43 1.0
2.0
0.67
1.0
1.5
0
2
4
6
t (s)
Figure 2.4.5 Variation of foam height with time [1].
8
10
12
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Kimihisa Ito
pneumatic method, and the bubble diameters ranged from 10 to 15 mm [1]. All the data points showed a good linear relationship, and the foam life increased with decreasing basicity index, i.e., the ratio CaO/SiO2. Mukai et al. [15] directly observed the foaming of CaO–SiO2–Al2O3–FeO slag in reaction with Fe-4.5 wt% C alloy at 1773 K using a X-ray radiographic technique. They measured the decay of foam with time after the formation of CO bubbles ceased and confirmed the validity of Equation (2.4.4) for slag foaming caused by chemical reactions.
2.4.1.4. Physical Model of Slag Foaming Ogawa et al. [16] developed a physical model to describe slag foaming using the results of cold and hot model experiments. The bubble size at the slag–metal interface, the void fraction of the foam, and the film life of a bubble at the top surface of the slag were calculated. These studies confirmed that the bubble size at the slag–metal interface is essentially determined by the static balance between the buoyancy force and the adhesive force at the slag–metal interface. Ito and Fruehan [1] treated slag foaming as a dynamic phenomenon and a special case of one-dimensional two-phase flow, and they measured the foaming index, S (s) [10,17], to make quantitative predictions about foaming in practical operations. A more detailed explanation about the foaming index will be furnished in Section 2.4.2. Ghag et al. [18] proposed a general model to describe foaming, which relates the structure of the foams stabilized by viscoelastic forces to the bubble rupturing processes. In this model, the effective elasticity resulting from the dynamic adsorption of surface active species was considered. Hong et al. [19] investigated the behavior of slag foaming in CaO–Li2O–SiO2–Al2O3 slag systems formed during iron oxide reduction by graphite at 1573 K. To fit their experimental results, they developed a simple model, termed as “drift-flux analysis,” based on the fluid mechanics of a one-dimensional two-phase flow. Gou et al. [20] developed a onedimensional multiphase fluid-dynamics-based model to determine the relationship between superficial gas velocity and void fraction in liquids when gases are injected at high rates. This model can be used to calculate slag heights in bath smelting vessels, as shown Figure 2.4.6. Although nonfoaming aqueous systems and expanded slag show similar tendencies, the foaming regime is different in these systems. Further, Gou et al. pointed out that the behavior of slag foam at high rates of gas injection is markedly different from the foams observed at low flow rates. The advances in the construction of physical models to describe slag foaming in metallurgical processes have been reviewed by Zhu et al. [21].
2.4.2. FOAMING INDEX The dynamic method for measuring the foaminess of aqueous solutions involves the supply of gas bubbles having well-defined diameters at a constant rate. The foaming index S (s) is used as the unit of foaminess [10,17] and is defined by Equation (2.4.5):
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Foams and Foaming
1
Void fraction a (−)
Slag foams
Expanded slags and other liquids
0.1 Nonfoaming aqueous systems
0.01
0.1
1
10
Superficial gas velocity (m s−1)
Figure 2.4.6 Relationship between superficial gas velocity and void fraction in foaming and nonfoaming systems [20].
S¼
Vf Q
ð2:4:5Þ
In the above equation, V f (m3) is the volume of the foam layer and Q is the rate of gas flow (m3 s1). The foaming index of molten slags is defined by modifying the definition of foam index used for aqueous foams [10], which will be explained in detail in the subsequent sections.
