ISIJ International, Vol. 40 (2000), No. 4, pp.

348–355

Foaming Characteristics of BOF Slags

Sung-Mo JUNG and Richard J. FRUEHAN

Department of Materials Science and Engineering, Carnegie Mellon University, Pittsburgh, PA 15213 USA.
(Received on September 30, 1999; accepted in final form on December 22, 1999 )

Slag foaming measurements were carried out for BOF type slags that exist during the first half of the
blowing period in order to better understand slopping of slag. The foam index (S ) decreases with increasing
FeO up to about 20 % FeO content and is almost constant for FeO from 20 to 32 % FeO. This is believed to
be because above about 25 % FeO, the viscosity is nearly constant. The foam index shows a minimum
value at basicity[5(CaO1MgO)/(SiO21Al2O3)] of 1.4 at 1 713 K; it increases at higher basicities due to the
precipitates such as 2CaOSiO2 or (Fe,Mg)O which stabilizes the foam. The effect of TiO2 and MgO on foam
index was also evaluated. An empirical equation for the foam index obtained by the previous researchers
was applied to the present experimental results. The foaming during the first half of the blowing in BOF
process was described based on the empirical relationship and the foam height was estimated for a BOS
converter as a function of decarburization rate.
KEY WORDS: slopping; BOF Slags; foam index; viscosity of slags; bubble size.

posed by Bikerman3) in which an equilibrium between for-

1. Introduction
mation and collapse of the foam was established by the
Slopping remains one of the major concerns in oxygen generated gas bubbles of definite size at a constant rate. The
steelmaking (OSM). Slopping results from excessive unit of “foaminess” was defined as the foam index (S ),
amounts of gas being generated in a highly foamable slag. given by
Most of the previous work on foaming has been done for
limited conditions, primarily relevant to iron smelting. For Vf
Σ5 ....................................(1)
example, FeO contents were less than 5 % in a limited tem- Qg
perature range. For steelmaking slags most measurements
have been for latter in the process, close to tap conditions. where Vf is the volume of the foam at steady state and Qg is
These conditions do not reflect those present during the first the gas flow rate. The parameter S has the unit of the time
part of oxygen steelmaking (OSM) when slopping occurs. and can be roughly interpreted as the average traveling time
Therefore, it is important to understand the fundamental of gas in the foamed liquid. Bikerman3) found that S is in-
features of slag foaming occurring during the first half of dependent of the amount of the liquid and the cross-sec-
the blow in the BOF process. tional area of the cylindrical container.
In recent investigations on slag foaming in the metallur- In the study of slag foams, Ito and Fruehan4) modified
gical processes, foams were often generated and maintained Bikerman’s definition of the dynamic measurement of foam
at steady state by using a constant rate of production of gas stability and referred to it as the foam index,
bubbles. Zhang and Fruehan1) injected argon gas into liquid
slag contained in an cylindrical alumina crucible at 1 773 K ∆h ∆H f H f
Σ5 5 5 ........................(2)
through an alumina nozzle (1.75 mm I.D.) and examined ∆v ∆vs vs
foaming by a X-ray video technique. The results showed
that the whole foam column was composed of polyhedron where h is the height of the foam layer at steady state, Hf is
shaped bubbles, and no initial transitional spherical bubbles the foam height defined as the difference of the level of
could be seen. In studying the kinetics of the reaction be- foamed liquid surface to the level of the liquid at rest, v is
tween FeO in the slag and carbon in the liquid iron, Zhang the linear gas velocity in the foam and vs the superficial gas
and Fruehan1) observed foams dominated by spherical bub- velocity which is defined by,
bles of much smaller size using the same X-ray video tech-
nique. The later type of foam was much more stable than Qg
that observed by Jiang and Fruehan,2) although the slag vs 5 ....................................(3)
A
compositions and temperatures were almost identical in
both experiments. The more stable foam resulted from Here A is the cross-sectional area of the container. Ito and
smaller bubbles generated by the chemical reaction. Fruehan4) also showed that the measured foam index is
The dynamic measurement of foamability was first pro- independent of the size of the container above a certain

