viscosity studies of high-temperature metallurgical slags

Viscosity Studies of High-Temperature Metallurgical Slags

Relevant to Ironmaking Process

Chen Han

Bachelor of Engineering

A thesis submitted for the degree of Doctor of Philosophy at

The University of Queensland in 2017

School of Chemical Engineering

Abstract:

Slags are molten oxides presenting in a number of high-temperature processes. In ironmaking

process, the metallurgical properties of blast furnace slags are determined largely by its

viscosity. Understanding and controlling the behavior of the slag phase is crucial in

improving the operational and economical efficiencies. However, high-temperature viscosity

measurement is practically difficult, time- and cost-consuming. There is a necessity to

develop a reliable mathematical model for the viscosity prediction through the review of

experimental data and fundamental theory.

As foundation work, abundant viscosity measurements and models have been examined and

evaluated, including over 3000 viscosity data in the CaO-MgO-Al2O3-SiO2 system and 16

viscosity models. Over the past 10 years, there has been increasing attentions on wide

composition range of slag viscosity due to the continuous consumption of complex iron ores.

In addition, the impacts of eight minor elements (including F, Ti, B, Fe, Mn, Na, K, and S) on

slag viscosity have been studied for practical purpose.

Slag viscosity is determined by its structure, which is the theoretical base of the mathematical

model. The structures of the quenched silicate slags were quantitatively investigated utilizing

Raman spectroscopy. It is accepted that the application of Raman spectroscopy can disclosure

the vibration units of molten slag, which can be interpreted the structural of silicate melts

(amorphous glass phase).

In the blast furnace operations, some solid phases such as oxide precipitates, coke or Ti(CN)

can be present in the slag. In addition, the precipitation of solid particles was commonly

observed in iron, steel, copper and other pyrometallurgy process. These solids can

significantly increase the viscosity of the slag causing operating difficulty. There is a research

gap that the solid impact on suspension was limited investigated under high-temperature

condition due to uncertainty.

Referring to the research gap of viscosity study of blast furnace slag, the following goals have

been achieved by the Ph.D. candidate:

1. Review and evaluated the experimental methodologies, viscosity data, and models

relevant to the blast furnace slag in CaO-MgO-Al2O3-SiO2 system (Chapter 2)

2. Based on the collected data and models, an accurate viscosity model has been developed

to predict the viscosity of blast furnace slag in CaO-MgO-Al2O3-SiO2 system (Chapter 4-

5)

3. Research on the viscosity impact of minor elements on the blast furnace final slag in CaO-

MgO-Al2O3-SiO2 based system. (Chapter 4-5)

4. Quantitative investigation of the microstructural units of silicate slag utilizing Raman

spectroscopy. (Chapter 6)

5. Investigation of the solid phase impact on the viscosity of liquid slag. (Chapter 7)

Declaration by author

This thesis is composed of my original work, and contains no material previously published

or written by another person except where due reference has been made in the text. I have

clearly stated the contribution by others to jointly-authored works that I have included in my

thesis.

I have clearly stated the contribution of others to my thesis as a whole, including statistical

assistance, survey design, data analysis, significant technical procedures, and professional

editorial advice, and any other original research work used or reported in my thesis. The

content of my thesis is the result of work I have carried out since the commencement of my

research higher degree candidature and does not include a substantial part of work that has

been submitted to qualify for the award of any other degree or diploma in any university or

other tertiary institution.

I have clearly stated which parts of my thesis, if any, have been submitted to qualify for

another award. I acknowledge that an electronic copy of my thesis must be lodged with the

University Library and, subject to the General Award Rules of The University of Queensland,

immediately made available for research and study in accordance with the Copyright Act

1968.

I acknowledge that copyright of all material contained in my thesis resides with the copyright

holder(s) of that material. Where appropriate I have obtained copyright permission from the

copyright holder to reproduce material in this thesis.

Publications during candidature

1. Chen. Han, Mao. Chen, Weidong Zhang, Zhixing Zhao, Tim Evans, Anh V. Nguyen and

Baojun. Zhao*, “Viscosity Model for Iron Blast Furnace Slags in SiO2-Al2O3-CaO-MgO

system”, Steel Research International, 2015, vol.85 (6), pp. 678-685

2. Chen. Han, Mao. Chen, Weidong. Zhang, Zhixing. Zhao, Tim. Evans and Baojun. Zhao*,

“Evaluation of Existing Viscosity Data and Models and Developments of New Viscosity

Model for Fully Liquid Slag in the SiO2-Al2O3-CaO-MgO System”, Metallurgical and

Material Transactions B, 2016, Vol 47 (5), pp. 2861-2874

3. Chen. Han, Mao. Chen, Ron. Rasch, Ying. Yu and Baojun. Zhao*, “Structure Studies of

Silicate Glasses by Raman Spectroscopy”, Advances in Molten Slags, Fluxes, and Salts:

Proceedings of The 10th

International Conference on Molten Slags, Fluxes and Salts, Seattle,

United States, 2016, pp. 175-182

4. Chen. Han, Mao. Chen, Weidong. Zhang, Zhixing Zhao, Tim. Evans and Baojun. Zhao,

“Viscosity Model for Blast Furnace Slags Including Minor Elements”, The 10th

CSM Steel

Congress & The 6th

Baosteel Biennial Academic Conference 2015, Shanghai, China, 2015, pp.

95-103

5. Chen. Han, Mao. Chen, Weidong. Zhang, Zhixing Zhao, Tim. Evans, Anh V. Nguyen and

Baojun. Zhao*, “Development of viscosity model for SiO2-CaO-MgO-Al2O3-“FeO” slags in

ironmaking process”, High Temperature Processing Symposium, 2015, Melbourne, Australia,

pp. 103-106

Publications included in this thesis

1. Chen. Han, Mao. Chen, Weidong Zhang, Zhixing Zhao, Tim Evans, Anh V. Nguyen and

Baojun. Zhao*, “Viscosity Model for Iron Blast Furnace Slags in SiO2-Al2O3-CaO-MgO

system”, Steel Research International, 2015, vol.85 (6), pp. 678-685 – incorporated as

Chapter 4.1

Contributor Statement of contribution

Chen Han (Candidate) Wrote the paper (100%)

Baojun Zhao* Discussed and edited paper (45%)

Mao Chen Discussed and edited paper (45%)

Tim Evans Discussed and edited paper (5%)

Anh V Nguyen Discussed and edited paper (5%)

Weidong Zhang Provided industrial advices (50%)

Zhixing Zhao Provided industrial advices (50%)

2. Chen. Han, Mao. Chen, Weidong. Zhang, Zhixing. Zhao, Tim. Evans and Baojun. Zhao*,

“Evaluation of Existing Viscosity Data and Models and Developments of New Viscosity

Model for Fully Liquid Slag in the SiO2-Al2O3-CaO-MgO System”, Metallurgical and

Material Transactions B, 2016, Vol 47 (5), pp. 2861-2874 – incorporated as Chapter 4.2









3. Chen. Han, Mao. Chen, Ron. Rasch, Ying. Yu and Baojun. Zhao*, “Structure Studies of

Silicate Glasses by Raman Spectroscopy”, Advances in Molten Slags, Fluxes, and Salts:

Proceedings of The 10th

International Conference on Molten Slags, Fluxes and Salts, Seattle,

United States, 2016, pp. 175-182 – incorporated as Chapter 6





Ron Rasch Assisted in the Raman spectra analysis (50%)

Ying Yu Assisted in the Raman spectra analysis (50%)

4. Chen. Han, Mao. Chen, Weidong. Zhang, Zhixing Zhao, Tim. Evans and Baojun. Zhao,

“Viscosity Model for Blast Furnace Slags Including Minor Elements”, The 10th

CSM Steel

Congress & The 6th

Baosteel Biennial Academic Conference 2015, Shanghai, China, 2015, pp.

95-103 – incorporated as Chapter 4.2;









5. Chen. Han, Mao. Chen, Weidong. Zhang, Zhixing Zhao, Tim. Evans, Anh V. Nguyen and

Baojun. Zhao*, “Development of viscosity model for SiO2-CaO-MgO-Al2O3-“FeO” slags in

ironmaking process”, High Temperature Processing Symposium, 2015, Melbourne, Australia,

pp. 103-106 – incorporated as Chapter 5.2



Contributions by others to the thesis

Contributions by Professor Baojun Zhao in experiment design, concept, analysis,

interpretation, drafting, and writing in the advisory capacity.

Statement of parts of the thesis submitted to qualify for the award of another degree

None

Acknowledgements

I express my sincere gratitude to my advisor team Prof. Baojun Zhao (principal), Prof Anh

Nguyen and Dr. Tim.Evans for their guidance and support the research projects and this

thesis completion

I would like to acknowledge the Beijing Shougang Co., Ltd, China and Rio Tinto Iron Ore,

Australia for financial support.

I thank to Dr. Mao Chen for fruitful discussions and assistance in preparing this thesis.

I am very grateful to the lab assistant Ms, Jie Yu, for her help and support on the completion

of experimental work.

Key Words

Slag viscosity, viscosity modelling, blast furnace slag, Raman spectrum

Australian and Newzealand Standard Research Classifications (ANZSRC)

ANZSRC: 091407 Pyrometallurgy 100%

Fields of Research (FoR) Classification

FoR code: 0914 Resources Engineering and Extractive Metallurgy 100%

Table of Contents

Chapter 1 : Introduction ............................................................................................................. 1

1.1 Background Introduction ........................................................................................... 1

1.2 Research Gap ............................................................................................................... 2

1.3 Aim of the Study .......................................................................................................... 2

Chapter 2 : Literature reviews .................................................................................................... 4

2.1 The technical review of high-temperature viscosity measurement.............................. 4

2.1.1 Liquid Viscosity Definition .............................................................................. 4

2.1.2 Viscometer ........................................................................................................ 7

2.1.2.1 Rotational Viscometer ................................................................................... 9

2.1.2.2 Falling-Body Viscometer ............................................................................. 10

2.1.2.3 Oscillating Viscometer................................................................................. 12

2.1.2.4 Other Viscometers ....................................................................................... 13

2.1.3 Post-Experimental Analysis ............................................................................ 14

2.1.3.1 Composition Analysis .................................................................................. 15

2.1.3.2 Surface Morphology Study .......................................................................... 17

2.1.3.3 Internal Structure Study ............................................................................... 20

2.2 The review of viscosity data of sub binary, ternary of CaO-MgO-Al2O3-SiO2 system

.......................................................................................................................................... 26

2.2.1 Binary System ................................................................................................. 26

2.2.1.1 SiO2-CaO ..................................................................................................... 26

2.2.2.2 SiO2-Al2O3 ................................................................................................... 27

2.2.2.3 SiO2-MgO .................................................................................................... 28

2.2.2 Ternary System ............................................................................................... 29

2.2.2.1 SiO2-CaO-Al2O3 .......................................................................................... 29

2.2.2.2 SiO2-Al2O3-MgO ......................................................................................... 32

2.2.2.3 Conclusion ................................................................................................... 33

2.3 Evaluation of Quaternary system CaO-MgO-Al2O3-SiO2 ......................................... 34

2.3.1 Experimental Techniques in Viscosity Measurements ................................... 35

2.3.2 Data Consistency ............................................................................................ 36

2.3.3 Cross Reference Comparison .......................................................................... 38

2.3.4 Summary of Experimental Data...................................................................... 39

2.3.5 Random Network Structure ............................................................................ 45

2.3.5 Minor Element Impact .................................................................................... 47

2.3.5.1 “FeO” ........................................................................................................... 47

2.3.5.2 TiO2 .............................................................................................................. 49

2.3.5.2 Na2O and K2O .............................................................................................. 51

2.4 The review and evaluation of viscosity model for silicate melts of CaO-MgO-Al2O3-

SiO2 system ...................................................................................................................... 53

2.4.1 Bottinga Model ............................................................................................... 53

2.4.2 Neural Network Model ................................................................................... 54

2.4.3 Giordano Model .............................................................................................. 54

2.4.4 CSIRO Model ................................................................................................. 55

2.4.5 KTH Model ..................................................................................................... 56

2.4.6 Urbain Model .................................................................................................. 57

2.4.6.1 Riboud Model .............................................................................................. 60

2.4.6.2 Kondratiev and Forsbacka Model ................................................................ 61

2.4.7 Iida Model ....................................................................................................... 61

2.4.8 NPL (Mills) Model ......................................................................................... 63

2.4.9 Shankar Model ................................................................................................ 64

2.4.10 Hu Model ...................................................................................................... 64

2.4.11 Shu Model ..................................................................................................... 65

2.4.12 Zhang Model ................................................................................................. 66

2.4.13 Gan Model .................................................................................................... 68

2.4.14 Tang Model ................................................................................................... 69

2.4.15 Ray Model ..................................................................................................... 70

2.4.16 Li Model........................................................................................................ 71

2.4.17 Quasi-Chemical Viscosity Model ................................................................. 72

2.4.18 Factsage 7.0................................................................................................... 73

2.4.19 Summary ....................................................................................................... 73

2.5 The viscosity study review of suspension system...................................................... 81

2.5.1 Effects of liquid viscosity & Solid Fraction ................................................... 82

2.5.2 Effects of Particle Size .................................................................................... 84

2.5.3 The review of viscosity model of suspension system ..................................... 86

Chapter 3 : Experiment Methodology...................................................................................... 90

3.1 High-Temperature Viscosity Measurement ............................................................... 90

3.2 Room Temperature Viscosity Measurement ............................................................. 92

3.3 Raman Spectroscopy Study ....................................................................................... 92

Chapter 4 : Viscosity Model Development in CaO-MgO-Al2O3-SiO2 System Based on

Urbain Model ........................................................................................................................... 94

4.1 CaO-MgO-Al2O3-SiO2 system in blast furnace composition range .......................... 94

4.1.1 Introduction ..................................................................................................... 94

4.1.2 Experimental Data Used for Model Development.......................................... 95

4.1.3 Silicate Melt Structure .................................................................................... 95

4.1.4 Description of Model ...................................................................................... 96

4.1.5 Expressions of Activation Energy .................................................................. 97

4.1.6 Model Performances ..................................................................................... 100

4.1.7 Industrial Applications .................................................................................. 102

4.1.8 Conclusions ................................................................................................... 104

4.2.1 Introduction ................................................................................................... 104

4.2.2 Experimental Methodology .......................................................................... 105

4.2.3 Viscosity Database ........................................................................................ 106

4.2.3.1 Collected Reference ................................................................................... 106

4.2.3.2 Minor Element Impact ............................................................................... 106

4.2.4 Result & Discussion ...................................................................................... 107

4.2.4.1 Comparisons of viscosities ........................................................................ 107

4.2.4.2 Viscosity Model Description ..................................................................... 108

4.2.4.3 Industrial Application ................................................................................ 112

4.2.5 Conclusions ................................................................................................... 114