2.4.2.1. Theory Let us suppose that gas bubbles are continuously generated in the molten slag bath held in a cylindrical container of cross-sectional area A (m2), the foamed slag is in a steady state, and the foam formation and collapse are at equilibrium. The foam height h (m) and foam layer thickness L (m) are defined as shown in Figure 2.4.7. The superficial gas velocity us (m s1) is defined by Equation (2.4.6): us ¼
Q A
ð2:4:6Þ
Ito and Fruehan [1] investigated a system in which gas bubbles with a definite diameter (10–15 mm) were continuously injected at a constant rate into a molten slag bath. Their experimental observations revealed that the foam height increased linearly with increasing superficial gas velocity, and the slope of this linear relation became constant after the flow rate reached a particular value, as shown in Figure 2.4.8. The slope of the line was found to be independent of the crucible diameter, provided the crucible
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Kimihisa Ito
h
Slag
Foam
L
Steady state
Qg=0
Figure 2.4.7 Illustration of foaming that defines foam height and foam layer thickness L (m).
1573 K CaO/SiO2=0.67
Foam height (m)
0.1
FeO=30%
Dcruicible(mm)
28 32 38 50
0.05 S 1
0
0.01
0.02
0.03
Superficial gas velocity (m s-1)
Figure 2.4.8 Relationship between foam height h (m) and superficial gas velocity us (m s1) for various crucible sizes [1].
was large enough to eliminate the wall effects. Consequently, the foaming index S, as defined by Equation (2.4.7), denotes the characteristic foaminess of the slag: S¼
Dh Dus
ð2:4:7Þ
The superficial gas velocity is also correlated to the void fraction and to the actual gas velocity u (m s1) by Equation (2.4.8): us ¼ au
ð2:4:8Þ
The foam height is expressed as a function of the void fraction and foam layer thickness by Equation (2.4.9), if the void fraction is assumed to be independent of the foam height: h ¼ aL
ð2:4:9Þ
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Foams and Foaming
Consequently, S can be expressed in terms of the foam layer thickness and the actual gas velocity as S¼
DL Du
ð2:4:10Þ
From Equation (2.4.10), it is clear that S signifies the average travelling time of the gas through the foamed layer. If the foam formation rate is proportional to the rate of gas flow and the collapse rate of the foam is proportional to its height, the rate equation describing the change in foam height can be represented by Equation (2.4.11): dh ¼ K1 Q K2 h dt
ð2:4:11Þ
where K1 and K2 in the above equation are the formation and collapse rate constants of the foam, respectively. When the system is in steady state, dh ¼0 dt
ð2:4:12Þ
K1 Q ¼ K2 h
ð2:4:13Þ
Therefore,
However, if the gas flow is halted (i.e., Q ¼ 0) when the system is in steady state, Equation (2.4.11) reduces to Equation (2.4.14): dh ¼ K2 h dt
ð2:4:14Þ
Integrating Equation (2.4.14) from t ¼ 0 to t ¼ t and from h ¼ h0 to h ¼ h yields the variation of foam height as a function of time, as shown in Equation (2.4.15): h K2 t ¼ ln 0 ð2:4:15Þ h From Equations (2.4.4) and (2.4.15), it is clear that the collapse rate constant K2 and the drainage rate constant k, are equivalent and are equal to 1/t. In a system where the void fraction can be assumed to be constant, the foaming index can be related to the foam life t. The rate equation that describes foam formation is written as dh dL a V f Q ¼ ¼a ¼ dt dt A dt A
ð2:4:16Þ
From Equations (2.4.11), (2.4.13), and (2.4.16), Equation (2.4.17) is obtained:
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Kimihisa Ito
15 1573 K, FeO=30% CaO–SiO2–FeO CaO–SiO2–FeO–P2O5
S (s)
10
5
0 0
5
10
15
t (s)
Figure 2.4.9 Relationship between the foam life t and foaming index S for CaO–SiO2–FeO slags [1].
t h ¼ A Q
ð2:4:17Þ
From Equations (2.4.6), (2.4.7), and (2.4.17), the foaming index can be related to the average foam life by Equation (2.4.18): t¼
Dh Dh ¼ DðQ=AÞ Dus
ð2:4:18Þ
Therefore, for foams with a uniform void fraction profile, the foaming index S is equal to the average foam life t. Figure 2.4.9 shows a comparison of the foaming index with foam life for CaO–SiO2–FeO slags at 1573 K, and experiments confirmed that the two values are in good agreement with each other [1].