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 ISIJ International, Vol. 40 (2000), No. 4

size when the effect of the container is negligible. They

measured the foam index for a slag of composition
CaO/SiO250.67; FeO530 % at 1 573 K in four different
sized crucibles(diameter: 25, 32, 38, 50 mm). The results
showed that foam indexes obtained were the same for all
the crucibles greater than that of the 32 mm diameter. They
also showed that in a CaO–SiO2–FeO system, S decreased
with increasing basicity up to 1.22 at 1 673 K. When
CaO/SiO2 was greater than 1.22, S increased due to the
presence of second-phase particles (CaO or 2CaOSiO2).
Second-phase particles have a large effect on foam stability
because they increase the bulk viscosity of the slag. Jiang
and Fruehan2) also conducted a larger scale experiment for
their slags at 1 773 K in which the diameter of the crucible
was 92 mm; Their results for the same slag at the same tem-
perature were similar.
It has been shown that the foam index is closely related
to the physical properties of the liquid slag by dimensional
analysis.1,2) In a recent study, Zhang and Fruehan1) mea-
Fig. 1. Schematic diagram of the experimental apparatus.
sured the foam index for the bath-smelting type of slags
(CaO–SiO2–Al2O3–FeO) with small bubbles generated by
argon gas injection through the nozzle of multiple small
orifices. An improved correlation was obtained by using
more accurate data for the slag viscosity, density, surface
tension, and bubble diameter in the dimensional analysis.
The correlation developed is expressed by

m 1.2 1)
Σ 5115 ..........................(4)
s 0.2rDb0.9
where S is the foam index (sec), m is the viscosity (N s/m2),
s is the surface tension (N/m), r is the density (kg/m3), and
Db is the bubble diameter (m).
It is the objective of this research to understand the fun-
damental features of slag foaming for CaO–SiO2–FeO–
MgO slags relevant to steelmaking processes during the
first half of the blowing in the converter. Also Ti is often in
Fig. 2. Foam height of CaO–SiO2–FeO–MgOsat slags as a func-
blast furnace hot metal which enters the slag. Therefore the tion of superficial gas velocity at 1 713 K.
effect of TiO2 on slag foaming was examined. The effect of
MgO was also measured. Another focus of this research is
to confirm if the correlation recently developed by Zhang made of a pure iron rod. In the present study, the foam
and Fruehan1) can be applied to the BOF slags. height was measured as the difference between the top
foam surface position and the liquid slag position at rest. In
order to obtain an accurate value for the foam index, a se-
2. Experimental ries of measurements at various gas flow rates were con-
A schematic diagram of the experimental apparatus is ducted for each slag composition studied, and the foam
shown in Fig. 1. An electric resistance furnace with a 150- index was determined from the slope of the line in a foam
mm hot zone length was used for the experiments to estab- height vs. superficial gas velocity plot, as shown in Fig. 2.
lish an isothermal condition. The slag sample weighed The master slag composed of CaO, SiO2, and MgO was
about 150 g, which corresponded to a slag depth of about 4 pre-melted in a MgO crucible using an induction furnace.
cm for a crucible diameter of 4.5 cm. This slag depth is suf- CaO, SiO2, and FeO was added to the master slag to adjust
ficient to eliminate the effect of the amount of the liquid on the slag compositions for actual experiments. FeO was pre-
foaming, as indicated by Bikerman.3) It took about 30–60 pared by sintering Fe3O4 powder in an iron crucible under
min to take each set of measurements during which the dis- Ar gas atmosphere at 1 573 K for about 12 hr. After the
solution of MgO from the crucible resulted in the final slag measurement was finished, the slag samples were chemical-
composition containing 6–22 % MgO. The argon gas was ly analyzed.
introduced into the molten slag through a pure iron pipe
with a knife edged nozzle (2.1-mm ID, 3.2-mm OD) which 3. Results and Discussions
was placed about 0.5–1.0 mm above the bottom of the cru-
bible. When the foam height reached a stable level, the sur- 3.1. Bubble Size
face position of the slag was detected with an electric probe It has been pointed out that the foam stability of liquid