Chapter 5 : Viscosity Model Development Based on Probability Theorem .......................... 115

5.1 CaO-MgO-Al2O3-SiO2 system in full composition range ....................................... 115

5.1.1 Introduction ................................................................................................... 115

5.1.2 Silicate melt structure ................................................................................... 115

5.1.3 Pre-Exponential Factor A ............................................................................. 116

5.1.4 Network Modifier Probability ....................................................................... 118

5.1.5 Activation Energy EA .................................................................................... 119

5.1.6 Model Performance ....................................................................................... 122

5.1.6.1 CaO-MgO-Al2O3-SiO2 system................................................................... 122

5.1.6.2 Viscosity Trend Prediction ........................................................................ 124

5.1.6.3 Sub-Ternary & Sub-Binary System ........................................................... 125

5.1.7 Industrial Application ................................................................................... 128

5.1.7.1 Blast Furnace Slag ..................................................................................... 128

5.1.7.2 Ladle Slag in Steelmaking Process ............................................................ 130

5.1.8 Conclusions ................................................................................................... 131

5.2 CaO-MgO-Al2O3-SiO2-“FeO” system in full composition range ........................... 132

5.2.1 Introduction ................................................................................................... 132

5.2.2. Model Description ....................................................................................... 132

5.2.2.1 Silicate structure of SiO2-CaO-Al2O3-MgO-“FeO” system ...................... 132

5.2.2.2 Temperature dependence ........................................................................... 133

5.2.2.3 Pre-exponential Factor A ........................................................................... 134

5.2.2.4 Fe2+

and Fe3+

Determination ...................................................................... 134

5.2.2.5 Network Modify probability ...................................................................... 134

5.2.2.6 Activation Energy ...................................................................................... 135

5.2.3 Model Performance ....................................................................................... 138

5.2.4 Industrial Application ................................................................................... 140

5.2.4.1 Blast Furnace Slag ..................................................................................... 140

5.2.4.2 Coppermaking Slag .................................................................................... 141

5.2.5 Conclusion .................................................................................................... 142

Chapter 6 : Structure studies of silicate slag by Raman spectroscopy ................................... 143

6.1 Introduction .............................................................................................................. 144

6.2 Methodology ............................................................................................................ 145

6.2.1 Sample Preparation ....................................................................................... 145

6.2.2 Raman Analysis ............................................................................................ 150

6.3 Raman Results ......................................................................................................... 151

6.3.1 Structure of alumina silicate system ............................................................. 151

6.3.2.1 Raman Peak Shift ....................................................................................... 154

6.3.2.2 Peak Intensity ............................................................................................. 156

6.3.2.3 Temperature Impact ................................................................................... 157

6.3.3 Bond energy and the lattice energy ............................................................... 158

6.3.4. Summary ...................................................................................................... 159

6.4 Thermodynamic Analysis ........................................................................................ 160

6.4.1 Degree of Polymerization ............................................................................. 160

6.4.2 Density .......................................................................................................... 162

6.4.3 Viscosity & Activation Energy ..................................................................... 163

6.5 Conclusion ............................................................................................................... 164

Chapter 7 : Experimental and modeling study of suspension system .................................... 165

7.1 Introduction .............................................................................................................. 165

7.2 Methodology ............................................................................................................ 166

7.2.1 Calibration..................................................................................................... 166

7.2.2 Viscosity Study of Suspension at Room Temperature ................................. 167

7.2.3 Viscosity Study of Suspension at Smelting Temperature ............................. 169

7.3 Results ...................................................................................................................... 170

7.3.1 Room Temperature ....................................................................................... 170

7.3.2 Smelting Temperature ................................................................................... 175

7.3.3 Effect of liquid viscosity and solid fraction .................................................. 177

7.3.4 Effect of particle diameter ............................................................................ 178

7.3.5 Effect of Temperature ................................................................................... 179

7.3.6 Effect of Shear Rate ...................................................................................... 181

7.4 Model Simulation..................................................................................................... 182

7.4.1 Model Review and Evaluation ...................................................................... 182

7.4.2 Model Optimization ...................................................................................... 185

7.4.3 Model Application ........................................................................................ 188

7.5 Conclusion ............................................................................................................... 190

Chapter 8 : Conclusions ......................................................................................................... 191

Chapter 9 : Reference............................................................................................................. 192

List of Table

Table 1.1 Blast furnace composition range [1] .................................................................. 1

Table 2.1 Category of different types of fluids .................................................................. 6

Table 2.2 Summary of Reviewed Viscometers.................................................................. 8

Table 2.3 Summary of post-experiment techniques ........................................................ 14

Table 2.4 the assigned peaks after peak deconvolution in the region 800-1200 cm-1

[41]

.................................................................................................................................. 22

Table 2.5 Summary of viscosity study at binary system SiO2-CaO ................................ 27

Table 2.6 Summary of viscosity data of SiO2-Al2O3 system ........................................... 27

Table 2.7 Summary of viscosity data of SiO2-MgO system ............................................ 28

Table 2.8 Summary of SiO2-Al2O3-CaO viscosity study................................................. 30

Table 2.9 Summary of viscosity study at SiO2-Al2O3-MgO system ............................... 32

Table 2.10 Viscosity impact of oxide in their binary and ternary system with silica ...... 34

Table 2.11 The summary of existing viscosity study in CaO-MgO-Al2O3-SiO2 system 41

Table 2.12 Summary of Brokis study of expression of SiO2 unit at various concentration

[111].......................................................................................................................... 46

Table 2.13 Summary of viscosity study at CaO-MgO-Al2O3-SiO2-”FeO” system ......... 47

Table 2.14 Summary of viscosity study at CaO-MgO-Al2O3-SiO2-TiO2 system ............ 49

Table 2.15 Summary of viscosity study at CaO-MgO-Al2O3-SiO2-Na2O and K2O system

.................................................................................................................................. 51

Table 2.16 the parameter D values of Bottinga model in CaO-MgO-Al2O3-SiO2

quaternary system [126] ........................................................................................... 54

Table 2.17 Model parameters for Giordano [128] ........................................................... 55

Table 2.18 Model parameters of Urbain Model [131] ..................................................... 59

Table 2.19 Equation parameters for Iida model [136, 137] ............................................. 62

Table 2.20 Model parameters of NPL model [138] ......................................................... 63

Table 2.21 The model parameters used to calculate E [145] ........................................... 67

Table 2.22 All possible condition in the CaO-MgO-Al2O3-SiO2 system, only the

condition 1 equations were included. The equations for other conditions is not

included due to text limitation [145]. ....................................................................... 68

Table 2.23 Model parameters of Gan model [147] .......................................................... 69

Table 2.24 Model parameters of Tang model [148] ........................................................ 70

Table 2.25 Model parameters of Li model [150] ............................................................. 71

Table 2.26 Summary of reviewed viscosity model in CaO-MgO-Al2O3-SiO2 system.... 77

Table 2.27 Summary of applicable oxides of existing viscosity model .......................... 79

Table 2.28 The brief review of viscosity study of suspension system at different system,

viscosity and temperature range, note: the relative viscosity means the ratio of

suspension viscosity to liquid viscosity .................................................................... 81

Table 2.29. Summary of 10 different viscosity model, f is the solid fraction within

suspension ................................................................................................................. 88

Table 4.1 Parameters B used in Equation 4-4 .................................................................. 99

Table 4.2 Model parameters N......................................................................................... 99

Table 4.3 Summary of typical BF composition range ................................................... 105

Table 4.4 Model parameters to calculate Ei of each minor element, the parameters of

SiO2, CaO, MgO, and Al2O3 were reported in the section 4.1.4 before ................. 109

Table 4.5 Optical basicity of oxide from Duffy ............................................................. 110

Table 4.6 Summary of model performance in BF slag composition range ................... 110

Table 5.1 Electronegativity χ of basic oxide cations and network former units ............ 119

Table 5.2 Activation energy parameters of all involved structural units in CaO-MgO-

Al2O3-SiO2 system .................................................................................................. 121

Table 5.3 The summary of model parameters in binary and ternary silicate system

containing CaO, MgO, and Al2O3. ......................................................................... 125

Table 5.4 Electronegativity χ of basic oxide cations and network former units ............ 135


Al2O3-SiO2 system .................................................................................................. 137

Table 5.6 The prediction deviation of viscosity models for CaO-MgO-Al2O3-SiO2-“FeO”

system ..................................................................................................................... 138

Table 6.2 The experiment designed condition and EPMA results ................................. 146

Table 6.3 The description of assigned peak information in Raman spectrum silicate

structural units, black ball is Si and white ball is O. white ball with – sign is O- .. 152

Table 6.4 Summary of the bond energy of each deconvoluted peaks ........................... 161

Table 7.1 Physical properties of silicon oil in present study ......................................... 167

Table 7.2: Experimental condition of viscosity measurement at room temperature ..... 167

Table 7.3. Viscosity measurements of suspension of solid proportion from 0-22 vol%

................................................................................................................................ 171

Table 7.4. Viscosity measurements of suspension of solid proportion from 25-32 vol %

................................................................................................................................ 172

Table 7.5. The elemental analysis of Baosteel and JingTang slag from EPMA analysis,

where the minor element include Na2O, K2O, FeO and etc ................................... 175

Table 7.6. Summary of optimized model....................................................................... 187

List of Figure

Figure 1.1 Technical description of blast furnace ironmaking process ............................. 1

Figure 2.1 Laminar shear of fluid between two plates....................................................... 5

Figure 2.2 Shear stress vs strain rate of Newtonian liquid and non-Newtonian fluid ....... 6

Figure 2.3 Schematic diagram of rotational cylinder viscometer ...................................... 9

Figure 2.4 geometry for rotational bob, (a) cylinder, (b) cylinder, (c) cone, (d) cone, (e)

parallel plate (f) parallel plate ................................................................................... 10

Figure 2.5 Schematic diagram of the falling sphere viscometer ...................................... 11

Figure 2.6 Counter balance viscometer [15] .................................................................... 11

Figure 2.7 Schematic diagram of the oscillating piston viscometer ................................ 12

Figure 2.8 Schematic diagram of the capillary viscometer.............................................. 13

Figure 2.9 Schematic diagram of ICP [31] ...................................................................... 17

Figure 2.10 Spherulite of aluminous enstalite under (a) natural and (b) polarized light

after the viscosity measurements [36] ...................................................................... 18

Figure 2.11 Bright-field TEM image [37] ....................................................................... 19

Figure 2.12 Raman spectrum of silica glass [38] ............................................................. 21

Figure 2.13 The Raman spectrum of SiO2-CaO system at different Ca/Si ratio [43] ...... 22

Figure 2.14 The pair distribution for the pure SiO2. A is the experimental curve, B is the

calculated curve [49] ................................................................................................ 24

Figure 2.15 (a) left, 29

Si NMR spectra of SiO2-Na2O glasses [52] .................................. 25

Figure 2.16 Activity of SnO plotted against mole fraction of SiO2 for the SiO2-SnO

system at 1100 oC. Kozuka experimental data and 1) Masson prediction, 2) Flory

expression k11=2.55. And 3) Flory expression with k11=1.443 [53] ........................ 26

Figure 2.17 isovicosity data by Licko in SiO2-CaO-MgO system at 1500 °C at 40 wt.%

and 50 wt.% SiO2 [56](b) The viscosity data of Bockris of SiO2-CaO and SiO2-

MgO system at 1750 °C [54] .................................................................................... 29

Figure 2.18 Examples showing viscosity measured below liquidus by Machin [74] and

Tang [99] .................................................................................................................. 37

Figure 2.19 Linearity comparison examples by Muratov [100], Machin[80], and

Yakushev [89]........................................................................................................... 38

Figure 2.20 Four sets viscosity measurement at 45 wt % SiO2, 15 wt% Al2O3, 30 wt%

CaO and 10 wt% MgO by Gul’tyai [83], Han [93], Kita [27] and Machin [27, 74, 83,

93] ............................................................................................................................. 38

Figure 2.21 Comparison of viscosity data by the present authors (UQ), Kim et al [35]

and Park et al [101] at composition of 36.5% SiO2, 17% Al2O3, 36.5% CaO and 10%

MgO .......................................................................................................................... 39

Figure 2.22 (a) Left, pure SiO2 structure. (b) Right, silicate mix with other basic oxide

solution ..................................................................................................................... 45

Figure 2.23 FeO replaced the CaO and MgO oxide at 40 wt% SiO2, 1500 oC for SiO2-

CaO-FeO system, 40 wt% SiO2, 1550 oC for SiO2-MgO-FeO system, by Bockris

[94], Chen [115], Ji [114]and Urbain [13] ................................................................ 48

Figure 2.24 The comparison between Urbain model of 1981 and 1987 version using the

viscosity database of before-evaluation, after-evaluation and BF composition [131,

132] ........................................................................................................................... 60

Figure 2.25 The shear stress enlarged from fully liquid system to solid/liquid system... 83

Figure 2.26 Viscosity deduced from data of van der Molten and Paterson (1979) [165]at

high solid fraction (circles) and from data of Mg3Al2Si3O12 by Lejeune (triangles)

[162] and other values at low solid fraction (squares) by Thomas [166] ................. 84

Figure 2.27 Experiment data of different particle size vs model prediction [167] .......... 85

Figure 2.28. The description of interaction between solid sphere and fluid particle ....... 87

Figure 3.1 Schematic diagram of furnace for viscosity measurement at high temperature

.................................................................................................................................. 91

Figure 3.2 Schematic diagram of crucible and spindle .................................................... 91

Figure 3.3 Schematic diagram of viscosity study at room temperature ........................... 92

Figure 3.4 (a) left, a photograph of phase equilibrium experiment. (b) Right, a schematic

diagram of a vertical tube furnace ............................................................................ 93

4.1 The linear relationship between EA and ln(A) ........................................................... 97

Figure 4.2 Comparison of the current viscosity model with others ............................... 101

Figure 4.3 Three model performance for 0 - 1 Pa.s, mean deviation for three models:

present model 12.5%, Zhang model 16.4% and Urbain model (1987 version) 16.3%

[131, 188]................................................................................................................ 102

Figure 4.4 Effect of MgO on viscosity of BF slag at 15 wt% Al2O3 and 1500 °C

predicted by the present model with comparisons to the experimental data [74] .. 103

Figure 4.5 Effects of Al2O3 concentration and temperature on slag viscosity at 40 wt%

SiO2 and 10 wt% MgO predicted by the present model with comparisons to the

experimental data of Gultyai [83], Hofmann [22] and Machin [68] ...................... 104

Figure 4.6 Comparison of viscosities for CaO-MgO-Al2O3-SiO2-TiO2 slag by Park [120]

and Liao [119] ........................................................................................................ 107