2.4.2.2. Experimental Measurements Experimental measurements of the foaming index have been reported for iron and steelmaking slags under various conditions [1,22–28]. The effect of the concentration of FeO on the foaming index of CaO–SiO2–FeO–MgO slags is shown in Figure 2.4.10 [22–24]. The foaming index decreased when the FeO content increased to up to about 20%. When the FeO concentration was increased further from 20% to 32%, the foaming index nearly remained constant. This is explained on the basis of the viscosity becoming almost constant when the FeO concentration increased above 25%. Figure 2.4.11 shows the effect of slag basicity on the foaming index of CaO–SiO2– FeO–MgO–Al2O3 slags [1,24]. The foaming index decreased with increasing basicity index [(CaO þ MgO)/(SiO2 þ Al2O3)] up to 1.4, at which point the slag was expected to be in the liquidus composition. However, the foaming index increased at higher
207
Foams and Foaming
5 CaO–SiO2–FeO–MgOsat [24] (1713 K, CaO/SiO2=0.93–1.1)
4
CaO–SiO2–FeO–Al2O3 [22] (1773 K, CaO/SiO2=1.0) CaO–SiO2–FeO–Al2O3 [22] (1773 K, CaO/SiO2=1.25)
S (s)
3
CaO–SiO2–15Al2O3–10MgO–FeO [22] (1773 K, CaO/SiO2=1.5)
2
1
0
10
20 30 FeO in slag (%)
40
Figure 2.4.10 Variation of foaming index S of the CaO–SiO2–FeO–MgOsat slags with the FeO content in the slag [24]. 10
CaO–SiO2–(18–21%)FeO–MgOsat, 1773 K [24] CaO–SiO2–30FeO–(3–5%)Al2O3, 1573 K [1]
S (s)
8
CaO–SiO2–30FeO–(3–5%)Al2O3, 1673 K [1]
6 4 2
0
0.4
0.8
1.2
1.6
2.0
Basicity index (CaO+MgO)/(SiO2+Al2O3) (-)
Figure 2.4.11 Variation of foaming index S of the CaO–SiO2–FeO–MgOsat slags with the basicity index [(CaO þ MgO)/(SiO2 þ Al2O3)], at 1713 K [24].
basicities, due to the precipitation of solid phases like 2CaOSiO2 or (Fe,Mg)O, which stabilized the foam. The temperature dependence of the foaming index for the CaO–SiO2–FeO–MgO slag system is shown in Figure 2.4.12 [24]. The logarithm of foaming index decreased with increasing temperature. From the data shown in Figure 2.4.9, the dependence of the foaming index on temperature T can be expressed by Equation (2.4.19): log S ¼
6610 3:90 T
ð2:4:19Þ
The apparent activation energy for the foam decay was estimated to be 126.5 kJ mol1 for CaO–SiO2–FeO–MgO slag, and as 160 kJ mol1 for 35%CaO–
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Kimihisa Ito
0.8 0.6
30%CaO–30%SiO2–30%FeO–10%MgO [24] 35%CaO–35%SiO2–30%FeO [1]
Log S (s)
0.4 0.2 0 -0.2 -0.4 -0.6 -0.8
5.6
6.0
6.4
104/T (K-1)
Figure 2.4.12 Dependence of foaming index S on temperature T for CaO–SiO2–FeO–MgO slags [24].
60 50
Slag/metal reaction < 1 mm Nozzle 2 mm Nozzle
S (s)
40 30 20 10 0
400
800
1/db
1200
1600
(m-1)
Figure 2.4.13 Variation of foaming index S as a function of the reciprocal of average bubble diameter [23].