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 ISIJ International, Vol. 40 (2000), No. 4

depends not only on its physical properties but also on the bubble diameters using Sano’s equation,6) the surface ten-
bubble size.5) In foams produced in the present foaming ex- sion and density values of the slag system designated by
periment, the following relationship between the volume of CSFM-4 in Table 1 were used. Because the consideration
bubbles (VB), bubble frequency ( f ), the gas flow rate (Vg) of viscosity effect on the bubble size was not taken into in
can be deduced by Eq. (5). Sano’s equation, there may be some discrepancy between
the measured bubble size and the calculated one. Compared
VB5Vg / f....................................(5)
to the average bubble diameter (about 12 mm) measured by
Assuming that bubbles are perfect spheres, Eq. (5) can Ito and Fruehan4) for CaO–SiO2–FeO–Al2O3 system, the
be rewritten as follows. average bubble diameter for the CaO–SiO2–FeO–MgO slag
1/3 system shows higher values (about 17 mm). A second rea-
 6Vg  son might be resulted from the difference of the shape of
Db5  ..............................(6)
p⋅ f  the nozzle tips used in the present work and in the experi-
ment performed by Ito and Fruehan.4) While the gas lance
As indicated in Eq. (6), the equivalent spherical bubble di- in the work by Ito and Fruehan4) was made of stainless pipe
ameter (Db) can be calculated by measuring the bubble fre- with knife edged nozzle (O.D.52.1 mm), the lance in the
quency (f) at a given gas flow rate. Figure 3 shows the mea- present research was made of iron pipe with flat edged noz-
sured bubble diameter as a function of gas flow rate. Bubble zle. According to the research by Sano et al.,6) the bubbles
frequency measurements, which were obtained using a produced through flat edged nozzle may be larger than
pressure transducer installed between the gas flow con- those through knife edged nozzle because the bottom part
troller and the gas lance in Fig. 1 which would indicate of the bubble sticking to the flat edged nozzle may expand
when a bubble was released. The measured bubble diameter to the external surface of the nozzle tips.
is larger than that calculated from the equation proposed by
3.2. The Effect of FeO Content on Foam Index
Sano et al.6) shown as a straight line. In the calculation of
The experimental results for determining foam index (S )
along with the analytical results for the slag compositions
are presented in Table 1. S is plotted in Fig. 4 as a function
of FeO content. It is indicated that the foam index S de-
creases with increasing FeO up to about 20 % FeO content.
This phenomena was also observed for bath smelting slag
systems (CaO/SiO251 and 1.25) measured by Jiang and
Fruehan2) and for Nippon steel’s bath smelting slag.2) Jiang
and Fruehan2) attributed the higher foaming index observed
for the lower basicity slag (CaO/SiO251) to the fact that
viscosities for the bath smelting slags are higher. One inter-
esting point found in the measurement by Jiang and
Fruehan2) is that a maximum foaming index occurred at
around 2 % FeO. From their experimental observations, it is
concluded that CaO–SiO2 slags do not foam when no FeO
is present in the slag, because it is too viscous to foam sig-
nificantly. That is, the slags with low FeO contents have a
Fig. 3. The relationship between mean bubble size and gas high melting point and viscosity, and no true foam is
flowrate at 1 713 K. formed due to the channeling of the gas bubbles through

Table 1. BOF Slag Foaming Measurement for CaO–SiO2–FeO–MgOsat system.

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Fig. 4. The change of the foam index for CaO–SiO2–FeO–

MgOsat slags as a function of FeO content at 1 713 K. Fig. 6. The change of foam index S with basicity index (CaO1
MgO)/(SiO21Al2O3) of the CaO–SiO2–FeO–MgOsat slags
at 1 713 K.

