Measuring and Modeling Viscosity of CaO-Al2O3-SiO2(-K2O) Melt GUO-HUA ZHANG and KUO-CHIH CHOU The effect of K2O on viscosity in CaO-SiO2-Al2O3 melt has been measured by a rotating spindle viscometer. It is indicated from the experimental results that viscosity first increases then decreases with the increasing content of K2O; the maximum viscosity occurs in the field of K2O/ Al2O3 > 1. After gradually adding K2O, the transformation of bridging oxygen (from being bonded with Al3+ ion charge compensated by Ca2+ ion to that compensated by K+ ion, for the higher priority of K+ ion relative to Ca2+ ion) increases the viscosity, whereas the increase of content of nonbridging oxygen decreases viscosity. The two factors lead to the complicate variation behavior of viscosity. The viscosity model proposed in our previous papers describes this phenomenon well. DOI: 10.1007/s11663-012-9668-9  The Minerals, Metals & Materials Society and ASM International 2012

I.

INTRODUCTION

THE viscosity of aluminosilicate slag plays significant roles in ironmaking and steelmaking processes, which are not only closely related to the practical operation, e.g., gas permeability of the blast furnace, foaming and the successfully separating of metal and slag during the basic oxygen steelmaking process, lubrication during the continuous casting process, etc., but also are intimately associated with the diffusion controlled kinetics, in which the higher the viscosity of melts, the slower the diffusion, thus, the more time will be required to achieve equilibrium. Therefore, it is of great importance for the fundamental research of viscosity. The content of alkali oxide in the metallurgical slag is usually very low, but its influence is significant. During the ironmaking process in blast furnace (BF), the alkali oxide not only results in many operating problems, such as burden movement, erratic change in permeability, and scaffolding in the furnace on the furnace wall, but also greatly affects the viscosity of slag, which is very important for BF operation. Sukenaga et al.[1] measured the effect of R2O (R = Li, Na, K) on the viscosity of CaO-SiO2-Al2O3 melt when keeping the ratio of CaO, SiO2, and Al2O3 constant. It was found that viscosity decreases with increasing the additive content of Li2O or Na2O, whereas the tendency is opposed for K2O.[1] Kim et al.[2] studied the viscosity variation of CaO-SiO2Al2O3-MgO-K2O system with K2O, and the same conclusion was also found that adding K2O would increase viscosity. However, the interpretation to this phenomenon is still inexplicit. One might anticipate the existence of Al2O3 results in the abnormal behavior of GUO-HUA ZHANG, Lecturer, and KUO-CHIH CHOU, Professor, are with the State Key Laboratory of Advanced Metallurgy and School of Metallurgical and Ecological Engineering, University of Science and Technology Beijing, Beijing, P.R. China. Contact e-mail: kcc126@ 126.com Manuscript submitted January 5, 2012. Article published online April 25, 2012. METALLURGICAL AND MATERIALS TRANSACTIONS B

K2O. Therefore, in this work, the viscosity variations of CaO-SiO2-Al2O3-K2O molten slag with K2O at different content of Al2O3 are studied. Furthermore, the measured viscosity data are compared with the estimated values calculated by the viscosity model proposed in our previous paper.[3–6]

II.

EXPERIMENTAL PROCEDURES

A. Samples Preparation Slag samples were prepared using reagent-grade SiO2, Al2O3, CaCO3, and K2CO3 powder, all of which were calcined at 1273 K (1000 C) for 10 hours in a muffle furnace to decompose any carbonate and hydroxide before use. Then, the prepared CaO and other reagents were precisely weighted according to the compositions shown in Table I and mixed in the agate mortar thoroughly. The mixtures were packed into a Mo crucible and premelted in an induction furnace at 1873 K (1600 C) for 2 hours with the protection of Ar gas, during which process the melt was stirred with a Mo bar to make the CO2 produced by the decomposing of K2CO3 escaping from the melt. After premelting, the slag sample, along with the crucible, was preserved in a desiccator. In Table I, the contents of K2O for all the composition points are low because of the evaporation of K2O at high temperature. The ratio of CaO and SiO2 is constant for all the 13 composition points, whereas the ratios of CaO, SiO2, and Al2O3 are constants in the same groups. B. Apparatus and Procedure for Viscosity Measurement The viscosity measurement was carried out using the rotating cylinder method with a Brookfield digital viscometer (Brookfield, Engineering Laboratories, Inc., Middleboro, MA). The schematic diagram of the experiment apparatus is shown in Figure 1 that consists of a rotating system, a heating system, and a measuring VOLUME 43B, AUGUST 2012—841

Table I.