Figure 4.7 the model prediction vs experimental results of CaO-MgO-Al2O3-SiO2-TiO2

slag system of Park [120], Shankar [32] and present (A) left, present model and (B)

right, Urbain Model (1981 version) [132] .............................................................. 111

Figure 4.8 Increase of prediction deviation in CaO-MgO-Al2O3-SiO2-FeO system with

increasing FeO concentration by Bills [64] , Gorbachev [189], Higgins [190] and

present study ........................................................................................................... 112

Figure 4.9 The comparison of viscosity reduction ability of 8 minor elements on BF slag

viscosity .................................................................................................................. 113

Figure 4.10 Comparison of model prediction and Liao’s measurements [119] ............ 114

Figure 5.1 Interaction among Ca2+

cations, silica and alumina ..................................... 116

Figure 5.2 The linear relationship between EA and ln(A) .............................................. 118

Figure 5.3 The performance summary of viscosity models in, (i) full CaO-MgO-Al2O3-

SiO2 composition, (ii) BF slag composition and (iii): ladle slag composition ....... 123

Figure 5.4 Comparison between experimental viscosity and calculated viscosity by

present model (12.5% deviation), Zhang model (19.4 deviations) [145] and Urbain

model (19.3 % deviation) [131] .............................................................................. 124

Figure 5.5 Comparisons between model predictions and Gul’tyai [65] and Hofmann [22]

results, 1500 °C in the system CaO-MgO-Al2O3-SiO2 .......................................... 125

Figure 5.6 The linear relationship between EA and ln(A) for (A): SiO2-Al2O3-CaO and

SiO2-Al2O3-MgO system and ................................................................................. 126

Figure 5.7 Comparisons between experiment viscosity and model prediction in the

systems (A) SiO2-Al2O3-CaO, (B) SiO2-Al2O3-MgO, (C) SiO2-CaO, (D) SiO2-MgO

and (E) SiO2-Al2O3 ................................................................................................. 128

Figure 5.8 Effects of WCaO/WSiO2 and MgO on slag viscosity at 1500 °C and 15 Al2O3

by the present model in comparisons with the data from Kim [122], Gul’tyai [83]

and Machin’s [74] ................................................................................................... 129

Figure 5.9 The model prediction of the iso-viscosity diagram at 1500 °C and 15 wt.%

Al2O3 and experiment data of Gultyai [83], Li [150], and Machin [68, 74] ........... 130

Figure 5.10 Effects of WCaO/WSiO2 and temperature on slag viscosity at 5 wt.% MgO and

30 wt.% Al2O3 by present model in comparisons with Song’s data [107] ............. 131

Figure 5.11 The comparison between experimental viscosity and calculated viscosity

using Current, Urbain [131] and Zhang model [145]. ............................................ 139

Figure 5.12 40 wt% SiO2, 1500 oC for SiO2-CaO-“FeO” system by Chen [193], Bockris

[194] and Ji [114], 40 wt% SiO2, 1550 oC for SiO2-MgO-“FeO” system by Chen

[115], Ji [195] and Urbain [60] ............................................................................... 140

Figure 5.13 Comparisons of the viscosities between model predictions and experimental

data for different “FeO”-containing slags (in wt%) by Higgins [190]; Vyaktin [84]

and Machin [80]...................................................................................................... 141

Figure 5.14 Viscosity as a function of “FeO” at 1250 oC, base slag 52% SiO2, 13.3%

Al2O3, 29.3% CaO, 5.3% MgO by Higgins [190] .................................................. 142

Figure 6.1 Schematic diagram of equilibrium experiment settings ............................... 145

Figure 6.2 Typical deconvolution of Raman spectrum of a 52.6 mol% SiO2-47.4 mol%

CaO sample............................................................................................................. 150

Figure 6.3 the Raman spectrum of SiO2-CaO system, which covers the CaO/SiO2 ratio

from 0.55 to 1.1 ...................................................................................................... 155

Figure 6.4 the Raman spectrum of SiO2—MgO—CaO system under CaO/SiO2=1 and

1500 oC condition, which covers the different MgO concentrations. .................... 155

Figure 6.5 (a) left, the Raman spectrum of SiO2—Al2O3—CaO system under

CaO/SiO2=1 and 1500 oC condition, which covers the different Al2O3

concentrations. (b) Right, the peak deconvolution outcomes of left spectra .......... 156

Figure 6.6 The relative area occupancy of different peaks of (a) SiO2-CaO-MgO system

ranging of CaO/SiO2 =1, (b) right, relative area occupancy of different peaks of

SiO2-CaO-Al2O3 system ranging of CaO/SiO2 =1 ................................................. 157

Figure 6.7 Raman spectrum of 45 SiO2- 10 Al2O3- 45 CaO mol% sample at 1300, 1500

and 1600 oC and wollastonite [202] ....................................................................... 158

Figure 6.8 DP index again basicity of SiO2-CaO, SiO2-CaO-MgO, and SiO2-CaO-Al2O3

system ..................................................................................................................... 162

Figure 6.9 DP index against the estimated densities of slag samples ............................ 162

Figure 6.10 DP index of each Raman spectrum against the activation energy .............. 163

Figure 7.1 Schematic diagram of room temperature measurements .............................. 169

Figure 7.2 Schematic diagram of (a) left, high-temperature viscosity measurement (b)

right, equilibrium experiments ............................................................................... 170

Figure 7.3 The viscosity measurements of Baosteel and Jintang blast furnace slag

sample ..................................................................................................................... 176

Figure 7.4 The relative viscosity of oil-paraffin system at different solid fraction and

liquid viscosity at 25 oC .......................................................................................... 178

Figure 7.5 The suspension viscosity at different solid fraction and particle size at (a) top,

0.1 Pa.s liquid viscosity and (b) bottom, 1 Pa.s liquid viscosity ............................ 179

Figure 7.6 The temperature dependence on the oil-paraffin system suspension viscosity

(a) 0.05 liquid viscosity suspension at 5, 10, 15 and 20 vol% and (b) 15 vol%

suspension at liquid viscosity 0.05, 0.2 and 0.5 Pa.s by Wright [163] ................... 181

Figure 7.7 The measured torque at different rotational speed for (a) 5% solid fraction at

0.05 and 1 Pa.s silicon oil. (b) 10, 20 and 30 % solid fraction at 0.5 Pa.s silicon oil

................................................................................................................................ 182

Figure 7.8 The model prediction vs experimental results at (a) top, different models and

(b) bottom, 1 Pa.s liquid viscosity .......................................................................... 184

Figure 7.9 The model prediction vs experimental results of (a) top JingTang slag and (b)

bottom, Baosteel slag .............................................................................................. 185

Figure 7.10 The comparison between experimental data and model predictions by

Wright [163] and Wu [9] ........................................................................................ 188

Figure 7.11 The comparison of model prediction and other researchers results at (a)

room temperature by Chong [153] and Namburu [160], (b) high temperature by

Louise [159] and Wright [163] ............................................................................... 189

1

Chapter 1 : Introduction

1.1 Background Introduction

In the iron-making process, blast furnace (BF) is still the principle technology in the

production of pig iron, which contributed over 90% of pig iron [1]. As shown in Figure 1.1,

the iron ore, fuels and fluxes are fed from the top, flowed down and undergo the carbothermic

reduction with increasing temperature and carbonic gas. Molten pig iron and slag are tapped

from the bottom of the furnace. Molten oxides, known as slag, are composed of gangue

minerals and ash from fuels during the high-temperature smelting process. To achieve the

optimal processing, the chemical compositions of the slags are significantly varied over a

wide range. Viscosity, as one of the most important physical properties of the slag, has been

intensively studied in last decades. The ideal slag should have an appropriate viscosity, which

flows fluently and removes most of the gangue minerals.

Figure 1.1 Technical description of blast furnace ironmaking process [1]

The blast furnace slag is composed of four major components SiO2, CaO, Al2O3 and MgO [2].

The typical industrial blast furnace slag compositions are summarized in 错误!书签自引用

无效。.

Table 1.1 Composition range of blast furnace slag [1]

2

Major Constituents Mass% Minor Constituents Mass%

SiO2 30-40 TiO2 0-2

CaO 30-45 Na2O 0-0.3

Al2O3 10-20 K2O 0-0.7

MgO 5-10 CaO/SiO2 1-1.3

1.2 Research Gap

During the BF operation, slag viscosity plays a significant role in controlling the process,

which has a direct impact on the metal/slag separation efficiency and other operation benefits.

Understanding and controlling slag viscosity at different compositions and temperatures will

assist in improving operation efficiency and minimizing the energy usage.

Abundant studies have been conducted on the viscosity measurements and model simulation

in the past century for variable oxide systems. The viscosity measurement techniques were

continuously developed [3]. It was found that improper selection of crucible/spindle material

would significantly increase the measurement uncertainty and confirmed that use of graphite

crucible cannot report reliable viscosity data at high temperature [3]. Nowadays, the Mo

material replaced the graphite crucible to hold the molten sample. It is necessary to evaluate

the published viscosity data and mathematical models for fundamental study and industrial

application. The reliability of viscosity data from early publications (around 1950s) should be

critically reviewed to establish the database and determine the appropriate prediction range of

the existing viscosity models.

Different characterization techniques were utilized to determine the chemical and physical

properties of slags. The application of Raman spectroscopy can disclosure the vibration units

of molten slag, which can be interpreted the structure of silicate melts (amorphous glass

phase). Kim reported a mathematical correlation between the peak area of Raman peak and

the external physical properties, including density and viscosity [4]. However, the role of

Al2O3 was not well studied, which is necessary to utilize the Raman spectrum on the SiO2-

CaO-MgO-Al2O3 based slag (blast furnace slag) to investigate the silicate structure units.

In the blast furnace operations, some solid phases such as oxide precipitates, coke or Ti(CN)

can be present in the slag. In addition, the precipitation of solid particles was commonly

3

observed in iron, steel, copper and other pyrometallurgy process [5]. These solids can

significantly increase the viscosity of the slag causing operating difficulty. There is a research

gap that the solid impact on suspension was limited investigated under high-temperature

condition due to uncertainty.

1.3 Aim of the Study

There is an increasing focus on process optimization and energy usage efficiency of blast

furnace ironmaking. During the operation, slag viscosity plays a significant role in controlling

the process, which has a direct impact on the metal/slag efficiency. Understanding and

controlling slag viscosity at different compositions and temperatures will assist in improving

operation production, efficiency, minimizing energy usage.

Referring to the research gap, the aims of the study include:

1. Review the experimental methodologies, viscosity data, and models relevant to the blast

furnace slag in CaO-MgO-Al2O3-SiO2 system

2. Based on collected data and models, establish an accurate viscosity model to predict the

viscosity of blast furnace slag in CaO-MgO-Al2O3-SiO2 system

3. Research on the viscosity impact of minor elements on the blast furnace final slag in

CaO-MgO-Al2O3-SiO2 based system.

4. To improve the fundamental understanding of silicate structure, utilized the Raman

techniques to study the SiO2-CaO based system and determine its correlation with

external physical properties.

5. Study the solid impact on suspension systems under room and smelting temperature

regions.

4

Chapter 2 : Literature reviews

This section would introduce the reviewed literature, which includes the following sections.

The Section 2.1 introduced the viscosity measurement techniques under high temperature

condition, which would be utilized to evaluate the existing viscosity data to develop the

viscosity database of CaO-MgO-Al2O3-SiO2 system in Section 2.3. Section 2.4 is the

mathematical model review and evaluations for the slag of CaO-MgO-Al2O3-SiO2 system.

From section 2.2-2.4, it should be noted that the scoping of the viscosity study is fully liquid

slag at high temperature. The viscosity study of solid containing slag will be reviewed in the

Section 2.5.

1. The technical review of high-temperature viscosity measurement

2. The review of viscosity study of sub binary and ternary of SiO2-Al2O3-CaO-MgO system

3. The evaluation of the viscosity data of CaO-MgO-Al2O3-SiO2 system

4. The review and evaluation of existing viscosity model for CaO-MgO-Al2O3-SiO2 system

5. The review of experimental data and mathematical model of suspension system

2.1 The technical review of high-temperature viscosity measurement

Viscosity, one of the most important physiochemical properties of slag, has been theoretically

and experimentally investigated by abundant researchers over the last decades. The proper

measurement techniques could directly determine the measurements’ reliability. Therefore, in

the present section, the measurement techniques would be discussed for the preparation of

viscosity data evaluation in Section 2.3.

2.1.1 Liquid Viscosity Definition

In fully liquid, the viscosity is an internal property, which is defined as the internal friction of

a fluid. For example, as Figure 2.1 shown, assuming a liquid between two closely spaced

parallel plates, a force (F) is applied to top plate causes the fluid dragged in the direction of F

[6]. The applied force is communicated to neighboring layers of fluid, however, with

diminishing magnitude, the fluid motion will progressive decrease as further away from the

upper plate. In this system, the dynamic viscosity Ƞ of fluid can be determined using

Equation 2-1.

5

Figure 2.1 Laminar shear of fluid between two plates

Equation 2-1: Dynamic Viscosity Calculation Formula

Ƞ = τ𝑑𝑈𝑥

𝑑𝑈𝑧

Where τ is an applied shear force and dUx/dUz is the velocity decreasing gradient (also

called strain rate).

There are two major categories, Newtonian and Non-Newtonian fluid, which is differently in

the ratio of applied shear force and dUx/dUz [7]. The details of each category and example

were summarized in Table 2.1. It is known that the Newtonian fluid behavior linear

proportional relationship between shear stress and strain rate at a constant temperature, which

reported a fixed viscosity for that fluid as shown in Figure 2.2. Other fluids, called non-

Newtonian fluid, have a polynomial relation between shear stress and strain rate, which

indicated that the viscosity is a variable parameter based on the shear rate.

6

Figure 2.2 Shear stress vs strain rate of Newtonian liquid and non-Newtonian fluid

Table 2.1 Category of different types of fluids

Category Description Example

Newtonian Fluid Liquid whose viscosity keep

constants with the rate of the shear

strain

Molten slag

Water

Non-Newtonian

Fluid

Shear Thinning

Fluid

Liquids whose viscosity increase

with the rate of shear strain

Modern paints

Ketchup

Shear Thickening

Fluid

Liquids whose viscosity decreases

with the rate of shear strain

Corn starch

Silica nanoparticles in

polyethylene glycol

Bingham Plastics Behave as a solid at low stresses

but flow as a viscous fluid at high

stresses

Mayonnaise

Toothpaste

7

A fully liquid slag belongs to the Newtonian fluid at constant condition (pressure,

temperature and etc) [8]. This characteristic had been practically confirmed by researchers

through the calculation of viscosity at the different shear rate.

However, the solid containing slag was reported a different fluidic rheology. For silicate

melts, at high-temperature condition, Wu discovered that the slag will become shear thinning

fluid above 15% solid fraction [9]. The viscosity of suspension system will be reviewed in

Section 2.5.