3.3. The Effect of Slag Basicity on Foam Index

Figure 6 shows the foam index for CaO–SiO2–FeO–
MgO slags at 1 713 K as a function of basicity index de-
fined as (CaO1MgO)/(SiO21Al2O3) in weight percent.
The foam index decreases with increasing (CaO1MgO)/
(SiO21Al2O3) up to 1.4, which is expected to be the liq-
uidus composition. In general the surface tension increases
and viscosity decreases with increasing basicity. Therefore,
low surface tension and high viscosity is expected to favor
the stability of slag foam. However, the foam index increas-
es with increasing basicity when the basicity index is higher
than 1.4. A similar tendency can be seen in the data of foam
index measured by Ito and Fruehan4) for CaO–SiO2–FeO–
Al2O3 slag system. The critical basicity indexes reaching
the minimum foam index are about 1.20 at 1 573 K and
1.22 at 1 673 K, which correspond to the liquidus tempera-
Fig. 5. The relationship between the viscosity of slag and FeO ture of CaO–SiO2–FeO–Al2O3 slag system. They4) reported
contents at 1 713 K.
that this is because solid particles such as 2CaOSiO2 pre-
cipitate at higher CaO contents, and the particles signifi-
the slag layer. This phenomena has also been observed in cantly increase foam stability. The similar finding can be
the previous research about the addition effect of P2O5 on seen in other previous research.7) When SiO2 is low and
foaming of CaO–SiO2 slags by Cooper and Kitchener.7) CaO high, the slags may crystallize at the steelmaking tem-
They have shown that foaming is absent with binary CaO– peratures, the crystallizing substance being in most cases
SiO2 melts but is marked when P2O5 in the range of 0 to 1.8 the orthosilicate Ca2SiO4, as can be confirmed in the
% is added to melts containing more than 50 % of SiO2. CaO–SiO2–FeO phase diagram.9) From the CaO–SiO2–FeO
The tendency in Fig. 4 can be explained on the basis of phase diagram, even basic slags are not saturated with CaO,
Fig. 5 plotting viscosity as a function of FeO content. The but rather with Ca2SiO4 or, in some cases, with 3CaOSiO2.
viscosities of both bath smelting slags and BOF slags de- If the slag is high enough in magnesia content as in the pre-
crease with increasing FeO content. In Fig. 5, the viscosi- sent slags saturated with MgO, magnesiowustite[(Fe,Mg)O]
ties of the slags were estimated using Urbain’s model8) may be the phase which crystallizes first. Therefore, the in-
based on the slag compositions shown in Table 1. From the crease of foam index caused by the precipitation of second-
result in Fig. 5, it is believed that the decrease of viscosity phase particles may be due to the role of the particles like
is the major contributor to foam instability of slags. 2CaOSiO2 or (Fe,Mg)O which increase the bulk viscosity.
The apparent result for the bath smelting slags and BOF Of course, high viscosity is required both to stop the
slag is that foam index S decreases with increasing the FeO drainage of the liquid from the thin films separating the
content up to about 20 % FeO. However, the foam index S bubbles in foams and the coalescence of bubbles approach-
is almost constant with increasing FeO content higher than ing each other in gas bubbles. It should be noted that pre-
20 % FeO in the slag. As indicated in Fig. 5, the viscosity cipitated second phase particles which are smaller than the
does not decrease significantly above 25 % FeO which is foam bubbles stabilize the foam. The increase in the bulk
the most likely reason for the foam index being constant. viscosity reduces the slag foam bubble drainage rate.

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 ISIJ International, Vol. 40 (2000), No. 4

Fig. 8. The change of the foam index for CaO–SiO2–FeO–

Fig. 7. The change of the foam index for CaO–SiO2–FeO–
MgOsat slags as a function of MgO content at 1 713 K.
MgOsat slags as a function of TiO2 content at 1 713 K.

However, large pieces of undissolved lime do not stabilize

the foam.
The slight difference of the basicity index for the mini-
mum foam index between CaO–SiO2–FeO–Al2O3 and CaO-
SiO2–FeO–MgO slag may be attributable to the fact that
MgO and Al2O3 are regarded as basic and acidic oxide, re-
spectively. CaO and MgO are being dealt with as the same
oxide for convenience in defining basicity index in Fig. 6.
The minimum is actually the liquidus composition and
therefore is not necessarily related to the basicity.
3.4. The Effect of TiO2 Content on Foam Index
Figure 7 shows the effect of TiO2 on the foam index for
the BOF slags. As the content of TiO2 increases, the experi-
mentally measured foam index increases. According to the
previous research,10) TiO2 increases the viscosity and lowers
the surface tension of FeO just as SiO2 does. However, it
was pointed out that TiO2 was not a networkbuilder because Fig. 9. The temperature dependence of the foam index for
Ti41 cations are too large. It is known that TiO2 introduced CaO–SiO2–FeO–MgO slag.
in an acid silicate melt lowers its viscosity in the same man-
ner as CaO or FeO. From the experimental tendency in Fig. contents measured using an iron crucible. The tendency in
7, it may therefore be speculated that TiO2 added combines Fig. 8 has been reported by Ren et al.11) who reported a re-
with MgO dissolved from the crucible wall to form duction in foaming intensity with increasing MgO contents
2MgOTiO2 (Tm51 756°C) precipitates. In reality, the calcu- at 1 623 K for basic compositions (CaO/SiO2$1).
lation of predicted foam index based on several models
which do not take the presence of precipitates into consid- 3.6. The Effect of Temperature on Foam Index
eration. Although the viscosity in the calculation decreased Figure 9 shows the temperature dependence of the foam
along with the increase of TiO2 content, the actual viscosity index for a 35%CaO–35%SiO2–30%FeO–10%MgO slag. It
affected by the formation of precipitates may increase, is indicated that the logarithm of foam index decreases with
which is believed to be the crucial reason for the increase of increasing temperature in the temperature range of 1 673 to
foam index observed in Fig. 7. 1 823 K. Generally since the temperature coefficient for sur-
face tension12) is positive and that for viscosity13) is nega-
3.5. The Effect of MgO on Foam Index
tive, decreasing temperature would favor the increase of the
Figure 8 shows the influence of MgO content on the foam index. From the data in Fig. 9, the temperature depen-
foaming behavior for a 35%CaO–35%SiO2–30%FeO slag dence of the foam index can be expressed by Eq. (7).
to which a proper amount of MgO was added for each mea-
surement. In order to facilitate the control of MgO content, 6 610
an Fe crucible was used for the slag container for these log Σ 5 23.90 .........................(7)
T
measurements. It is shown that the foam index decreases
with increasing MgO additions. In Fig. 8, the foam index The temperature dependence given by Eq. (7) can be used
obtained for 28CaO–28SiO2–28FeO–14MgOsat slag is in to predict the foam index at other temperature for the slag
relatively good agreement with the results at lower MgO and experimental conditions employed in this study. From