Compositions for Viscosity Measurement (Mole Fraction) Al2O3

K2O

61

0

0

38.2

59.8

2.0

0 1.0 (1.0) 3.0 (2.8) 5.0 (4.7)

37.4

58.6

4.0

0 1.0 (1.0) 3.0 (2.9) 5.0 (4.7)

35.1

54.9

10.0

0 1.0 (1.0) 3.0 (2.9) 5.0 (4.7)

No.

CaO

SiO2

1 Group I 2 3 4 5 Group II 6 7 8 9 Group III 10 11 12 13

39

system. An electric resistance furnace with U-shape MoSi2 heating elements was used for system heating. The temperature was controlled within ±2 K with a proportional integral differential controller and a Pt-6 wt pct Rh/Pt-30 wt pct Rh thermocouple that was placed just under the Mo crucible holding the molten slag for viscosity measurement (both positions of thermocouple and crucible were in the uniform temperature zone of the furnace). A spindle and a crucible, both made of molybdenum, were employed for the viscosity measurement. The dimensions of the spindle and the crucible are also shown in Figure 1. The viscometer was calibrated by using castor oil at room temperature. During the viscosity measurement, both the crucible and the spindle should be properly aligned along the axis of the viscometer, which is very important because a slight deviation from the axis can cause large experimental errors. After adjusting the positions of crucible, the furnace was heated up to 1813 K (1540 C) with a constant Ar gas flow rate of 200 mL/min before immersion of the rotating spindle into the slag and centered within the melt. The bottom of the spindle was 10 mm above the crucible bottom. The viscosity measurement was carried out at every 25 K interval on cooling. At each experimental temperature before measuring, the melt has been kept for 30 minutes to ensure the melt uniform. Then, the measurements were carried out five times with different rotated rate, which varied between 100 and 200 rpm, and the average value was adopted as the viscosity value. The variations of viscosity caused by the different rotating speeds were less than 1.5 pct, confirming that the slag melt was Newtonian. After completing the viscosity measurements, the furnace was reheated up to 1813 K (1540 C) to pull out the spindle, which was cleaned by HF for the next experiment. The K2O contents of slag were analyzed by X-ray fluorescence after completing the viscosity measurements, which were in brackets in Table I. It can be observed that no significant changes have been found concerning the contents of K2O in the slag before and after the experiments. 842—VOLUME 43B, AUGUST 2012

III.

RESULTS

A. Effect of Al2O3 on Viscosity The viscosities of 13 compositions at different temperatures were measured and given in Table II. The measurements were performed at the temperature range from 1663 K to 1813 K (1390 C to 1540 C). For compositions 1, 2, 6, and 10, where the ratio of CaO and SiO2 are same and no K2O, the temperature dependence of viscosity follows the Arrhenius law (Figure 2). Furthermore, the viscosity increases with increasing the content of Al2O3. This fact can be explained as follows: For all these four compositions, the contents of CaO are higher than that of the Al2O3. As a result, Al2O3 exhibits an acidic oxide behavior and incorporates into the network of SiO2 with the charge compensation of CaO that will increase the degree of polymerization of melts and so the viscosity increases. B. Effect of K2O on Viscosity The variations of viscosity with temperatures and K2O contents for (38.2CaO-59.8SiO2-2.0Al2O3)-K2O (group I), (37.4CaO-58.6SiO2-4.0Al2O3)-K2O (group II), and (35.1CaO-54.9SiO2-10.0Al2O3)-K2O (group III) systems are shown in Figures 3 through 5, respectively. For (38.2CaO-59.8SiO2-2.0Al2O3)-K2O system, contents of K2O are less than that of Al2O3 for compositions 2 and 3, whereas it is more for compositions 4 and 5. From Figure 3, it can be concluded that viscosity increases with increasing the content of K2O until it equals 2.8 pct (composition 3); then, viscosity decreases with the further increase of K2O content. In other words, the viscosity exhibits a maximum with the content of K2O, and the position of maximum is in the field of K2O/Al2O3 > 1. The phenomenon that the viscosity increases with K2O content was also proved by the experimental results of Sukenaga et al.[1] and Kim et al.[2] However, the viscosity maximums are not found in their work for the high content of Al2O3. For (37.4CaO-58.6SiO2-4.0Al2O3)-K2O system, the contents of K2O are less than that of Al2O3 for compositions 6, 7, and 8, whereas it is more for composition 9. The viscosity increases as increasing content of K2O in this group, with the possible viscosity maximum in the field of K2O/Al2O3 > 1. For (35.1CaO-54.9SiO2-10.0Al2O3)-K2O system, all the four compositions 10, 11, 12, and 13 fulfill the condition that the content of K2O is less than that of Al2O3. From Figure 5, it can be observed that the viscosity increases monotonously with the K2O content. According to the preceding analyses, the following conclusions may be drawn: Viscosity exhibits a maximum with the content of K2O in CaO-SiO2-Al2O3-K2O system; the position of maximum is in the field of K2O/ Al2O3 > 1. In practical slag systems, e.g., blast furnace slag and the mould powder for continuous casting, the contents of K2O are always very small and less than that of the Al2O3. Therefore, viscosity increases with increasing content of K2O. METALLURGICAL AND MATERIALS TRANSACTIONS B