35%SiO2–30%FeO slag [1]. The value reported for 48%CaO–32%SiO2–10% FeO–10%Al2O3 slag at temperatures ranging from 1723 to 1873 K was 139.6 kJ mol1. It can be noted that there was no significant difference in these activation energies. Zhang and Fruehan [23] measured the effect of the bubble size on the foaming index as shown in Figure 2.4.13, in which the foaming index is plotted against the reciprocal of average bubble diameter. In order to vary the sizes of the bubbles widely, foams were generated either by injecting argon gas or by inducing slag–metal reactions. The foaming index was found to be inversely proportional to the bubble diameter for a particular slag system, and therefore, smaller bubbles stabilized slag foaming. The effects of the type of the gas and its pressure on slag foaming were also studied by Zhang and Fruehan [26]. The foaming index was found to depend on the physical
209
Foams and Foaming
4 3 mm Spheres 10 mm Disks
S (s)
3
10 mm Spheres Coal char 6 mm Spheres 8 mm Spheres
2
1
0
0.1 0.2 0.3 0.4 0.5 Surface coverage, Aparticle/Acrucible (-)
0.6
Figure 2.4.14 Variation of foaming indexes of slags exhibiting initial foaming indexes of 1.8 and 3.6 s, as a function of the surface coverage by coke [28].
properties of the gas used for foaming. However, the foaming index was not affected by gas pressures ranging from 1 to 2 atm. Zhang and Fruehan also studied the effect of the presence of coke and coal char particles on the foaming index [28]. They used two different slags, 30%CaO–60%SiO2–10% CaF2 and 25.5%CaO–51%SiO2–8.5%CaF2–150%Al2O3, with foaming indexes of 1.8 and 3.6 s, respectively at 1773 K, for their experiments. The foaming indexes of these slags were experimentally measured in the presence of coke spheres or coke disks. The foaming index plotted as a function of the coverage ratio of the slag surface by the carbonaceous materials is shown in Figure 2.4.14. Foaming was drastically suppressed when the coverage by carbonaceous materials increased, in both the slag systems, although the initial foaming indexes of the systems differed from each other by a factor of two.
2.4.2.3. Dimensional Analysis and Empirical Equations It is expected that the foaming index can be related to the physical properties of the slag. Hence, dimensional analysis was applied to derive a relationship which describes the foaming index as a function of slag properties [22,23,29]. It can be assumed that foaming index, as described in Equation (2.4.20), is based on the information obtained from pneumatic experiments, in which the injected bubble diameters were varied within a specific range: S ¼ f ðr,m,s,gÞ
ð2:4:20Þ
In the above equation, r is the density (kg m3) of the liquid slag, m is the slag viscosity (N s m2), s is the slag surface tension (N m1), and g is gravitational acceleration (m s2). With five variables and three fundamental dimensions, two dimensionless
210
Kimihisa Ito
numbers, NS and Mo (expressed in Equations 2.4.21 and 2.4.22), were obtained by Jiang and Fruehan [22]: Sgm s gm4 Mo ¼ 3 rs
NS ¼
ð2:4:21Þ ð2:4:22Þ
Mo is the Morton number, which is generally used to describe the motion of bubbles in a liquid. The relationship between the two dimensionless numbers was calculated from the experimentally measured foaming indexes and the physical properties of the slag, and consequently, Equation (2.4.23) was derived: log Mo ¼ 2log NS þ 5:11