2.1.2 Viscometer

The viscometer is an instrument for measuring liquid viscosity under steady flow condition.

At high temperatures, it is practically difficult to examine and observe the relevant rheology

property of slag/matte. In pyro-metallurgical field, generally, the velocity of liquid slag and

matte is slow and steady, which can be assumed as an ideal flow.

At high-temperature condition, a technique that could accurately measure the viscosity at

wide slag composition is still a challenging area in the pyro-metallurgy field. In this section,

the common methods of viscosity measurement technique of molten slag will be reviewed

and compared.

From the existing literature, the following viscometers are often used in viscosity

measurement of molten slag, which are:

Rotational Spindle Viscometer

Falling Viscometer

Oscillating Viscometer

Two extra viscometers were reviewed, which is specifically to the certain liquid system:

Capillary Viscometer

Ultrasonic Viscometer

The major features of above viscometer were summarized in Table 2.2.

8

Table 2.2 The Summary of Reviewed Viscometers

Viscometer Section Description Disadvantage

Rotational 2.1.2.1

A wide viscosity measurement ranges cover 10-4

-

107 Pa.s. It require high accuracy torque

measurements, hard to clean thick fluids

The major disadvantage is the interaction between rotational

cylinder and crucible wall, which will reduce the measured torque

accuracy [10].

Falling Body 2.1.2.2

A wide viscosity measurement ranges cover 10-3

-

107 Pa.s, simple, good for high temperature and

pressure, not good for viscoelastic fluids.

The major disadvantage is the thermal expansion of falling

ball. And it required a certain distance to achieve freefalling,

which is practically difficult at high-temperature condition [11].

Oscillating 2.1.2.3

A wide viscosity measurement ranges covers 10-5

-

10-2

Pa.s, good for low viscosity liquid, need constant

and steady instrument

The major disadvantage is similar as falling ball viscometer

shown above [11].

Capillary 2.1.2.4

Simple, very high shears and range, but very

inhomogeneous shear. The capillary viscometer is

often utilized for high viscous and non-Newtonian

fluid.

The capillary viscometer could not control the PO2 during

viscosity measurement, which is not suitable for high-temperature

condition [12].

Ultrasonic 2.1.2.4

Good for high viscosity fluids, small sample

volume, gives shear and volume viscosity, and elastic

property data.

The ultrasonic viscometer could not provide accurate and

precise measurements at high-temperature condition [18].

9

2.1.2.1 Rotational Viscometer

The rotational viscometer is the most widely used viscometer in nowadays research. The

basic schematic diagram is shown in Figure 2.3. The bob located in the central position of the

crucible and rotated at a constant rate. The resistance force from fluid was recorded as torque.

The torque at known rotation rate was measured to calculate liquid viscosity as Equation 2-2.

Equation 2-2: Viscosity calculation using data from rotational viscometer [13]

Ƞ =𝜏

𝛾 ∗ 𝐾

Where Ƞ is the slag viscosity, 𝜏 is the measured torque, 𝛾 is the rotational speed and 𝐾 is the

instrument parameter.

Figure 2.3 Schematic diagram of rotational cylinder viscometer

It has found that reactive force from the bob rotation, called edge effect, reduce the reliability

of the measured torque, which causes that the calculated viscosity data inconsistent with

shear rate [14]. Different shapes of bobs were designed to minimize the interaction, which

improve the measured torque for accurate viscosity measurements. The most common

cylinder shape includes the cylinder, disc, cone, spindle and etc., which were demonstrated in

Figure 2.4. Other shapes were developed, such as spindle and thin disc to minimize the wall

edge effect [13].

10

Figure 2.4 geometry for rotational bob, (a) cylinder, (b) cylinder, (c) cone, (d) cone, (e)

parallel plate (f) parallel plate

In summary, it is widely accepted that rotational viscometer is mostly used and reliable

viscometer, which covers a wide range from 10-4

to 107 Pa.s. The major physical uncertainty

of rotational viscometer is the edge effect causing by the settings of container and bob, which

has been considered and minimized from Chen’s research [13]. And the major chemical

uncertainty generally is from the reaction among molten slag, crucible, spindle, and

atmosphere. The post-experimental analysis is significantly necessary to ensure the viscosity

measurement reliability, such as examine the slag sample concentration and container/sensor

condition.

2.1.2.2 Falling-Body Viscometer

Falling-Ball viscometer

The falling-ball viscometer is one of the earliest developed methods to determine the

viscosity of a Newtonian fluid. In this method, as Figure 2.5 shown, a sphere is allowed to

fall freely a measured distance through a viscous liquid medium and its velocity is measured.

The viscosity can be measured directly through the falling velocity as Equation 2-3 shown.

Equation 2-3: Viscosity Formula of Falling Sphere Method [11]

Ƞ = 2𝑔𝑟2(𝜌𝑠 − 𝜌𝑙)

9𝑈

Where Ƞ is the slag viscosity, g is the specific gravity, r is the effective radius of the falling

sphere, 𝜌𝑠 is the density of sphere, 𝜌𝑙 is the density of liquid and U is the falling velocity.

11

Figure 2.5 Schematic diagram of the falling sphere viscometer

Counter-balanced Viscometer

The working mechanisms of counter-balance viscometer are similar as the falling-ball

viscometer. As Figure 2.6 shown, a standard weight is put on one arm of balance and crucible

containing liquid slag is set in another arm inside the furnace. The viscosity of liquid slag is

calculated from the movement of weight through a certain fixed distance. The improvement

from counter-balanced viscometer is that the flexible control of settling rate of falling items,

which improve the measurements reliability comparing to falling ball viscometer [15].

Figure 2.6 Counter balance viscometer [15]

12

There are several disadvantages involved using falling body viscometer at the high-

temperature condition. The falling item requires a certain distance to reach a constant speed,

called free falling velocity. However, the hot zone of the furnace is generally too short for

freefalling of the ball, which could not determine the reliable velocity. It practically increased

the difficulty of crucible settings to reach steady position and temperature. Another major

disadvantage is that the thermal expansion of the ball materials. Riebling determined that the

thermal expansion of the falling ball is able to cause 10-100 Pa.s uncertainty in viscosity

measurements, which is dependent on the ball material and settle length [11].

2.1.2.3 Oscillating Viscometer

The oscillating viscometer is another technique used to measure the slag viscosity of the

small sample. As Figure 2.7 shown, when the piston is contained within the fully liquid

vessel and oscillated about its vertical axis, the motion of piston will cause a gradual damping.

The damping effects arise as a result of the viscous coupling of the liquid to the piston. From

observations of the amplitudes and time periods of the oscillations, a viscosity of the liquid

can be calculated. The oscillating method is best suited for use with low values of viscosity

within the range of 10-5

Pa.s to 10-2

Pa.s [16]. The closed design has made this design popular

on measuring low viscosity liquid, such as pure metals.

Figure 2.7 Schematic diagram of the oscillating piston viscometer

13

2.1.2.4 Other Viscometers

Capillary Viscometer

The capillary viscometer is based on the fully developed laminar tube flow theory (Hagen-

Poiseuille flow) and is shown in Figure 2.8. The capillary tube length is much larger than its

diameter; therefore, the impact of entrance flow on viscosity measurement can be neglect.

The shear stress and strain rate can be measured from mathematical expression of tube

diameter and length, which used to calculate liquid viscosity as Equation 2-4. The main

advantage of capillary over rotational viscometers is low cost and the ability to achieve high

shear rates, even with high viscosity samples. The main disadvantage is high residence time

and variation of shear across the flow, which might change the structure of complex test

fluids. In addition, because of its long tubes, capillary viscometer does not suit viscosity

measurement of high-temperature melts [15].

Equation 2-4. Viscosity Formula of Capillary Viscometer [17]

𝑛 =𝜏

𝛾=

∆𝑃 ∗ 𝐷4𝜋

128𝑄𝐿

Where P, D, Q, and L are pressure, tube diameter, fluid volume flow and tube length

respectively.

Figure 2.8 Schematic diagram of the capillary viscometer

14

Ultrasonic viscometer

The ultrasonic viscometer is a newly developed technique to measure viscosity based on

wave absorption of liquid. Liquid viscosity plays an important role in the absorption of

energy of an acoustic wave traveling through a liquid. The mechanical vibrations in a

piezoelectric are generated and go through the liquid sample and will be received by another

similar transducer in the end. The decay rate and amplitude of wave will be analyzed to

calculate fluid viscosity. Ultrasonic methods have not been and are not likely to become the

mainstay of fluid viscosity determination because they are more technically complicated than

conventional viscometry techniques [18]. Ultrasonic absorption measurements play a unique

role in the study of volume viscosity as providing volume viscosity data.

2.1.3 Post-Experimental Analysis

The experimental method used to characterize the internal structures of silicate melts can be

classified in terms of a) Composition analysis, b) Surface morphology and c) internal

structure. Table 2.3 provides a summary of several experimental techniques that have been

used to study the complex silicate system (molten slag). The methods described in Chapter

2.1.3.1 are commonly used to determine the composition of silicate. Chapter 2.1.3.2 outline

the methods for surface morphology study. Chapter 2.1.3.3 introduce the techniques for

internal structure analysis of silicate.

Table 2.3 Summary of post-experiment techniques

Chapter Method Exciting

Radiation

Application

2.1.3.1 EDS Focus beam of

electron

Obtain the composition of metal

element

EPMA-WDS Focus beam of

electron

Obtain the composition of most

elements except [O]

ICP-MS Pulse from

magnetic field

Obtain the composition of most

elements after calibration of that

15

element

2.1.3.2 SEM Focus beam of

electron

Surface morphology

TEM Focus beam of

electron

Surface morphology

Crystal information

and etc.

2.1.3.3 Raman & FTIR Laser light Stretch and vibration of internal

structure

XRD X-ray Crystal structure determination

NMR Pulse from

magnetic field

Magnetic properties of atomic

nuclei. Order-disorder

2.1.3.1 Composition Analysis

The composition analysis of post-experimental sample confirmed the reliability of viscosity

data. Three techniques were widely used: a) EDS, b) EPMA and c) ICP.

Energy Dispersive X-ray Spectroscopy (EDS)

EDS is an analytical technique used for the elemental analysis of metals or chemical

characterization of a sample [19]. During operation, a high-energy beam of charged is

focused into the sample, which excites the ground state electrons. The excited electrons at

inner shell may eject from the shell while creating an electron-hole where the electron was.

An electron from an outer, higher energy shell then fills the hole, and the energy difference

between electrons may be released in the form of an X-ray. The number and energy of the X-

rays can be measured by an energy dispersive spectrometer and recorded. The quantitative

analysis can be performed by counting the x-rays at the characteristic energy levels for each

element.

The accuracy of EDS spectrum can be affected by various factors. There are several common

issues of X-ray techniques. These X-rays are emitted in any direction, and so they may not all

escape the sample. The likelihood of an X-ray escaping the specimen, and thus being

16

available to detect and measure, depends on the energy of X-ray and the amount and density

of material it has passed through, which reduced accuracy in inhomogeneous and rough

samples. For major elements, it is usually possible to obtain a statistical precision of 3%

relative error [20]. In the review of viscosity study of CaO-MgO-Al2O3-SiO2, 7 authors

reported the composition analysis utilizing EDS [21-27].

EPMA-WDS

The Electron Probe Micro Analyser (hereinafter, “EPMA”) is an instrument to for elemental

analysis, by irradiating electron beams onto the substance surface and measuring the

characteristic of X-ray [28]. In the operation, the electrons emitted from the electron source

are accelerated at a certain accelerating voltage and collimated through electron lenses. When

accelerated electrons hit a specimen, in addition to the X-rays, particles and electromagnetic

waves carrying various kinds of information are emitted, which is also called wavelength-

dispersive X-ray spectroscopy (WDS). With EPMA, signals such as the characteristic-X-rays,

secondary electrons, backscattered electrons, etc. are detected by the appropriate detectors

and that information is utilized to find the area of interest on a specimen, and for analysis.

Quantitatively, EPMA-WDS report more accuracy elemental analysis than EDS [20].

Comparing their energy resolution, a Si Ca X-ray line on an EDS system will typically be

between 160 eV wide. On a WDS system, this same X-ray line will only be about 15 eV wide.

This means that the amount of overlap between peaks of similar energies is much smaller on

the WDS system. Therefore, the reliability and accuracy of WDS are overwhelming the EDS

as from pure to multi-component system. Another major problem with EDS systems is their

low court rates. Typically, a WDS system will have a count rate that 10 times of an EDS

system. In the review of viscosity study of CaO-MgO-Al2O3-SiO2, only 2 authors reported

the composition analysis utilizing EPM--WDS technique [29, 30].

Inductively Coupled Plasma Mass Spectrometry (ICP)

The inductively coupled plasma mass spectrometry, known as ICP, is a type of mass

spectrometry which is capable of detecting metals and several non-metals at concentrations as

low as 10-15 (limited series) [31]. As Figure 2.9 shown, when plasma energy is given to an

analysis sample from outside, the component elements (atoms) are excited. When the excited

17

atoms return to low energy position, emission rays (spectrum rays) are released and the

emission rays that correspond to the photon wavelength are measured. The element type is

determined based on the position of the photon rays, and the content of each element is

determined based on the wave intensity. To generate plasma, first, argon gas is supplied to

torch coil, and high-frequency electric current is applied to the work coil at the tip of the

torch tube. Using the electromagnetic field created in the torch tube by the high-frequency

current, argon gas is ionized and plasma is generated. This plasma has high electron density

and temperature (10000K) and this energy is used in the excitation-emission of the sample.

Solution samples are introduced into the plasma in an atomized state through the narrow tube

in the center of the torch tube. In the review of viscosity study of CaO-MgO-Al2O3-SiO2,

only 4 authors reported the composition analysis utilizing ICP technique [32-35].

Figure 2.9 Schematic diagram of ICP [31]

2.1.3.2 Surface Morphology Study

The surface morphology provides a visible information on the structure of the silicates. Two

most common techniques are SEM and TEM.

Scanning Electron Microscope

A scanning electron microscope (SEM) is a type of electron microscope that produces images

of a sample by scanning it with a focused beam of electrons. The electrons interact with

atoms in the sample, producing various signals that contain information about the sample's

surface topography and composition. The electron beam is generally scanned in a raster

https://en.wikipedia.org/wiki/Electron_microscope

https://en.wikipedia.org/wiki/Electron

https://en.wikipedia.org/wiki/Topography

https://en.wikipedia.org/wiki/Raster_scan

18

scan pattern, and the beam's position is combined with the detected signal to produce an

image. SEM can achieve resolution better than 1 nanometer.

The common application of SEM is to examine the surface of post-experiment sample. In the

viscosity study of fully liquid slag, it is expected that only one phase existing, which could be

confirmed by SEM image. Different phase can be observed with the application of different

light. In the study of alumina silicate melts, as an example, the application of polarized light

exposure the crystal part within samples as Figure 2.10 shown. The crystals appear as well-

rounded and homogeneously distributed, which have nearly the same size [36].