Fig. 1—Schematic illustration of the apparatus for viscosity measurement.

IV.

MODELING THE VISCOSITY OF CaO-SiO2Al2O3-K2O SYSTEM

A. Viscosity Calculation of CaO-SiO2-Al2O3-K2O System The viscosity model developed in our previous papers[3–6] will be used to estimate the viscosity of the compositions studied in this work and compare with the measured values. The detailed descriptions of the model METALLURGICAL AND MATERIALS TRANSACTIONS B

can be found in the early publication, and only a brief introduction about the application to CaO-SiO2-Al2O3K2O system will be given. The temperature dependence of viscosity is described by the Arrhenius law, lng ¼ lnA þ E=ðRTÞ

½1

where g is the viscosity, poise; A is the preexponent factor, poise; E is the activation energy, J/mol; R is VOLUME 43B, AUGUST 2012—843

Table II. Measured Viscosity Values at Various Temperatures (dPas) No. 1 Group I 2 3 4 5 Group II 6 7 8 9 Group III 10 11 12 13

1813 K (1540 C)

1788 K (1515 C)

1763 K (1490 C)

1738 K (1465 C)

1713 K (1440 C)

10.9

12.9

15.5

19.1

23.9

12.6 12.7 13.5 11.8

15.3 15.3 16.7 14.4

18.6 18.9 20.5 17.7

23.0 23.2 25.1 21.6

28.7 29.1

14.4 14.6 14.7 15.2

17.5 17.8 18.2 18.7

21.5 21.7 22.2 22.8

26.7 27.0 27.6 28.5

33.3 34.1 34.5

21.3 21.6 21.8 22.2

26.5 26.8 27.5 28.1

33.4 33.7 34.3 35.3

42.5 43.0 44.6 45.3

55.1 55.6 57.1 58.6

1688 K (1415 C)

1663 K (1390 C)

72.2 73.4 74.6 76.8

96.9 98.6 100.2 101.9

27.0

Fig. 2—Variations of viscosity with the content of Al2O3 at different temperatures.

Fig. 3—Variations of viscosity with the content of K2O for group I at different temperatures.

the gas constant, 8.314J/(mol  K); and T is the absolute temperature, K. The temperature compensation effect is considered, which relates the preexponent factor A and the activation energy E. To fulfill the viscosity variation of pure SiO2 melt in the model, the linear relation for MxO-SiO2 binary system is expressed as follows:

behavior of pure SiO2. For CaO-SiO2-Al2O3-K2O quaternary system, the value of parameter lnA is assumed to be the linear addition of values for the binary systems Mx Oy -SiO2 ; thus, parameter k can be calculated as follows, X X k¼ ðxi ki Þ= xi ½3

lnA ¼ kðE  572516Þ  17:47

where the E of 572516 and the lnA of 17.47 are the Arrhenius parameters describing the viscosity variation

E¼

i;i¼CaO;Al2 O3 ;K2 O

½2

i;i¼CaO;Al2 O3 ;K2 O

The activation energy for CaO-SiO2-Al2O3-K2O system in Eqs. [1] and [2] is expressed as