ð2:4:23Þ
The final equation derived that related the foaming index with slag viscosity, density, and surface tension is shown in Equation (2.4.24). The units used in this equation are SI units as used in Equation (2.4.20): m S ¼ 115 pffiffiffiffiffiffi rs
ð2:4:24Þ
Kim et al. [27] proposed similar relationships (such as those shown in Equations 2.4.25 and 2.4.26), based on the foaming index measurements they carried out on CaO–SiO2– FeO–MgOsat–X systems (X was Al2O3, MnO, P2O5, and CaF2): m S ¼ 214 pffiffiffiffiffiffi ðfor CaO based slagsÞ rs m S ¼ 999 pffiffiffiffiffiffi ðfor MgO saturated slagsÞ rs
ð2:4:25Þ ð2:4:26Þ
Skupien and Gaskell [30] repeated Jiang and Fruehan’s [22] dimensional analysis and correlated NS and Mo by using experimentally obtained surface tensions and viscosities to derive Equation (2.4.27): S¼
100m0:54 r0:39 s0:15
ð2:4:27Þ
Since equations from (2.4.24) to (2.4.27) are obtained from the data of pneumatic foaming experiments with similar geometries, in which the bubble diameters in the foam are estimated to be around 10 mm. It should be noted that above four equations are applicable only for the slag foam containing bubbles with diameters about 10 mm. Based on the experimental data shown in Figure 2.4.13, Zhang and Fruehan [23] reconsidered the dimensional analysis to include the average bubble diameter db(m) as
211
Foams and Foaming
a new independent variable. Now, with six independent variables, another dimensionless number Ar was obtained, in addition to NS and Mo. Ar, the Archimedes number, signifies the ratio of the buoyancy force to the viscous force and is related to the slag properties by Equation (2.4.28): Ar ¼
gdb3 r2 m2
ð2:4:28Þ
Subsequently, Equation (2.4.29) was obtained by regression analysis: NS ¼ 900Mo0:39 Ar0:28
ð2:4:29Þ
The final mathematical description of the foaming index is represented in Equation (2.4.30): S ¼ 115
m1:2 s0:2 rdb 0:9
ð2:4:30Þ
The viscosity used in these correlations should be the bulk viscosity including the effect of second phase particles. If the particles are small compared to the bubble size, they will increase the bulk viscosity, decreasing the drainage rate, and hence increase the foam index. This was discussed in detail by Ito and Fruehan [1] and Zhu et al. [21]. Ghag et al. [18] proposed a different type of relationship based on a foaming model in which the structure of the foam is stabilized by viscoelastic forces. The final relationship that included the effective elasticity Eeff (N m1), resulting from the dynamic adsorption of surface active species, was derived from the data of cold model studies using water– glycerol–SDBS solutions at 293 K; however, there is no direct evidence for the applicability of their model to the foaming of metallurgical slags.
2.4.2.4. Mass-Limited Foaming When the foam index and the gas flow rate are high enough to foam all of the available slag, the foam height will no longer increase with the gas flow rate but will be relatively constant with increasing flow rate. This is discussed by Zhu et al. [21] in more detail. Depending on a number of slag properties and the gas flow rate, the gas fraction cannot exceed 80–90% of the foam. This means the foam volume cannot exceed 4–10 times the static slag volume.