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 ISIJ International, Vol. 40 (2000), No. 4

Fig. 11. The calculated foam index for CaO–SiO2–FeO–MgO

slag during the course of the blowing time in the BOS
process.

Table 2. Tha slag composition in the BOS process defined ap-

Fig. 10. The result of the dimensional analysis considering the proximately during the first half of the blowing.
effect of the bubble size. NS 5Sm g/s , Mo5m 4g/s 3r ;
and Ar5r 2D 3b g/m 2

Eq. (7), the apparent activation energy for the decay of the
foam can be estimated to be 126.5 kJ/mol. For this value,
Ito and Fruehan4) obtained 160 kJ/mol as the activation en-
ergy for the decay of the foam for 35%CaO–35%SiO2– of the blowing reasonably enough. Equation (4) indicates
30%FeO slag in the temperature range of 1 523 to 1 673 K. that viscosity is the most important physical properties in
And Ozturk and Fruehan14) reported the value of 139.6 determining foam index with surface tension, density, and
kJ/mol as the apparent activation value for foam decay for bubble size also being important. That is, the foam stability
48%CaO–32%SiO2–10%FeO–10%Al2O3 slag in the tem- increases with increasing viscosity and decreasing the bub-
perature range of 1 723 to 1 873 K. It was found that there ble size, surface tension and density of slags, as was previ-
was no significant difference between the activation energy ously mentioned. In applying Eq. (4) to the present results,
for the foam decay and that for the viscous flow in the case the average measured value in Fig. 3 was used to estimate
of both present result and their results.4,14) the size of the bubbles produced by injecting gases through
an orifice into liquid slags.
3.7. Application of the Existing Correlation to the
Present Experimental Results
4. Foaming in Steelmaking Process
It has been proved that the foam index for bath smelting
slags by Ito and Fruehan,15) Jiang and Fruehan2) and ladle Understanding slag foaming in the converter is crucial
slags by Roth et al.16) has the quantitative relationship with not only for the prevention of slopping but also for the con-
the slag physical properties. According to the previous re- trol of the reactions occuring in the BOS process. The slag
search,1) it is obvious that the foam stability of slags are af- foaming in the BOS process can be estimated using the
fected by viscosity, surface tension, density, and the average foaming index formula previously derived as a function of
bubble diameter. For the case where the bubbles were pro- the physical properties of BOS slags. Based on the estmat-
duced by injecting gas from an orifice, the average bubble ed foam index, the foam height in the converter during the
diameter can be estimated by the viscosity, surface tension, first half of the blowing can be calculated using the follow-
nozzle geometry, and gas flow rate or simply measured as ing Eq. (8) derived by Ito and Fruehan.15) Here Vg* is a su-
in the present study. One of the objectives of this research is perficial gas velocity and h* height before foaming begins.
to confirm if the experimentally determined foam indexes
h5S (Vgs2Vg*)1h*............................(8)
in the present work agree with those calculated by the equa-
tion derived by Zhang and Fruehan.1) Figure 11 shows the estimated foam index for
Zhang and Fruehan1) described the following equation CaO–SiO2–FeO–MgO slags as a function of the blowing
which reflects the dependence of the foam index on the vis- time quantified by percentage with respect to the entire pro-
cosity, surface tension, density, and the average bubble di- cessing time in BOS process. The three slag compositions
ameter by the dimensional analysis. The estimation of the were selected to simulate the stages 1, 2, and 3 which corre-
slag properties is given in Appendix. As can be seen in Fig. spond to the 17 % stage, 33 % stage, and 50 % stage of the
10, the correlation (4) developed by Zhang and Fruehan entire blowing time in the BOS operation, respectively
predicts the foam index for BOF slags during the first half based on the real process data supplied by Inland Steel