572516  2 Ca Ca K K nOSi þ aAl nOAl þ aCa nOCa þ aK nOK þ aAl;Ca nOAl;Ca þ aAl;K nOAl;K þ aCa Si nOCa þ aSi nOK þ aAl;Ca nOCa þ aAl;K nOK þ aAl;K nOCa Si

Si

Al;Ca

Al;K

Al;K

½4

844—VOLUME 43B, AUGUST 2012

METALLURGICAL AND MATERIALS TRANSACTIONS B

Table III. i

Values of Model Parameters for CaO-SiO2Al2O3-K2O Systems

ki  105

aiSi

ai

aAl;i

aiAl;i

aCa Al;K

–2.088 –3.2 –2.594

7.422 16.59 5.671

17.34

4.996 4.156

7.115 17.34

7.593

Ca K Al

xSiO2 2xAl2 O3 þ xSiO2

½5

2xK2 O 2xAl2 O3 þ xSiO2

½6

nOCa ¼ 2ðxCaO þ xK2 O  xAl2 O3 Þ Si

nOCa ¼ 2ðxK2 O þ xCaO  xAl2 O3 Þ Al;K

Fig. 4—Variations of viscosity with the content of K2O for group II at different temperatures.

nOCa

Al;Ca

¼ 2ðxK2 O þ xCaO  xAl2 O3 Þ

2ðxAl2 O3  xK2 O Þ ½7 2xAl2 O3 þ xSiO2

nOCa Si

nOSi ¼ 2xSiO2 

½8

2

nOAl;K ¼ 4xK2 O 

nOCa

Al;K

½9

2

nOAl;Ca ¼ 4ðxAl2 O3  xK2 O Þ 

nOCa

Al;Ca

2

½10

In the case of xK2 O >xAl2 O3 , all the Al3+ ions are compensated by K+ ions. The numbers of different types of oxygen can be calculated as follows: Fig. 5—Variations of viscosity with the content of K2O for group III at different temperatures.

nOK ¼ 2ðxK2 O  xAl2 O3 Þ

where nOi is the number of oxygen Oi bonded with i ion; nOAl;i is the number of bridging oxygen bonded with Al3+ ion charge balanced by i ion; nOiSi is the number of nonbridging oxygen bonded with Si4+ ion and i ion; nOj is the number of nonbridging oxygen bonded

nOCa ¼ 2xCaO

Si

Si

nO K

Al;K

xSiO2 2xAl2 O3 þ xSiO2

xSiO2 2xAl2 O3 þ xSiO2

¼ 2ðxK2 O  xAl2 O3 Þ

Al;i

with j ion and Al3+ ion charge balanced by i ion; and a describes the deforming ability around the different types of oxygen relative to bridging oxygen OSi . It should be pointed out that when charge compensating Al3+ ion, the K+ ion has the higher priority than Ca2+ ion.[6] Thus, there is no nonbridging oxygen OK Al;Ca in melt. All the 13 compositions in the current study fulfill the conditions of xCaO þ xK2 O >xAl2 O3 and xCaO þ xK2 O xAl2 O3 1? Why could the current model give a good description in the tendency of viscosity variation, but the maximum viscosity point is different? Why do other viscosity models only give a tendency to decrease? These questions will be answered in the following sections. (a) It can be thought that in the absence of Al2O3, adding K2O to CaO-SiO2 unquestionably decreases the viscosity. Or, the existence of Al2O3 leads to the complex situation for the variation of viscosity with composition.[4,6] When there is enough basic oxide, all the Al3+ ions will incorporate into the network of SiO2 and substitute the position of Si with the charge compensation of cation from basic oxide. The basic oxide participated in the charge compensation will not act as the network modifier, while it increases the viscosity by enhancing the degree of polymerization. When all the Al3+ ions have been compensated, the viscosity starts to decrease with further increasing basic oxide content since the new added basic oxide works as network modifier and decreases the degree of polymerization. Therefore, a maximum viscosity should appear with xMx O =xAl2 O3 . The former experiment findings for CaOAl2O3-SiO2[12] and Na2O-Al2O3-SiO2[13] systems also proved this conclusion. In the current study, there are two basic oxides: CaO and K2O, and the mole fraction of CaO is enough to compensate all the Al3+ ions (xCaO >xAl2 O3 ). Therefore, as adding K2O, K+ ion will substitute the position of Ca2+ ion to compensate Al3+ ion because of the high priority of K+ ion.[6] The addition of K2O may lead to the following two changes: more nonbridging oxygen will be formed because of the increase of the total content of basic oxides, which decreases viscosity; bridging oxygen OAl;Ca is gradually changed to OAl;K (schematic diagram is shown in Figure 10), which increases viscosity because the chemical bonds around OAl;K are stronger than those around OAl;Ca (aAl;Ca ¼ 4:996>aAl;K ¼ 4:156). When the content of K2O is low, the latter factor may be dominated; thus, the viscosity exhibits increasing tendency with the addition of K2O. When all the bridging oxygen OAl;Ca is completely changed to OAl;K , the further addition of K2O will not increase the content of OAl;K , but only increase the content of nonbridging oxygen. So, the viscosity decreases. Therefore, the viscosity first increases and then decreases with the addition of K2O to CaO-SiO2Al2O3 system. (b) If the equilibrium constant of the substitution reaction of K+ ion for Ca2+ ion to compensate Al3+ ion is infinite, the position of viscosity maximum will be METALLURGICAL AND MATERIALS TRANSACTIONS B