Figure 2.10 Spherulite of aluminous enstalite under (a) natural and (b) polarized light after

the viscosity measurements [36]

https://en.wikipedia.org/wiki/Raster_scan

19

Transmission Electron Microscope

Transmission electron microscopy (TEM) is a microscopy technique in which a beam

of electrons is transmitted through an ultra-thin specimen, interacting with the specimen as it

passes through it. An image is formed from the interaction of the electrons transmitted

through the specimen. The image of TEM is formed as electrons went through the sample,

which can obtain many characteristics of the sample, such as morphology, crystallization, and

stress. On the other hand, SEM shows only the morphology of samples.

In Vail study, the microstructure of various polymer-organically modified layered silicate

hybrids, synthesized via static polymer melt intercalation, is examined with transmission

electron microscopy [37]. As Figure 2.11 shown, in these hybrids, individual silicate layers

are observed near the edge, whereas small coherent layer packets separated by polymer-filled

gaps are prevalent toward the interior of the primary particle. In general, the features of the

local microstructure from TEM give useful detail to the overall picture and enhance the

understanding of various thermodynamic and kinetic issues. However, few study was

constructed on the glass form of silicate melts.

Figure 2.11 Bright-field TEM image [37]

https://en.wikipedia.org/wiki/Microscope


20

2.1.3.3 Internal Structure Study

In the past decades, abundant experimental and theoretical studies have been carried out so

far on the determination of silicate structure, thermodynamic and mechanical properties.

Many spectroscopic methods have been developed to determine the structure of slags and

distinctively identify the ionic structural units composing them. However, due to amorphous

properties, novel methods continue to evolve to elucidate the structure of the ionic slag

structure for metallurgical slag, many well-proven spectroscopic methods has been developed

and are now widely applied to correlate the viscous behavior with structure melts at high

temperature. These methods include Raman spectroscopy, NMR, and XRD, which will be

reviewed in the present section. Based on the spectroscopic results, the network structure

theory was proposed, developed and mostly accepted by present researchers to describe the

silicate slag structure.

Raman Spectroscopy

Raman spectroscopy is a spectroscopic technique used to observe vibrational, rotational, and

other low-frequency modes in a system. It relies on inelastic scattering, or Raman scattering,

of visible laser light near infrared range. The laser light interacts with molecular vibrations

other excitations in the system, resulting in the energy of the laser photons being shifted up or

down. The shift in energy gives information about the vibrational modes in the system.

Although, the silicate glass is an amorphous state; it is becoming popular to utilize Raman to

disclosure the structural information of molten slag of a multi-component system. The Raman

investigation had been constructed for pure silica glass, CaO-SiO2, CaO-Al2O3-SiO2 and

other multicomponent system by researchers. Several bands were detected by Raman

Spectrum in the fused silica glass (amorphous phase) in the shift range of 0-1500 cm-1

as

Figure 2.12 shown. The two major bands located in the region of 300-600 cm-1

and 800-900

cm-1

. Sharp peaks appear in the position of 390, 420, 510, 560 and 590 cm respectively. The

peaks in the 400-600 cm-1

was generally assigned to Si-O-Si bond-bending vibration and

formed the silicate network referring to its area.

Galeener and co-workers proposed another theory by applying the energy minimization

argument method [38]. The bond angle referring to peak D1 and D2 were calculated and

https://en.wikipedia.org/wiki/Spectroscopy

https://en.wikipedia.org/wiki/Inelastic_scattering

https://en.wikipedia.org/wiki/Raman_scattering

https://en.wikipedia.org/wiki/Infrared

21

suggested that the 606 and 495 peak can be assigned to 3-fold and a 4-fold ring of tetrahedral

SiO4 respectively [38]. The ring structure were mentioned and discussed by later researchers

[39-41]. However, there is limited experimental evidence for this theory.

Figure 2.12 Raman spectrum of silica glass [38]

The Raman spectrum of CaO-SiO2 system was investigated to understand the impact of CaO

addition into amorphous SiO2 [42, 43]. Comparing the spectrum of pure SiO2 glass (Figure

2.12) and CaO-SiO2 system (Figure 2.13), the peaks located at 500 cm-1

shrinks and 800-

1200 cm-1

enlarged, which indicated the broken of silica tetrahedral network. The addition of

CaO would break SiO4 tetrahedral network and form different [Ca]2+

[44]- combinations,

which can be assigned to the peaks at 800-1200 cm-1

. For Raman spectrum region of 800 to

1200 cm-1

, the bands were deconvoluted to several peaks for analysis, which reflects different

silicate-oxide units [43]. As Figure 2.13 shown, with the decreasing of Ca/Si ratio from 1.4 to

0.5, the intensity of peak M shrinks and peak C significantly enlarged. Through analysis

multi-components, four peaks were assigned and summarized in the Table 2.4. After the peak

deconvolution, the structural can be qualitatively determined by the ratio of non-bridging

oxygen/Si (NBO/Si).

22

Figure 2.13 The Raman spectrum of SiO2-CaO system at different Ca/Si ratio [43]

The structure of silicate glasses was continually investigated utilizing Raman spectra [41, 43,

45-48]. Park proposed a research of quantitative structural information such as the relative

abundance of silicate discrete anions (Qn units) and the concentration of three types of

oxygens, viz. free-, bridging- and non-bridging oxygen can be obtained from micro-Raman

spectra of the quenched CaO-SiO2-MgO glass samples [41]. Various transport properties

such as viscosity, density, and electrical conductivity can be expected as a simple linear

function of ‘‘ln (Q3/Q2),’’ indicating that these physical properties are strongly dependent on

a degree of polymerization of silicate melts [41].

Table 2.4 the assigned peaks after peak deconvolution in the region 800-1200 cm-1

[41]

Peak Raman

Shift

(cm-1

)

Structural

Description

NBO/Si Structural

Units

23

Q1 850-880 SiO4 with zero

bridging oxygen

4 Monomer

Q2 900-930 Si2O5 with one

bridging oxygen

3 Dimer

Q3 950-980 Si2O6 with 2

bridging oxygen

2 Chain

Q4 1040-

1060

Si2O7 with three

bridging oxygen

1 Sheet

X-ray diffraction

X-ray crystallography is a technique used for determining the atomic and molecular structure

of a crystal, in which the crystalline atoms cause a beam of incident X-rays to diffract into

many specific directions. By measuring the angles and intensities of these diffracted beams,

a crystallographer can produce a three-dimensional picture of the density of electrons within

the crystal. From this electron density, the mean positions of the atoms in the crystal can be

determined, as well as their chemical bonds, their disorder, and various other information.

On 1968, Mozzi utilized x-ray diffraction to analysis the vitreous silica and reported that the

Si-O distance is around 1.62 A; while the Si-O-Si angle is approximately 144o [49]. As

Figure 2.14 shown, the calculated spectrum agreed with the experimental values for the first

three peaks.

https://en.wikipedia.org/wiki/Crystal

https://en.wikipedia.org/wiki/Atom

https://en.wikipedia.org/wiki/X-rays

https://en.wikipedia.org/wiki/Diffraction

https://en.wikipedia.org/wiki/Crystallography


https://en.wikipedia.org/wiki/Chemical_bond

https://en.wikipedia.org/wiki/Entropy

24

Figure 2.14 The pair distribution for the pure SiO2. A is the experimental curve, B is the

calculated curve [49]

A high-temperature XRD technique has been carried by Waseda and Toguri for in-situ XRD

measurements, which confirm the similarity of the melts structure to the corresponding

glasses [50]. However, because of the amorphous materials, it is difficult to gather useful

information from CaO-MgO-Al2O3-SiO2 system. A limited study was performed in the fully

liquid system.

Nuclear Magnetic Resonance Spectroscopy

Nuclear magnetic resonance spectroscopy, most commonly known as NMR spectroscopy, is

a research technique that exploits the magnetic properties of certain atomic nuclei. This type

of spectroscopy determines the physical and chemical properties of atoms or the molecules in

which they are contained. It relies on the phenomenon of nuclear magnetic resonance and can

provide detailed information about the structure, dynamics, reaction state, and chemical

environment of molecules. The intramolecular magnetic field around an atom in a molecule

changes the resonance frequency, thus giving access to details of the electronic structure of a

molecule and its individual functional groups.

MMR spectroscopy has been used extensively, similar to Raman spectroscopy in the

identification of silicate melts structure. 29Si and 27 Al elements were selected for analysis

of silicate melt slag. Most of the binary silicate based slag were investigated using 29

Si NMR.

In the structural investigation of the SiO2-Na2O system by Maekawa, as shown, the peak

deconvolution was utilized to quantitatively analysis the correlation between structures and

composition, which theoretically determined that the modify ability decreased as Li+>Na

+>K

+

https://en.wikipedia.org/wiki/Research

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https://en.wikipedia.org/wiki/Atomic_nucleus

https://en.wikipedia.org/wiki/Spectroscopy

https://en.wikipedia.org/wiki/Atom

https://en.wikipedia.org/wiki/Molecule

https://en.wikipedia.org/wiki/Nuclear_magnetic_resonance

25

at the same basic oxide concentration [51]. As shown in Figure 2.15, this theoretical

discovery was confirmed from the experimental measurement by Kim in the CaO-MgO-

Al2O3-SiO2-Na2O/K2O system [52].

Figure 2.15 (a) left,

29Si NMR spectra of SiO2-Na2O glasses [52]

On 1970, Masson utilizes polymer theory to estimate the molecular size in binary silicate

melts [53]. As Figure 2.16 shown, the derived results were in good agreement with

experimental spectrum over the entire range of compositions up to the maximum degree of

poly utilized NMR to obtain the polymerization degree allowed by the theory in the SiO2-

SnO binary system.

26

Figure 2.16 Activity of SnO plotted against mole fraction of SiO2 for the SiO2-SnO system at

1100 oC. Kozuka experimental data and 1) Masson prediction, 2) Flory expression k11=2.55.

And 3) Flory expression with k11=1.443 [53]

2.2 The review of viscosity data of sub binary, ternary of CaO-MgO-Al2O3-SiO2 system

A critical review of viscosity data is important for industrial application and fundamental

research. In the present section, a careful review of experimental method and viscosity data

will be demonstrated first for the binary and ternary of SiO2-CaO-Al2O3-MgO system in

section 2.2.1 and 2.2.2 respectively. In Section 2.2.3, the viscosity study of the minor element

on blast furnace slag, which includes TiO2, CaF2, MnO, FeO and etc, were reviewed as well.

Please note, only the quaternary system viscosity data of CaO-MgO-Al2O3-SiO2 were

carefully reviewed and evaluated in the Section 2.3. The viscosity data of other systems were

collected and utilized as supporting information of the viscosity database, which improved

the understanding of the viscosity impact of oxide on silicate network.. In the Section 2.2.4,

the evaluation criteria will be introduced and utilized to select reliable data for the SiO2-CaO-

Al2O3-MgO system.

2.2.1 Binary System

2.2.1.1 SiO2-CaO

SiO2 and CaO are the two major components for CaO-MgO-Al2O3-SiO2 ironmaking slags,

which have been investigated by 5 researchers on a wide composition and temperature ranges,

which is summarized in Table 2.5.

27

Table 2.5 Summary of viscosity study at binary system SiO2-CaO

Composition

(wt%)

Viscosity

(Pa.s)

Temperature

oC

Methodology Description

Bockris [54] 45-75% SiO2

25-55% CaO

0.02-2.38 1400-2120 Rotational viscometer

Graphite crucible

Hofmaier [22] 45-75% SiO2

25-55% CaO


Ar atmosphere

Kozakevitch [55] 55-75% SiO2

25-45% CaO


Ar atmosphere

Licko [56] 56-63% SiO2

37-44% CaO

0.15-2.38 1400-1700 Falling ball viscometer

Urbain [57] 45-75% SiO2

25-55% CaO


Mo crucible and bob

Ar atmosphere

2.2.2.2 SiO2-Al2O3

For SiO2-Al2O3 system, the addition of Al2O3 also reduced the viscosity compared to pure

SiO2.

However, the reduction ability of Al2O3 is lower than CaO and MgO content.

3 types of research of viscosity measurements on this system have been constructed. The

methodology and viscosity ranges are shown in Table 2.6.

Table 2.6 Summary of viscosity data of SiO2-Al2O3 system

Composition

(wt%)

Viscosity

(Pa.s)

Temperature

oC


28

Elyutin [58] 93-68% SiO2

7-32% Al2O3


Ar atmosphere

Kozakevitch

[59]

45-55% SiO2

45-55%

Al2O3


Ar atmosphere

Urbain [57] 23-91% SiO2

9-77% Al2O3

0.04-

8000

1650-2200 Rotational viscometer

2.2.2.3 SiO2-MgO

In the SiO2-MgO system, similar to SiO2-CaO system, the addition of MgO significantly

reduced the slag viscosity compared to pure SiO2. In addition, by comparing of CaO and

MgO at same condition, it is found that CaO has stronger reduction ability than MgO. At

1800 oC, the viscosity of SiO2-MgO is slightly higher than SiO2-CaO system at various silica

concentration, which indicated that the modify ability of CaO is stronger than MgO at fixed

condition [60].

3 types of research of viscosity measurements on this system have been constructed. The


Table 2.7 Summary of viscosity data of SiO2-MgO system

Composition

(wt%)

Viscosity

(Pa.s)

Temperature

oC


Bockris [54] 55-62% SiO2

38-45% MgO


Ar atmosphere

Hofmaier [61] 56% SiO2

44% MgO


Ar atmosphere

29

Urbain [60] 55-65% SiO2

35-45% MgO


Mo crucible

Ar atmosphere

Review of the viscosity measurements in SiO2-CaO-MgO ternary system by Licko shows that

the replacement of CaO by MgO will reduce the slag viscosity as shown in Figure 2.17 (a).

At 1500 °C, 40 and 50 wt% SiO2 condition, the replacement of MgO by CaO can cause

server viscosity reduction, which indicated the CaO has stronger network modify ability than

MgO. The viscosity measurements by Brokris of SiO2-CaO and SiO2-MgO binary system

support this conclusion as Figure 2.17 (b) shown. Under same basic oxide concentration, the

viscosity of SiO2-CaO system is larger than the SiO2-MgO system at 1850 oC. The viscosity

different between SiO2-CaO and SiO2-MgO system decreased above 50 wt% basic oxide

concentration; because the viscosity impact of CaO reduced at high concentration.