2.4.3. SLAG FOAMING IN INDUSTRIAL PROCESSES If the void fraction a is kept constant in the foamed slag and the flow regime is maintained unchanged with the gas velocity, the foam height h in practical metallurgical
212
Kimihisa Ito
processes can be estimated using the foaming index of the slag from Equation (2.4.31), which can be derived by integrating Equation (2.4.7): Dh S¼ Dus h ¼ S us us þ h
ð2:4:7Þ ð2:4:31Þ
1 where u* s (m s ) is the superficial gas velocity and h* (m) is the foam height when the foaming begins. Both u* s and h* are usually expected to be negligibly small in real processes, and consequently, the foam height in the furnace, Hf (m), is given by Equation (2.4.32):
Hf ¼ Sus
ð2:4:32Þ
If the cross-sectional area of the furnace A (m2) is known, Hf (m) can be estimated from the total gas flow rate in the furnace and the foaming index of the slag, by using Equations (2.4.6) and (2.4.32): us ¼
Q A
ð2:4:6Þ
2.4.3.1. Electric Arc Furnace The control of slag foaming is important in an electric arc furnace (EAF) operation, as the slag foam protects the refractory from the high intensity arc, allowing for high power input and productivity. Carbon is injected into the slag to make slag foam by the generation of CO bubbles, which are formed by the reaction of the carbon with FeO in the slag. The CO bubbles used for slag foaming can also be produced by the decarburization of the metal. The foam height can be estimated by substituting the values of the generation rate of CO and foaming index in Equations (2.4.6) and (2.4.32). Matsuura and Fruehan [31] examined slag foaming in a steelmaking EAF aimed at achieving high productivities with a mathematical model of the EAF, to compute the CO generation rate and slag chemistry for evaluating Equation (2.4.32). They calculated the effects of the amounts of pig iron, carbon, oxygen, and slag on the foam height and concluded that the foam was usually essentially limited by the amount of slag in the furnace. When the amount of total carbon (pig iron, coke, and coal) and oxygen was reduced, the foam height, limited by the CO generation rate, decreased. Oosthuizen et al. [32] estimated the slag foam depth using a dynamic EAF model describing the time evolution of the EAF and the off-gas system variables. Industrial data on foaming of basic slags in an EAF were used to estimate the relationship between the foam index and FeO content in the slag.
213
Foams and Foaming
As discussed in Section 4.2.4 and by Zhu et al. [21] and Matsuura and Fruehan [31], when the gas rate is high, the foam is simply limited by the volume of slag available. For the EAF, it was assumed the volume fraction of gas in the foam cannot exceed 80% so the foam volume cannot be greater than four times the slag volume. This restriction applies to much of the EAF process when high pig iron and oxygen amounts are used. At lower CO rates, the foam index can be used to calculate the foam volume.
2.4.3.2. Bath Smelting Furnace During bath smelting (a smelting process that reduces thick layered slags), it is important to stably maintain the slag height and avoid any abnormal slag foaming. Therefore, the prediction and the control of slag foaming is one of the key requirements of this process. Jiang and Fruehan [22] calculated the foam height in a bath smelting furnace using Equation (2.4.32) and compared their results with real pilot trials [33]. The results obtained from the calculations are summarized in Figure 2.4.15. In Figure 2.4.15, PRD and PCR denote the prereduction degree of the iron ore and the postcombustion ratio, respectively. The calculated foam height increased with increasing T. Fe content in the slag. The predicted foam height was in good agreement with the observed values, when PRD ¼ 0% and PCR ¼ 40%, which were close to the real conditions. The dotted curve shows the calculated foam heights when excess coke was present. These values were obtained by using the observation that the presence of carbonaceous materials reduced the foaming index by a factor of 2 (Figure 2.4.14). The calculated values also agreed well with the observations obtained from real slag foaming trials. Ogawa et al. [34] experimentally investigated the mechanism of controlling slag foaming by the use of carbonaceous materials using a 1-ton bath smelting furnace. 3.0 1: PRD = 0, PCR = 60 2: PRD = 0, PCR = 40
Foam height (m)
2.5
3: PRD = 30, PCR = 40
3 2
2.0
Slag foaming without coke
1
1.5 1.0 0.5
Real slag foaming with coke in slag
0
2
4 T. Fe in slag (%)
6
8
Figure 2.4.15 Comparison of the estimated and real foaming heights in a bath smelting process that uses a 5-ton converter [22].
214
Kimihisa Ito
5
Slag foaming ratio (-)
Overflow
4
3
5.0 6.0
2
3.4 3.1
1 Ore feed rate = 2.3 (kg/min)
0
0.1 0.2 0.3 0.4 0.5 Mass ratio of coke/slag (-)
0.6
Figure 2.4.16 Effect of coke to slag mass ratio on the slag foaming ratio [34].