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 ISIJ International, Vol. 40 (2000), No. 4

increasing temperature in the temperature range of 1 673 to

1 823 K for 35%CaO–35%SiO2–30%FeO–10%MgO slag.
This is primarily because the foam index is inversely pro-
portional to viscosity the foam index decreases and the
temperature coefficient for viscosity is negative. The foam
index decreases with increasing MgO additions to
35CaO–35SiO2–30FeO slag.
The correlation developed by Zhang and Fruehan pre-
dicts the foam index for the present BOF slags during the
first half of the blowing reasonably well. The measured
foam indexes are slightly larger than those calculated. This
may be because the uncertainty in viscosity estimation for
BOF slags is relatively larger than that for bath smelting
slags and ladle slags based on Urbain’s model. The foam
height was estimated for a 200-ton converter (Diameter5
6.0 m) as a function of decarburization rate. The calcula-
Fig. 12. The expected foam height of BOF slag during the first tions indicate that slopping is more likely early in the blow
half of the blowing as a function of the decarburization
rate.
if the decarburization rate is high.
Acknowledgements
Company. Because BOF slags usually contain 6 to 8 %
MgO at the end of the BOS operation, the MgO content in The authors wish to acknowledge The American Iron
Table 2 was approximately defined by the solubility of and Steel Institute (AISI), the Center for Iron and
MgO.17) It was indicated that the MgO content of just a few Steelmaking Research and its member companies, and the
percent intensifies the foaming action of acidic and neutral US Department of Energy for supporting this research.
slags.18) The predicted foam index decreases as the BOS
operation proceed in the range of 0.8 to 1.5 which corre- REFERENCES
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This is believed to be due to the effect of viscosity which 22) S. I. Popel: Metallurgicheskie shlaki i primenenie ihk v stroit
decreases as FeO content increases. At FeO contents higher el’stve’, (Metallurgical slags and their use in building), Akad. Stroit i
than 20 % FeO, foam index is almost constant. In a Arkhitekt, SSSR, Ural’sk Filial, (1962), 97–127.
CaO–SiO2–FeO–MgOsat system, the foam index decreases
with increasing basicity up to 1.4 at 1 713 K; when
Appendix. Estimation of Physical Properties
(CaO1MgO)/(SiO21Al2O3) was greater than 1.4, foam
index increased due to the precipitates like 2CaOSiO2 or In order to estimate the foam index using Eq. (7), it is
(Fe,Mg)O. As the content of TiO2 increases, the experimen- necessary to estimate slag properties. Due to the experi-
tally measured foam index increases. It is expected that mental difficulties at high temperatures, accurate measure-
TiO2 added combines with MgO from the crucible wall or ment of the physical properties of slags in many cases has
the slag to form 2MgOTiO2 (Tm52 029 K) precipitate. It is not been made. Therefore, models were developed to esti-
indicated that the logarithm of foam index decreases with mate the values for the properties such as density, surface

© 2000 ISIJ 354

 ISIJ International, Vol. 40 (2000), No. 4

–
Table A1. Recommended values for partial molar volume V Table A3. Equations for B-parameters in Urbain model for
of various slag constituents at 1 773 K.19) viscosity.