at K2O/Al2O3 = 1 because in this case, the number of K+ ions is exactly the number required by the charge compensation of Al3+ ions, and the number of OAl;K ions reaches the maximum. However, the equilibrium constant is not infinite. Therefore, some K+ ions act as network modifiers but do not substitute the positions of Ca2+ ions even if K2O/Al2O3 £ 1; thereby, in the case of K2O/Al2O3 = 1, there are still bridging oxygen ions OAl;Ca . The addition of K2O will form more OAl;K until all the Ca2+ ions are replaced by K+ ions. This will occur in the field of K2O/Al2O3 > 1; thus, the maximum viscosity should appear in this field. (c) The current model introduces the priority order for different cations according to the value of ðr 2Q þr Þ2 Mzþ

O2

(where Q is the valence of cation and r is the radii).[6] The smaller the value of ðr 2Q , the higher the þr Þ2 Mzþ

O2

priority will be. Therefore, K+ ion has a higher priority than Ca2+ ion for its lower valence and larger radii than Ca2+ ion. So, K+ ion will substitute the position of Ca2+ to compensate Al3+ ion when adding K2O to CaO-SiO2-Al2O3 melt. In our model, a strict order is set for different cations when charge compensating Al3+ ions.[6] The substitution reaction of K+ ion for Ca2+ ion is infinite. At K2O/Al2O3 = 1, all the Al3+ ions are compensated by K+ ions, and the number of OAl;K achieves the maximum, so does the viscosity. (d) The other viscosity models, e.g., Riboud et al.,[7] Urbain,[8] Mills and Sridhar,[9] Shu,[10] and Nakamoto et al.[11] can only give a decreasing tendency of viscosity with the content of K2O. The reason for this may be that all the models except NPL do not consider the priority order of different cations when compensating Al3+ ions. The Riboud model does not reflect the charge compensation effect of Al3+ ions. The models by Urbain, Shu, and Nakamoto et al. consider the multicomponent aluminosilicate system containing several basic oxides to be the ideal mixing of several MxO-Al2O3-SiO2 ternary systems; although the NPL model establishes the order according to the optical basicity values of different basic oxides, the larger optical basicity of K2O relative to CaO also lead to the decrease of the viscosity when adding K2O. VI.

CONCLUSIONS

1. The effect of K2O on the viscosity of CaO-SiO2-Al2O3 melt has been measured by a rotating spindle viscometer. The experiment results show that the viscosity first increases and then decreases with increasing the additive content of K2O. The position of viscosity maximum occur in the range of K2O/Al2O3 > 1. VOLUME 43B, AUGUST 2012—847

2. The substitution of K+ ion for Ca2+ ion to compensate Al3+ leads to forming a stronger bridging oxygen bond OAl;K relative to OAl;Ca , which may be the reason for increasing viscosity with the addition of K2O. When the content of K2O is high enough, the viscosity will decrease with the addition of K2O for decreasing the number of OAl;K , but the number of nonbridging oxygen atoms increases. 3. The calculation results of viscosity by models show that the model proposed in our previous work can describe the viscosity variation for CaO-SiO2-Al2O3K2O system with the addition of K2O.

ACKNOWLEDGMENT The authors wish to thank the Chinese Natural Science Foundation for their kind support under the contract 51174022.

848—VOLUME 43B, AUGUST 2012

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METALLURGICAL AND MATERIALS TRANSACTIONS B