Figure 2.4.16 shows the relationship between the coke to slag mass ratio in the furnace and the slag foaming ratio which is defined by Equation (2.4.33), for various iron ore feed rates: slag foaming ratio ¼
Vs þVg Vg
ð2:4:33Þ
In the above equation, V s (m3) is the volume of slag and V g (m3) is the volume of gas in the foamed slag. The slag foaming ratio increased with increasing iron ore feed rate and decreasing amount of coke, which suggested that the presence of coke exerted a suppression effect on slag foaming. It was experimentally confirmed that the stable operation of bath smelting in a 100-ton scale furnace was possible, as far as sufficient carbonaceous material was present in the slag.
2.4.3.3. Basic Oxygen Furnace In hot metal pretreatment processes, slag foaming has been a key challenge both in desiliconization and dephosphorization processes. Kitamura and Okohira [35] investigated the slag foaming caused by the reaction between the FeO-containing slag and hot metal in the CaO–SiO2–Al2O3–P2O5–TiO2–MnO–MgO–CaF2 system. The maximum slag foam height was observed when the basicity index [CaO/SiO2] was around 1.2, which slightly increased with increasing temperature and CaF2 concentration. The achievement of maximum values can be attributed to the combination of decreasing foaming index and increasing CO generation rate that accompany the increase in slag basicity. In the high basicity region, the slag foaming height increased with the increase in temperature and CaF2 concentration.
215
Foams and Foaming
Foam height (m)
8
6
200-ton converter Dconverter = 6.0 m
Stage 1 (1633 K) CaO/SiO2 = 0.8 35%FeO, 2%MgO
4 Stage 2 (1693 K) CaO/SiO2 = 1.2 32%FeO, 4%MgO
2
0
Stage 3 (1753 K) CaO/SiO2 = 1.5 23%FeO, 6%MgO
0.002 Decarburization rate
0.004
0.006
([mass%C] s−1)
Figure 2.4.17 Variation of calculated foam heights during the first half of the blowing process in the BOF, as a function of the decarburization rate [24].
Jung and Fruehan [24] estimated the foam height of slags during the first half of the blowing process in the basic oxygen furnace (BOF). The superficial gas velocity of a 200-ton converter (6.0 m in diameter) was assumed to be dominated by the decarburization reaction of steel. The results of the calculations using Equation (2.4.32) are shown in Figure 2.4.17. The foam height linearly increased with increasing decarburization rate and decreased with the progress of the stages. Bramming et al. [36] developed a vessel vibration measurement technique that employed a triaxial accelerometer mounted on a trunnion. The transfer of kinetic energy from the foaming slag to the vessel resulted in vibration excitation at the vessel walls. Consequently, the frequency band with the best correlation to the foam level was determined by FFT analysis. The results showed a correlation between vessel vibrations and foam heights, which can be used for the control of dynamic foam levels and slopping.
2.4.3.4. Suppression of Foaming Zhang and Fruehan [28] found that coke and coal char have the same strong antifoam effect on the liquid slag. The foaming index of the slag was drastically decreased when the coverage of liquid slag surface by carbonaceous materials increased. In the case of slag foams generated by the reaction of FeO with coke, X-ray characterization revealed that small bubbles coalesced on the interface between the carbonaceous materials such as coke and the slag [34] because of the poor wettability between them. The large bubbles formed by the coalescence of the small bubbles can rise through the foaming slag layer at relatively high speeds, leading to lower foam heights.
REFERENCES [1] K. Ito, R.J. Fruehan, Metall. Trans. B 20B (1989) 509. [2] C.F. Cooper, J.A. Kitchener, JISI 230 (1959) 48.