Table A2. Recommended values for partial surface tension s–

of various slag constituents at 1 773 K.19)

slags based on their chemical composition. The applicabil-

ity of these models has been reviewed and it was concluded
that the models developed by Urbain et al.8) and Riboud et
tension, and viscosity. The uncertainties vary according to al.18) were in closer agreement with the experimentally
the physical property being estimated so that experimental measured viscosities than the others. However, it was found
uncertainties are about 62% for density, about 610%, and that the Urbain model gives a slightly better fit than the
about 625% for viscosity measurements. It is unreasonable Riboud model. In the present study, Urbain’s model was
to expect any predictive model to produce data which are used for the estimation of slag viscosities. Both of these
more accurate than those obtained experimentally, for the models use the Frenkel equation, as given in Eq. (A-4),
models use experimental results to derive values for the where A and B are viscosity parameters, T is the tempera-
various partial molar parameters. ture K, and m is in N m22 s,
An additive method for the estimation of densities in al- m 5A · T · exp(B/T) ........................(A-4)
loys and slags has been widely used. In this method, the
molar volume V, can be obtained from Eqs. (A-1) and (A- In this model the parameters A and B are calculated by di-
– viding the slag constituents into three categories.
2) below where M, x, and V are the molecular weight, mole
fraction, and the partial molar volume, respectively, and the glass former: xG5xSiO21xP2O5..................................(A-5)
subscripts 1, 2, and 3 denote the various oxide constituents modifier: xM5xCaO1xMgO1xFeO12xTiO21xK2O13xCaF2
of the slag.
1xMnO12xZrO2 ..................................(A-6)
x1 M11x2 M 21x3 M 3
r5 ..................(A-1) amphoterics: xA5xAl2O31xFe2O31xB2O3 .....................(A-7)
V
The normalized values x*G, xM*, and x*A are obtained by
V5x1V̄ 11x2V̄ 21x3V̄ 3 ......................(A-2) dividing the mole fractions, xG, xM, and xA by the term
The partial molar volume is usually assumed to be equal (112xCaF210.5xFeO1.51xTiO21xZrO2).
to the molar volume of the pure component V°.19) The
xG
recommended values for V° for the various oxides at xG*5 .......(A-8)
1 773 K are given in Table A1. In order to calculate the val- 112 xCaF2 10.5xFeO1.5 1xTiO2 1x ZrO2
ues for the molar volume of CaO, SiO2, FeO, MgO, and
xM
TiO2 based on those obtained in Table A1, 0.01% K21 was *5
xM ......(A-9)
used as the temperature dependence of the molar volume.19) 112 xCaF2 10.5xFeO1.5 1xTiO2 1x ZrO2
Methods for estimating the surface tension of slags based
on the addition of the partial molar contributions s– of the xA
x *A 5 .....(A-10)
individual constituents have been reported by Appen et 112 xCaF2 10.5xFeO1.5 1xTiO2 1x ZrO2
al.,20) Boni and Derge21) and Popel.22) All these methods Urbain proposed that the parameter B was influenced both
make use of Eq. (A-3)
by the ratio a and by xG*. The parameter B can be expressed
s 5x1s¯11x2s¯21x3s¯3 ......................(A-3) in the form of Eq. (A-12) where B1, B2, and B3 can be ob-
tained by Eq. (A-13).
where the subscripts 1, 2, 3, etc., denote the various slag
constituents. Values of s¯i are often taken to be the surface xM
*
tension of the pure component s °i. This method of estimat- a5 ..........................(A-11)
* 1x *A
xM
ing the surface tension works well for certain slag mixtures
but breaks down when surface-active constituents, such as B5B01B1xG*1B2(xG*)21B3(xG*)3 ...........(A-12)
P2O5, are present. Surface-active components migrate pref-
Bi5ai1bia 1cia 2 .......................(A-13)
erentially to the surface and cause a sharp decrease in the
surface tension and only very small concentrations are re- B0, B1, B2, and B3 can be calculated from the equations list-
quired to cause an appreciable decrease in s . The recom- ed in Table A3 and these parameters are then introduced
mended values for s ° for the various oxides at 1 773 K are into Eq. (A-12) to calculate B.
given in Table A2. In order to calculate the values for the The parameter A can be calculated from B by Eq. (A-14)
surface tension of CaO, SiO2, FeO, MgO, and TiO2 based and the viscosity of the slag (in N m22 s) can then be deter-
on those shown in Table A2, 0.15 mN m21 K21 was applied mined by using Eq. (A-15).
as the temperature dependence of the surface tension 2ln A50.2693B111.6725 ...............(A-14)
(ds /dT) of the present slag system.19)
Several models exist for the estimation of viscosities of m 50.1[AT exp(103B/T)]..................(A-15)

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