Figure 2.17 isovicosity data by Licko in SiO2-CaO-MgO system at 1500 °C at 40 wt.% and

50 wt.% SiO2 [56](b) The viscosity data of Bockris of SiO2-CaO and SiO2-MgO system at

1750 °C [54]

2.2.2 Ternary System

2.2.2.1 SiO2-CaO-Al2O3

SiO2-Al2O3-CaO ternary system is one of the pseudo-quaternary system; such as CaO-MgO-

Al2O3-SiO2 and SiO2-Al2O3-CaO-FeO. The study of this ternary system directly supports the

quaternary phase study of ironmaking slag.

30

The role of Al2O3 in silicate melts is amphoteric. From Saito, at SiO2/CaO=0.3, the addition

of Al2O3 has a negative impact on the slag viscosity at 1800 oC [62]. However, by Leiba’s

study, it has been found that at the low SiO2/CaO ratio, the addition of Al2O3 has a positive

impact on the viscosity and vice versa [63]. At different SiO2/CaO ratio, the amphoteric

behavior of Al2O3 was studied in terms of its structure unit [AlO4]. The silicate structure

details will be reviewed in the later section.

15 researchers of viscosity measurements on this system have been constructed. The


Table 2.8 Summary of SiO2-Al2O3-CaO viscosity study

Composition

(wt%)

Viscosity

(Pa.s)

Temperature

oC

Bills [64] 40-50% SiO2

15-20% Al2O3

35-40% CaO

0.8-28.1 1250-1500


20-50% Al2O3

10-30% CaO

0.04-357 1500-2080

Urbain [60] 20-70% SiO2

20-50% Al2O3

10-40% CaO

0.03-292 1300-2180

Gultyai [65] 30-55% SiO2

10-20% Al2O3

35-50% CaO

0.27-13.35 1250-1550

Johannsen [66] 50-70% SiO2

10-27% Al2O3

4-1520 1200-1450

31

10-30% CaO

Kato [67] 32-57% SiO2

10-35% Al2O3

30-47% CaO

0.24-6.9 1320-1500

Kita [27] 35-50% SiO2

15-30% Al2O3

30-35% CaO

1.3-25.6 1305-1500

Kozakevitch [59] 10-60% SiO2

10-65% Al2O3

10-60% CaO

0.04-4.24 1450-2000

Leiba [63] 30-32% SiO2

13-21% Al2O3

50-54% CaO

0.4-9.3 1450-1600

Machin [68] 30-70% SiO2

5-40% Al2O3

10-50% CaO

0.3-16300 1150-1500

Rossin [69] 27% SiO2

29% Al2O3

43% CaO

0.09-0.68 1550-1985

Saito [62] 30-70% SiO2

5-40% Al2O3

10-50% CaO

0.06-0.36 1400-1600

Scarfe [70] 43% SiO2

37% Al2O3

2.15-36.6 1375-1625

32

20% CaO

Solvang [71] 25-47% SiO2

13-36% Al2O3

30-43% CaO

0.3-2.75*1011

780-1550

Taniguchi [72] 43% SiO2

37% Al2O3

20% CaO

4.78-7.94*1012

845-1580

2.2.2.2 SiO2-Al2O3-MgO

Similar to Al2O3-CaO-SiO2 ternary system, SiO2-Al2O3-MgO is another important pseudo-

quaternary, which supports viscosity study of the quaternary system. The Al2O3 will

contribute a positive impact on the viscosity at the low SiO2/MgO ratio and vice versa.

8 researchers of viscosity measurements on this system have been constructed. The


Table 2.9 Summary of viscosity study at SiO2-Al2O3-MgO system

Composition

(wt%)

Viscosity

(Pa.s)

Temperature

oC


20-55% Al2O3

8-22% MgO

0.03-257 1500-2120

Johannsen [66] 65-68% SiO2

16-18% Al2O3

13-19% MgO

0.04-0.33 1300-1450

Lyutikov [73] 50-60% SiO2 0.17-11.6 1400-1800

33

10-35% Al2O3

9-40% MgO

Machin [74] 60-65% SiO2

10-25% Al2O3

10-30% MgO

2-1240 1250-1500

Mizoguchi [75] 50-65% SiO2

9-32% Al2O3

15-30% MgO

54-63 1500-1575

Riebling [76] 43-71% SiO2

11-40% Al2O3

8-32% MgO

0.33-148 1500-1720

Toplis [77] 45-73% SiO2

17-41% Al2O3

7-16% MgO

1.34-408 1400-1640

Urbain [60] 20-71% SiO2

20-55% Al2O3

9-22% MgO

0.039-169.5 1530-2115

Zhilo [78] 47-56% SiO2

12.5-39% Al2O3

19-32% MgO

0.038-6 1400-1675

2.2.2.3 Conclusion

The viscosity data of binary and ternary system were utilized as the supporting information

for the SiO2-CaO-Al2O3-MgO system. The role of metals oxide can be empirically

determined from the collected viscosity data at constant condition (temperature and pressure),

34

which is summarized in Table 2.10. The network theory would be demonstrated in the section

2.3.4, which explains the fundamental mechanisms of oxide impact on pure silica.

Table 2.10 Viscosity impact of oxide in their binary and ternary system with silica

Viscosity Impact

Binary Ternary

SiO2 Positive Positive

Al2O3 Positive Negative at low (CaO+MgO) content

Positive at high (CaO+MgO) content

CaO Negative Negative

MgO Negative Negative

2.3 Evaluation of Quaternary system CaO-MgO-Al2O3-SiO2

The CaO-MgO-Al2O3-SiO2 quaternary system is the four major components of blast furnace

final slag. 3135 viscosity data for 607 compositions in this system have been collected from

37 publications and critically reviewed in this section, which covers composition range of 10-

67 wt% SiO2, 0-40 wt% Al2O3, 0-60 wt% CaO, 0-38 wt% MgO and temperature between

1350 and 1550 °C [12, 21, 24-27, 30, 32, 34, 52, 65, 67, 68, 70, 72, 74, 79-99].

Techniques for the measurement of slag viscosity at high temperatures are difficult and have

the potential for large uncertainties in the results. The 37 publications of viscosity study were

published from 1940s to 2010s crossing 70 years. In present study, three sequential steps

were used to evaluate the data, which check:

the review experimental techniques

the data self-consistency

the cross reference comparison

35

In addition, the viscosity impacts of the minor element, including FeO, TiO2, Na2O and K2O,

were reviewed in the section 2.3.5.

2.3.1 Experimental Techniques in Viscosity Measurements

The proper selection and setting of viscometer will reduce measurement uncertainty. Three

types of viscometer were used: rotational viscometer (27 publications), oscillation plate

viscometer (7 publications) and falling-body viscometer (2 publications). It is widely

accepted that the rotational viscometer is a more reliable viscosity measurement technique

compared to other viscometers. For rotational viscometer, one uncertainty is the edge-effect

from the crucible wall at high rotational speed; limited researchers reported the setting

parameters of crucible/spindle: spindle weight, distances between the spindle and crucible,

and thermal expansion, which have studied and reported as uncertainty factor by Chen [13].

The oscillating plate viscometer suits better for low values of viscosity within the range of 10-

5 to 10

-2 Pa.s, such as pure liquid metal system. For falling-ball viscometer, it has been found

that the thermal expansion of the sensor (ball) significantly increases viscosity measurement

uncertainty, ranges from 1 to 100 Pa.s, which depends on the temperature and the falling ball

material. The falling-ball viscometer results were rejected because of potential uncertainty.

From 1997 to 1999, K.C Mills constructed the globe project “Round Robin”, which

determine the accuracy and reliability of various experimental techniques from different labs

using the referenced materials. Altogether 21 participants measured the referenced materials

and provide valuable information for the crucible and spindle materials. Mill et al reported

that the graphite container/sensor materials can cause significant uncertainty (>50%) in the

high temperature viscosity measurement. Under graphite crucible condition, Bockris et al

reported that graphite material may reduce the SiO2 and form SiC particles on the crucible

wall at high temperature, which may change slag composition and contribute to experimental

uncertainties [54]. Software Factsage 6.2 was used to estimate the reaction temperature

between SiO2 and graphite. The graphite container/sensor data were carefully reviewed, and

high-temperature sets were rejected (>1520 °C). In the contrast, the uncertainty of viscosity

measurements by Mo crucible is under 10%, which is confirmed as the reliable materials. At

high temperatures (1400 – 1550 °C) conditions, the aggressive molten slags may react with

the container and sensor materials leading to changes in slag composition or container/sensor

geometry [14]. Pt, Pt/Rh alloy, Fe, Mo, and graphite, are major materials for containers and

sensors utilized in the reviewed studies. Most of the researchers (18) use N2, CO or Ar gas to

36

prevent potential oxidation reaction between crucible/spindle. Air atmosphere was only

utilized in experiments with Pt sensor/container. Despite the chemical reactions, the geometry

of container/sensor can be physically changed at high temperatures due to thermal expansion

and softening. The hardness of metal keeps reducing when the temperature approaches the

melting point. The melting temperature of pure Fe and Pt is 1500 and 1700 °C respectively.

Therefore, these viscosity measurements, which are taken from improper container/sensor

materials and temperature, are not reliable and will not be accepted for model evaluation.

In 37 publications, three publications reported non-equilibrium viscosity measurements, in

which the viscosity data were recorded during the continuous cooling process. The viscosity

and internal structure of the molten slag do not correspond to the recorded temperature when

the furnace is continuous-cooling. For same composition slag sample, the viscosity measured

on continuous cooling is shown to be lower than the viscosity measured at the steady

condition at the same temperature. Therefore, non-equilibrium viscosity measurements are

not the actual slag viscosity at designed temperature and they will not be accepted in the

database.

Some of the viscosity measurements were constructed below the liquidus temperature with

the given composition. However, the slag compositions, the presence of solid and

container/sensor geometry changes can only be examined by post-experimental technology.

However, none of the slag samples was immediately quenched after viscosity measurements

in all 37 publications. Therefore, the viscosity measurements require further investigations

for removal or not.

In summary, the reported methodology is not sufficient to filter out the reliable results. The

self and cross consistency of viscosity data should be checked.

2.3.2 Data Consistency

Liquidus temperature is an important indicator to discover inappropriate measurements of the

viscosity. The phase diagram of CaO-MgO-Al2O3-SiO2 has been well studied. Software

Factsage 6.2 is utilized to predict the liquidus temperature of slag. The viscosity of bulk slag

with solid precipitated significantly increased. For example, in Figure 2.18, the viscosity

measurements were reported by Tang et al and Machin. Only the last points of two sets were

rejected because of dramatic increasing. The second last point of Tang’s was accepted. To

prevent the prediction error of liquidus temperature, the viscosities taken below liquidus

37

temperature have been critically reviewed and abnormal ones were removed from the

database.

Figure 2.18 Examples showing viscosity measured below liquidus by Machin [74] and Tang

[99]

It is accepted that the slag viscosity and temperature follow the Arrhenius-type equation.

According to the Equation 2-5, the natural logarithm of viscosity has a linear correlation to

reciprocal of absolute temperature. Figure 2.19 shows an example of viscosity measurements

with high and low consistency. Clearly, the data from Muratov and Yakushev et al have low

reliability and they are excluded from the database [98, 100]. In Yakushev’s data, the last

three points dramatically increased, which were taken under liquidus temperature[98]. Due to

insufficient information of post-experiment analysis from published paper, the reasons for

other non-linear results are not clear. Data linearity is a good indication to evaluate the

measurements reliability in the absence of enough experimental conditions.

Equation 2-5 Logarithm form of Arrhenius equation

ln(η) = ln(𝐴) +𝐸

𝑇

Where η is viscosity, A is the pre-exponential factor, E is the activation energy of system and

T is the absolute temperature (K)

38

Figure 2.19 Linearity comparison examples by Muratov [100], Machin[80], and Yakushev

[89]

2.3.3 Cross Reference Comparison

For CaO-MgO-Al2O3-SiO2 slag system, the experimental measurements and modelling focus

on the blast furnace composition range. The viscosities measured from different researchers

at close compositions were carefully compared to cross check the reliability of the data. As

shown in Figure 2.20, there were four sets of viscosity measurements in the same

composition and three sets of data are close. Data from Kita are excluded from the database

as they are significantly different from others.

Figure 2.20 Four sets viscosity measurement at 45 wt % SiO2, 15 wt% Al2O3, 30 wt% CaO

and 10 wt% MgO by Gul’tyai [83], Han [93], Kita [27] and Machin [27, 74, 83, 93]

39

In case the available viscosity data are not consistent and the information reported is not

enough for the evaluation, the viscosities at this composition were measured by the present

authors using a recently developed technique at the University of Queensland. Figure 2.21 is

an example, where it can be seen that the results of Park et al are confirmed by the author's

measurements and Kim et all’s data are not accepted. The methodology was detailed

discussed in a previous publication. The main feature of this technique is the possibility of

quenching the slag sample immediately after the viscosity measurement. Electron probe X-

ray microanalysis (EPMA) with wave spectrometers was used for microstructural and

elemental analyses of the quenched samples. In addition, the possible errors associated with

the high-temperature viscosity measurements have been analyzed and significantly

minimized, which include effects of bob weight, distances to the crucible and thermal

expansion during rotational viscometer measurements.

Figure 2.21 Comparison of viscosity data by the present authors (UQ), Kim et al [35] and

Park et al [101] at composition of 36.5% SiO2, 17% Al2O3, 36.5% CaO and 10% MgO

2.3.4 Summary of Experimental Data

3135 viscosity data for 607 compositions in this system have been collected from 37

publications, critically reviewed and summarized in Table 2.11. The viscosity measurements

taken at graphite crucibles, such as Gul’tyai and Gupta were mostly rejected [83, 87]. The

data of three authors, Kim, Sheludyakov, and Tsybulnikov, were fully rejected because

measurements were carried out at non-equilibrium condition [35, 86, 88]. The viscosity data

of Kato and Taniguchi were also fully rejected because of large uncertainty at the falling ball

40

viscometer. Over 50% of Machin’s data were rejected, due to most of measuring

temperatures were under liquidus temperature of slag for more than 50 oC.

The rejection reasons include:

Lower than liquidus temperature (436 data)

Use of graphite crucible at high temperature condition (273 data)

Non-equilibrium measurement (252 data)

Low linearity with unknown reasons (197 data)

Conflict with other authors’ results at same composition (82 data)

Extreme large or small viscosity data, >40 Pa.s or <0.01 Pa.s (68 data)

Only 2 viscosity points at one composition (36 data)

In summary, 1760 viscosity measurements were accepted and utilized for viscosity model

development in CaO-MgO-Al2O3-SiO2 system.