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Kimihisa Ito
[3] J.H. Swisher, C.L. McCabe, TMS-AIME 230 (1964) 1669. [4] S. Hara, M. Ikuta, M. Kitamura, K. Ogino, Tetsu-to-Hagane 69 (1983) 1152. [5] Y. Ogawa, N. Tokumitsu, in: Proceedings of 6th International Iron and Steel Congress, ISIJ, Nagoya, 1990, p. 147. [6] Y. Ogawa, N. Tokumitsu, Tetsu-to-Hagane 87 (2001) 14. [7] S. Yokoyama, M. Takeda, K. Ito, M. Kawakami, Tetsu-to-Hagane 78 (1992) 223. [8] A. Kapilashrami, A.K. Lahiri, M. Gornerup, S. Seetharaman, Metall. Mater. Trans. B 37B (2006) 145. [9] R. Khanna, M. Rahman, R. Leow, V. Sahajwalla, Metall. Mater. Trans. B 38B (2007) 719. [10] J.J. Bikerman, Foams, Springer-Verlag, New York, NY, 1973. [11] S. Hara, M. Kitamura, K. Ogino, Tetsu-to-Hagane 75 (1994) 2174. [12] S. Hara, T. Yunoki, K. Ogino, Tetsu-to-Hagane 75 (1989) 2182. [13] J.W. Gibbs, The Scientific Papers of J. Willard Gibbs, Longmans, London, 1906. [14] P. Kozakevitch, J. Metals 21 (1969) 57. [15] K. Mukai, T. Nakamura, H. Terashima, Tetsu-to-Hagane 78 (1992) 1682. [16] Y. Ogawa, D. Huin, H. Gaye, N. Tokumitsu, ISIJ Int. 33 (1993) 224. [17] B.J. Akers, Foams, Academic Press, London, 1976, p. 1. [18] S.S. Ghag, P.C. Hayes, H.-G. Lee, ISIJ Int. 38 (1998) 1208. [19] L. Hong, M. Hirasawa, M. Sano, ISIJ Int. 38 (1998) 1339. [20] H. Gou, G.A. Irons, W.-K. Lu, Metall. Mater. Trans. B 27B (1996) 195. [21] T.X. Zhu, K.S. Coley, G.A. Irons, Metall. Mater. Trans. B 43B (2012) 751. [22] R. Jiang, R.J. Fruehan, Metall. Trans. B 22B (1991) 481. [23] Y. Zhang, R.J. Fruehan, Metall. Mater. Trans. B 26B (1995) 803. [24] S.-M. Jung, R.J. Fruehan, ISIJ Int. 40 (2000) 348. [25] B. Ozturk, R.J. Fruehan, Metall. Mater. Trans. B 26B (1995) 1086. [26] Y. Zhang, R.J. Fruehan, Metall. Mater. Trans. B 26B (1995) 1088. [27] H.S. Kim, D.J. Min, J.H. Park, ISIJ Int. 41 (2001) 317. [28] Y. Zhang, R.J. Fruehan, Metall. Mater. Trans. B 26B (1995) 813. [29] K. Ito, R.J. Fruehan, Metall. Trans. B 20B (1989) 515. [30] D. Skupien, D.R. Gaskell, Metall. Mater. Trans. B 31B (2000) 921. [31] H. Matsuura, R.J. Fruehan, ISIJ Int. 49 (2009) 1530. [32] D.J. Oosthuizen, J.H. Viljoen, I.K. Craig, P.C. Pistorius, ISIJ Int. 41 (2001) 339. [33] N. Tokumitsu, M. Matsuo, K. Hatayama, H. Ishikawa, Y. Yamamoto, Y. Hayashi, in: Process Technol. Conf. Proc., Toronto, ISS of AIME, vol. 7, 1988, p. 99. [34] Y. Ogawa, H. Katayama, H. Hirata, N. Tokumitsu, M. Yamauchi, ISIJ Int. 32 (1992) 87. [35] S. Kitamura, K. Okohira, ISIJ Int. 32 (1992) 741. [36] M. Bramming, S. Millman, A. Overbosch, A. Kapilashrami, D. Malmberg, B. Bjorkman, ISIJ Int. 51 (2011) 71. [37] D. Lotun, L. Pilon, ISIJ Int. 45 (2005) 835.