41

Table 2.11 The summary of existing viscosity study in CaO-MgO-Al2O3-SiO2 system

Sources Method Atmosphere Container Sensor Temperature (°C)

Post

Experiment

Techniques

Viscosity

(Pa.s) No of Data Accepted

Forsbacka [21] RB Ar+5%CO Mo Mo 1580-1750 EDS 0.08-0.6 50 50

Gao [30] RB CO C Mo 1450-1550 XRD

FT-IR 0.33-2.21 36 36

Gul'tyai [83] RB N2 C C 1250-1550 N/A 0.2-10 633 234

Gupta [87] RB Ar C C 1400-1550 N/A 0.28-3.24 493 245

Han [93] RB Ar C Pt-10Rh 1300-1500 N/A 0.3-0.8 5 3

Hofmann [82] RB Air Pt Pt 1450-1600 EDS 0.1-3 59 41

Hofmann [61] RB n/a C N/A 1400-1550 EDS 0.11-2.17 24 4

Johannsen [24] RB n/a Pt/20Rh Pt/20Rh 1250-1450 EDS 20-900 13 4

Kawai [79] RB n/a C C 1500-1600 N/A 0.09-90 69 19

42

Kim [102] RB Ar C N/A 1400-1550 XRF 0.136-2.41 13 8

Kim [103] RB Ar Pt-10Rh Pt-10Rh 1425-1500 N/A 0.04-5.1 79 61

Kim [35] RB Ar Pt/10Rh Pt/10Rh 1450-1500 ICP 0.3-0.5 122 0

Koshida [25] RB N/a N/a N/a 1360-1500 EDS 0.03-3.81 32 22

Li [104] RB Ar Mo Mo 1400-1550 FT-IR 0.1-1 104 104

Lee [91] RB Ar Pt/10Rh Fe 1400-1450 N/A 0.3-1 14 13

Lee [105] RB Ar Pt/10Rh Fe 1400-1450 XRF

FT-IR 0.3-0.9 12 9

Mishra [90] RB N2 C n/a 1350-1575 N/A 0.1-4.6 179 81

Muratov [100] RB n/a Mo Mo 1300-1650 N/A 0.2-5 57 20

Nakamoto [26] RB Ar Fe Fe 1250-1450 EDS 0.29-2.89 6 6

Park [106] RB Ar Pt-10Rh Pt-10Rh 1325-1500

XRD

FT-IR

Raman

0.15-0.8 16 16

43

Saito [95] RB Ar Pt-20Rh Pt-20Rh 1400-1600 N/A 0.1-1.3 20 20

Scarfe [70] RB Air Pt Pt/10Rh 1175-1600 N/A 0.4-100 64 49

Shankar [32] RB Ar Mo Mo 1400-1600 ICP 0.16-2.55 30 29

Song [107] RB Ar Mo Mo 1475-1630 SEM-EDS 0.12-0.56 63 56

Tang [99] RB Ar Mo Mo 1267-1525 N/A 0.31-10.03 105 101

Vyatkin [84] RB n/a C C 1300-1500 N/A 0.3-5 15 15

Yao [82] RB Ar C Mo 1400-1550 XRF 0.1-1 48 48

Kita [27] OP n/a Pt Pt 1250-1502 EDS 0.6-10 12 12

Machin [68] OP Air Pt Pt-alloy 1250-1500 X-ray 0.2-2.83

562 390 Machin [74] OP Air Pt Pt-alloy 1250-1500 X-ray 1-30

Machin [80] OP Air Pt Pt-alloy 1250-1500 X-ray 0.2-60

Sheludyakov

[108] OP n/a Pt Pt 1240-1410 N/A 1-40 18 0

Tsybulnikov [88] OP n/a Mo Mo 1500-1700 N/A 0.1-0.4 14 0

44

Yakushev [98] OP n/a Mo Mo 1461-1725 N/A 0.08-0.7 92 64

Kato [67] FB Air Pt Pt 1347-1476 N/A 0.3-2 10 0

Taniguchi [72] FB n/a Pt Pt 1100-1650 N/A 0.4-400 46 0

45

2.3.5 Random Network Structure

Zachariasen firstly proposed the ideas of the network structure of the binary system of

silicate slags [109]. The binary system was continuously developed and extended to

the multi-component system. In the CaO-MgO-Al2O3-SiO2 system, they can be

categorized into three groups, which are the acidic oxide (SiO2), basic oxide (CaO and

MgO) and amphoteric oxide (Al2O3). As Figure 2.22 shown, pure SiO2 forms a

network structure using (SiO4) tetrahedral units, which contribute for viscosity

ascending. When the basic oxides are added, the O2-

(free oxygen) from basic oxide

will bind with O0 (bridging oxygen) to break the silicate network and reduce the

viscosity [111].

Al2O3 can behaviour as either acidic or basic oxide. When there are sufficient basic

oxides, excess cations (Ca2+

and Mg2+

) balance the (AlO4)5-

charges, the Al2O3 acts as

an acidic oxide, Al3+

can form tetrahedron structure (AlO4)5-

as (SiO4)4-

and

incorporate into the silicate network. In the case of insufficient basic oxides, Al2O3

will behaviour as Ca2+

or Mg2+

to break the (SiO4)4-

network.

Figure 2.22 (a) Left, pure SiO2 structure. (b) Right, silicate mix with other basic oxide

solution

Although, the network model is widely accepted as the best structural model of the

silicate melts. The applicability to the multi-component alkali and alkaline is much

46

more questionable, such as TiO2 and CaF2. The random network model has been

optimized for certain alkaline glass system. However, limited literatures discussed the

possible structural units between silicate network and basic oxides; because the

present techniques could not determine the structural units at smelting temperature

conditions. Most of theories were the estimation based on the experimental

measurements and post sample analysis. For example, Bockris and co-workers

proposed a theory of the structure units of CaO-SiO2 system by assuming the co-

existing form of silicate with basic oxide for binary slag system. The summary of

structure description of silicates is given in Table 2.12 [111].

Table 2.12 Summary of Brokis study of expression of SiO2 unit at various

concentration [111]

SiO2 concentration (wt %) Type of silicate units

0-33 [SiO4]O2-

ions

33-45 Chains of general form SinO3n+1

45-66 Mixture of discrete polyamines based on

Si3O10 and Si6O15

66-90 Discrete silicate polyamines based upon a

six-membered ring Si6O15

90-100 Essentially SiO4 network with number of

broken bonds approximately equal to

number of added O atoms from MeO and

a fraction SiO2 molecules and radicals

containing Me

100 Continuous networks of SiO4 tetrahedral

with some thermal bonds

47

2.3.5 Minor Element Impact

In the ironmaking process, the four major components, SiO2, Al2O3, CaO, and MgO

occupied over 96% of the final slag. The rest 4% were contributed by the other metal

oxides, including “FeO”, F, S, and Cu2O, which is called minor elements. A limited

study was constructed on the viscosity impact of minor elements, which will be

reviewed in the present study.

2.3.5.1 “FeO”

There are two different slags on the CaO-MgO-Al2O3-SiO2-“FeO” system, one is

ironmaking final slag and another is copper-making slag. In the present study, only

the ironmaking final slag will be studied according to the scoping, as a summary in

Table 2.13. Only 2 researchers constructed the viscosity study of CaO-MgO-Al2O3-

SiO2-“FeO” system in the composition range of ironmaking slag, which report 30-40

wt% SiO2, 30-40 wt% CaO, 10-15 wt% Al2O3, 0-10 wt% MgO and 0-5 wt% FeO.

Iron saturation is always considered by researchers, which control the oxidation status

of Fe element. In conclusion, the “FeO” addition has a negative impact on the slag

viscosity.

Table 2.13 Summary of viscosity study at CaO-MgO-Al2O3-SiO2-”FeO” system

Composition Viscosity

(Pa.s)

Temperature

(oC)


Tang [112] 31-40 %SiO2

15-16 %Al2O3

30-40 %CaO

15-17 %MgO

0-1 %FeO


Mo crucible and bob

Ar atmosphere

48

Kim [94] 28-34 %SiO2

10-18 %Al2O3

40-48 %CaO

3.5-10 %MgO

1-5 %FeO


Mo crucible and bob

Ar atmosphere

It is confirmed that the addition of “FeO” content will reduce the slag viscosity [113].

In addition, the modify ability of “FeO” content could be determined from viscosity

measurement. Kim proposed that, if the SiO2 and Al2O3 content kept constant, the

replacement of either CaO or MgO by “FeO” content will increase the slag viscosity,

which indicated that the viscosity reduction ability of “FeO” is weaker than the CaO

and MgO [94]. As Figure 2.23 shown, the viscosity firstly decreased and then

increased with the replacement of both CaO and MgO by FeO at fixed temperature

condition.

Figure 2.23 FeO replaced the CaO and MgO oxide at 40 wt% SiO2, 1500 oC for

SiO2-CaO-FeO system, 40 wt% SiO2, 1550 oC for SiO2-MgO-FeO system, by Bockris

[94], Chen [115], Ji [114]and Urbain [13]

49

2.3.5.2 TiO2

TiO2 is a gangue mineral containing in the iron ore, which is removed in the slag

phase. In the ironmaking process, there are two types of slag containing TiO2; normal

blast furnace slag contain <1 wt% TiO2 and another in PanSteel could achieve 30 wt%

TiO2. The PanSteel from Panzhihua of China reported final slag containing large

amounts of TiO2 due to vanadium-titanium magnetite ore in that region, which would

achieve over 30% TiO2 in the slag. The viscosity study of slag is completed by

Chinese researchers. Also, extra TiO2 were added in the recent ironmaking process.

Because, the formation of Ti(C, N) fill the defect spot inside the furnace wall, which

can extend the usage life of blast furnace. The viscosity study of two types of TiO2

slag is summarized in Table 2.14.

Table 2.14 Summary of viscosity study at CaO-MgO-Al2O3-SiO2-TiO2 system


(Pa.s)

Temperature

(oC)


Handfield

[116]

21-40 %SiO2

15-16 %Al2O3

20-30 %CaO

5.2-5.7 %MgO

5-26 %TiO2

0.03-

0.36


Pt crucible and bob

Air atmosphere

Van

[117]

24-37 %SiO2

11-16 %Al2O3

19-26 %CaO

13-20 %MgO

24-37 %TiO2


Mo crucible and bob

Ar atmosphere

50

Saito [62] 32-36 %SiO2

16-18 %Al2O3

32-36 %CaO

5-10 %MgO

10-20 %TiO2

0.109-

0.629


Graphite crucible and bob

Ar atmosphere

Xie [118] 19-30 %SiO2

9-19 %Al2O3

19-30 %CaO

7-16 %MgO

17-33 %TiO2

0.01-

0.06

1350-1500

Rotational viscometer


Ar atmosphere

Shankar

[32]

32-40 %SiO2

21-29 %Al2O3

28-40 %CaO

2-5 %MgO

0-2.17 %TiO2

0.16-

2.55



Ar atmosphere

Liao

[119]

26-44 %SiO2

12 %Al2O3

22-32 %CaO

7 %MgO

15-30 %TiO2



Ar atmosphere

Park

[120]

28-40 %SiO2

17 %Al2O3

30-40 %CaO

10 %MgO

0.14-

1.05


Mo crucible and bob

Ar atmosphere

51

5-10 %TiO2

In terms of the viscosity impact of TiO2, there are two contradictive opinions. Liao

believed that the TiO2 has a similar structural unit as SiO2, which positively increase

the slag viscosity (TiO2>20wt%) [119]. When the TiO2 concentration decreased, in

Park’s viscosity measurement, it has been found the addition of TiO2 reduce the slag

viscosity of blast furnace type slag [121].

2.3.5.2 Na2O and K2O

The viscosity impact of Na2O and K2O is different, which is negative and positive

respectively. Most of the basic oxides were reported a negative impact on the slag

viscosity, such as CaO, MgO, FeO, CuO and etc. However, it is found that the

addition of K2O would increase the slag viscosity in CaO-MgO-Al2O3-SiO2 system.

The mechanism of viscosity increasing is not fully explained. Both Kim and Park

estimated that the K+ has a strong combination with AlO4 and form KAlO4 units, and

hence increase the slag viscosity by network formation. The reviewed publications

were summarized in Table 2.15.

Table 2.15 Summary of viscosity study at CaO-MgO-Al2O3-SiO2-Na2O and K2O

system


(Pa.s)

Temperature

(oC)


Na2O

Kim [122] 30-40 %SiO2

10-15 %Al2O3


Pt crucible and bob

52

20-40 %CaO

5-10 %MgO

10-15 %Na2O

Ar atmosphere

Kim [123] 15-30 %SiO2

5-16 %Al2O3

10-40 %CaO

4-8 %MgO

1-10 %Na2O


Pt crucible and bob

Air atmosphere

Takahira

[124]

25-45 % SiO2

10-15 %Al2O3

30-40 %CaO

5-10 %MgO

1-5 %Na2O


Mo crucible and bob

Ar atmosphere

K2O

Kim [122] 30-40 %SiO2

1-15 %Al2O3

35-45 %CaO

3-15 %MgO

1-5 %K2O


Pt crucible and bob

Ar atmosphere

Wu [125] 25-40 %SiO2

1-15 %Al2O3

30-45 %CaO

5-15 %MgO

3-10 %K2O


Mo crucible and bob

Ar atmosphere

53

2.4 The review and evaluation of viscosity model for silicate melts of CaO-MgO-

Al2O3-SiO2 system

Abundant viscosity models were developed to predict the viscosity of molten slag at

various systems. In the present sections, the models, which covered CaO-MgO-Al2O3-

SiO2, will be reviewed. Some models only release the equations and did not include

parameters, which is not capable of calculating the slag viscosity. These models were

reviewed from section 2.4.1 to 2.4.6. The other models, suitable for CaO-MgO-Al2O3-

SiO2 system, were reviewed from section 2.4.6 to 2.4.18. In addition, the prediction

performance of each model will be shown in the section 2.4.22, which utilized the

evaluated viscosity database in the CaO-MgO-Al2O3-SiO2 system.

2.4.1 Bottinga Model

The Bottinga model has been developed for magmatic silicate liquid of geological

interest [126]. Authors used a total of 2440 observations, which span the temperature

range 1100 to 1800 oC and the composition range 35 to 91 mol% SiO2 for D

parameters optimization. The Equation 2-6 were proposed to calculate the viscosity

utilizing parameter D and slag composition.

Equation 2-6. Bottinga model Equation [126]

log(η) = ∑ 𝑋𝑖𝐷𝑖

Where η viscosity in Poise, Xi is the weight fraction of metal oxides and Di are the

model parameters, which are constant over restricted composition and temperature

range.

An example of parameter D value of CaO-MgO-Al2O3-SiO2system is shown in Table

2.16 below, it can be seen that the temperature gap between two values is large and

54

cause deviations on viscosity predictions. In addition, the four components CaO, MgO,

Al2O3 and SiO2 in different molar fractions has new sets parameters, which altogether

report 470 model parameters.

Table 2.16 the parameter D values of Bottinga model in CaO-MgO-Al2O3-SiO2

quaternary system [126]

When XSiO2 is from 0.45-0.51

Component 1400 oC 1450

oC 1500

oC 1550

oC

SiO2 10.5 9.8 9.2 8.56

CaAl2O4 1.74 2.84 4.09 4.84

MgAl2O4 4.82 6.04 6.63 7.91

CaO 3.61 3.47 5.17 4.5

MgO 2.23 2.05 2.62 2.7

2.4.2 Neural Network Model

Hanao used neural networks theory to describe viscosity of blast furnace-type slags

[127]. The neural network is a typical fully computer-based models without any

consideration of silicate structure. The neural network model did not report a set of

equations or parameters for viscosity calculation. The software will compare the input

variable with existing database and calculate the viscosity value. The input includes

molar fraction SiO2, Al2O3, CaO, MgO, Temperature, and basicity. This theory can

apply in any other fields with large quantity of database [127].

2.4.3 Giordano Model

The Giordano model is a purely empirical models, which is developed based on

Vogel-Fulcher-Tamman equation to describe slag viscosity [128]. The VFT equation

55

is shown below, where A, B, and C are model parameters. Model parameters were

fitted to each slag compositions as Equation 2-7 shown. Therefore, the model reports

an outstanding agreement with entire database (5% relative error) but is limited to use

for un-fitted composition.

Equation 2-7. VFT model equation [128]

log(η) = A +B

𝑇 − 𝐶

Where η is the viscosity of Poise, T is the temperature in K, A, B and C is the

parameters given by Giordano shown in Table 2.17.

Table 2.17 Model parameters for Giordano [128]

A B C Relative Error

Slag Sample 1 -7.38 27568.73 -24.48 0.05

Slag Sample 2 -4.77 9184.3 473.71 0.08

Slag Sample 3 -6.05 13653.62 165.01 0.03

Slag Sample 4 -3.82 9055.89 362.25 0.08

2.4.4 CSIRO Model

Zhang proposed a structurally-based model to predicate the viscosity of a large

silicate melts system, including, pure oxides SiO2, Al2O3, CaO, MgO, Na2O K2O and

binary systems SiO2–Al2O3, SiO2–CaO, SiO2–MgO, SiO2–Na2O, SiO2–K2O, Al2O3–

CaO, Al2O3–MgO, Al2O3–Na2O, Al2O3–K2O, as a fundamental study for the system

SiO2–Al2O3–CaO–MgO [129]. The completed model reported a good agreement

between experimental data and calculated viscosity using only one set of model

parameters. The critical model parameters were calculated using the concentration of

different oxygen species, which were obtained by the cell model formalism. However,

56

the model parameters were not published. Only the equation can be reviewed, as

shown in Equation 2-8.

Equation 2-8 CSIRO model equation [129]

η = AW ∗ T ∗ exp (Ew

η

RT)

Where η is the viscosity, T is the temperature in (K), R is the gas constant, AW

and

Ew

n are the pre-exponential term and the activation energy, respectively.

Ewη = a + b(N𝑂0)3 + 𝑐(𝑁𝑂0)2 + 𝑑(𝑁𝑂−2)

Where a, b, c and d are fitting parameters optimized against experimental data. The

values of NO and NO2- were obtained by the Cell model formalism.

ln(AW) = a′ + b′ ∗ Ewη

Where a’ and b’ are fitting parameters in the publications [129]

2.4.5 KTH Model

The KTH viscosity model was developed on the basis of the Erying equation, which

is based on the absolute reaction rate theory for the description of flow processes

[130]. The completed model reported a good agreement between experimental data

and calculated viscosity using as a function of temperature and composition. However,

the model parameters were not published. Only the equation can be reviewed, as


Equation 2-9 Model equation of KTH model [130]

η =ℎ𝑁ρ

𝑀exp (

∆𝐺∗

RT)

57

Where η is the viscosity, T is temperature in (K), R is the gas constant, h is Planck’s

constant, N is Avogadro's number, ρ is average density and ∆𝐺∗ is the gibbs energy of

activation per mole.

2.4.6 Urbain Model

Urbain’s model is one of the most widely used slag viscosity models and based on the

Weymann-Frenkel liquid viscosity model [131]. Urbain proposed two versions

models on 1981 and 1987 respectively. The application range of Urbain model

include the oxide CaO, MgO, SiO2, S and F containing slag, which covers most of

slag system. Although, the Urbain model covers wide range of slag system; the

prediction deviations is large in the particular slag system. Another disadvantage of

Urbain model is the consideration of amphoteric oxide, which regarded Al2O3 as

positive terms to slag viscosity without correlation with basic oxide concentration.

Therefore, in the conditions of low abundance of basic oxide slag, Urbain model

reported a high variance of viscosity prediction. For the Urbain model 1981 and 1987

version, the mathematical equations and parameters were similar except the

calculation of individual B parameters.

The development Urbain model was based on the CaO-Al2O3-SiO2 system and

classified the slag components into three categories: glass former; modifier and

amphoteric [132]. In the CaO-MgO-Al2O3-SiO2 system, the XG, XM and XA were

calculated as follows. The XG* was obtained by division of

(1+XCaF2+0.5XFeO1.5+XZrO2). For example, the XG*=XG/ (1+XCaF2+0.5XFeO1.5+XZrO2).

Equation 2-10 Urbain Model Equation [132]

X𝐺 = X𝑆𝑖𝑂2+ ⋯

X𝑀 = X𝐶𝑎𝑂 + X𝑀𝑔𝑂 + ⋯

X𝐴 = X𝐴𝑙2𝑂3+ ⋯ X𝐹𝑒2𝑂3

+ X𝐵2𝑂3

58

𝑋𝐺∗ =𝑋𝐺

1 + XCaF2 + 0.5XFeO1.5+ XZrO2

η = 𝐴 ∗ 𝑇 ∗ exp (1000𝐵

𝑇)

ln(𝐴) = 0.29 ∗ 𝐵 + 11.57

Where XA is the molar composition of that component, η is the viscosity in poise, T is

the temperature in K, A and B are model parameters.

The XA were fitted into a third order polynomial equation to calculate the parameter B.

Parameter B in Urbain model equalled to the role of activation energy of Arrhenius

equation. The parameters B were expressed by third order polynomial equation of 4

model terms B0-3 as equation shown.

Equation 2-11 Urbain Model Equation [132]

𝐵0 = 13.8 + 39.9355 ∗ α + 44.049 ∗ α2

𝐵1 = 30.481 − 117.1505 ∗ α + 139.9978 ∗ α2

𝐵2 = −40.9429 + 234.0486 ∗ α − 300.04 ∗ α2

𝐵3 = 60.7619 − 153.9276 ∗ α + 211.1616 ∗ α2

B = 𝐵0 + 𝐵1 ∗ (𝑋∗𝐺)3 + 𝐵2 ∗ (𝑋∗

𝐺)2 + 𝐵3 ∗ (𝑋∗𝐺)3

α =X𝑀

X𝐴+X𝑀

Where XA and XM is the molar composition of that component

On 1987, Urbain suggested a different method to determine the individual parameter

B of BCa and BMg; and then determined the mean B as Equation 2-12 shown. The

modified equations of B improve the prediction accuracy CaO, MgO and MnO

including system, especially CaO-MgO-Al2O3-SiO2. The B of Ca, Mg and Mn (if

necessary) was calculated individually, which combine to the final B. The required

model equations and parameters were shown in Table 2.18.

59

Equation 2-13. Urbain model equation [131]

𝐵 =𝑀𝐶𝑎 ∗ 𝐵𝐶𝑎 + 𝑀𝑀𝑔 ∗ 𝐵𝑀𝑔 + 𝑀𝑀𝑛 ∗ 𝐵𝑀𝑛

𝑀𝐶𝑎 + 𝑀𝑀𝑔 + 𝑀𝑀𝑛

𝐵𝑖(𝑖=𝐶𝑎,𝑀𝑔) = 𝐵𝑖(𝑖=𝐶𝑎,𝑀𝑔)0 + 𝐵𝑖(𝑖=𝐶𝑎,𝑀𝑔)

1 + 𝐵𝑖(𝑖=𝐶𝑎,𝑀𝑔)2

𝐵𝑖 (𝑖=𝐶𝑎,𝑀𝑔)0,1,2 = 𝐵0,𝐶𝑎 + 𝐵1,𝐶𝑎 ∗ 𝑅 + 𝐵2,𝐶𝑎 ∗ 𝑅2

Basicity index (R) =𝑀𝐶𝑎 + 𝑀𝑀𝑔

𝑀𝐶𝑎 + 𝑀𝑀𝑔 + 𝑀𝐴𝑙

Table 2.18 Model parameters of Urbain Model [131]

Constant B1* α B2* α2

CaO

MgO

MnO

CaO MgO MnO CaO MgO MnO

0 13.2 41.5 -45 20 15.9 -18.6 -25.6

1 30.5 -117.2 130 26 -54.1 33 -56

2 -40.4 232.1 -298.6 -110.3 138 -112 186.2

3 60.8 -156.4 213.6 64.3 -99.8 97.6 -104.6

The Urbain model of 1987 version is more suitable for the viscosity prediction of

CaO-MgO-Al2O3-SiO2 system. As Figure 2.24 shown, the 1987 Urbain models

reported smaller prediction deviation comparing to the 1981 version, due to Urbain

optimization on the parameter calculations. Please note, the quantity of viscosity

measurements of before-evaluation group is 3105, which was the original viscosity

data without evaluation process in Section 2.3. The quantity of viscosity

measurements of after-evaluation group is 1760.

60

Figure 2.24 The comparison between Urbain model of 1981 [132] and 1987 version

[131] using the viscosity database of before-evaluation, after-evaluation and BF

composition

2.4.6.1 Riboud Model

Riboud optimized the Urbain model to estimate the viscosity in mould fluxes [133].

Riboud simplified the Urbain’s expression of B term, the model term A is not

dependent on B, which was calculated using slag composition. As Equation 2-14

shown, the network modifiers parameter, CaO, and MgO have the same contribution

(value=1.73) to the viscosity, which did not obey their network modify ability. It is

accepted that different basic oxide has various ability to break silicate network.

Equation 2-14. Riboud model equation [133]

η = 𝐴 ∗ 𝑇 ∗ exp (1000𝐵

𝑇)

𝑙𝑛𝐴 = −19.81 + 1.73(𝑋𝐶𝑎𝑂 + 𝑋𝑀𝑔𝑂) − 35.76𝑋𝐴𝑙2𝑂3

𝐵 = 31140 − 23896(𝑋𝐶𝑎𝑂 + 𝑋𝑀𝑔𝑂) + 68833𝑋𝐴𝑙2𝑂3

Where η is the viscosity of Poise, A and B is the parameters, T is the temperature in K,

XCa and XMg are the molar composition of slag system

61

2.4.6.2 Kondratiev and Forsbacka Model

The modified-Urbain viscosity model was also constructed at the University of

Queensland by Kondratiev and Forsbacka for the viscosity prediction of coal ash slag

[134, 135]. Kondratieve first proposed the model for viscosity prediction of coal ash

slag of CaO-FeO-Al2O3-SiO2 system [134]. Later, Forsbacka optimized the

parameters using excel-solver and extend the prediction range to MgO, CrO and

Cr2O3 containing system [135]. The proposed model reported similar mathematical

structure as Urbain model, which changed the equations and parameters of B

calculation. The model was able to describe the viscosity of complex slags reasonably

well in most experimental cases, which agreed well with experimental measurements

in the ‘Round Robin’ project [135].

2.4.7 Iida Model

Iida proposed the mathematical model to estimate the slag viscosity, which is based

on Arrhenius type of equation and slag basicity property [136, 137]. The core

parameters A,𝜇0 E are determined based on temperature as Equation 2-15 shown.

Bi was defined as slag basicity. In the CaO-MgO-Al2O3-SiO2 system, it is accepted

that (wt% CaO/SiO2) slag basicity is an indication of the ironmaking operation

performance. Referring to the viscosity, a high basicity slag would report a low

viscosity. Iida considered and encountered the amphoteric oxide Al2O3 and regarded it

as a network former, which will reduce the slag basicity. Iida reported that the

viscosity predictions closely fit with the experimental data for a large number of blast

furnace type slags. The relevant equations and parameters are shown in 错误!未找到

引用源。 and Table 2.19 respectively.

Equation 2-15. Iida Model Equations [136, 137]

η = 𝐴 ∗ 𝜇0 ∗ exp (𝐸

𝐵𝑖∗)

62

A = 1.745 − 1.962 ∗ 10−3𝑇 + 7 ∗ 10−7𝑇2

𝐵𝑖∗ =𝑎𝐶𝑎𝑂 ∗ 𝑊𝐶𝑎𝑂 + 𝑎𝑀𝑔𝑂 ∗ 𝑊𝑀𝑔𝑂

𝑎𝐴𝑙2𝑂3 ∗ 𝑊𝐴𝑙2𝑂3 + 𝑎𝑆𝑖𝑂2 ∗ 𝑊𝑆𝑖𝑂2

𝜇0 = ∑ 𝜇0𝑖𝑋𝑖

𝜇0𝑖 = 1.8 ∗ 10−7(𝑀𝑖 ∗ (𝑇𝑚)0.5

𝑖

(𝑉𝑚)𝑖2/3

exp (𝐻𝑖

𝑅 ∗ (𝑇𝑚)0.5𝑖

) )

𝐻𝑖 = 5.1 ∗ (𝑇𝑚)1.2𝑖

E = 11.11 − 3.65 ∗ 10−3𝑇

Where Mi is the formula weight of i component, Tmi is the melting temperature, R is

gas constant, Hi melting enthalpy of i component, Bi is the slag basicity, W is the wt%

of each oxide, aoxide is the model parameters, E is the enthalpy of slag.

Table 2.19 Equation parameters for Iida model [136, 137]

SiO2 Al2O3 CaO MgO

A 1.48 0.1 1.53 1.51

Temperature Μ

oC SiO2 Al2O3 CaO MgO

1400 3.76 7.95 23.82 39.66

1450 3.43 7.12 20.67 34.01

1500 3.11 6.36 17.83 28/96

1550 2.92 5.89 16.15 26.03

63

2.4.8 NPL (Mills) Model

Mills’ viscosity model (also called NPL) is based on optical basicity parameter, which

is firstly determined and named by Duffy J.A [138, 139]. The metal oxides were

reported various peak intensity under UV light. Assume CaO is 1, the other oxides

basicity were determined and demonstrated by Duffy [139, 140].

The NPL model was developed based on the Arrhenius-type equation. As Equation

2-16 shown, the AOP

, Mills calculated the slag basicity with insertion of oxide

composition*optical basicity. The AOP

term were directly linked to the parameter A

and B for viscosity calculation. The predictions of NPL model were in reasonable

agreement with experimental data for reported multicomponent system.

Equation 2-16. NPL (Mills) model equation [138]

η = 𝐴 ∗ exp (𝐵

𝑇)

B = Exp (−1.77 ∗2.88

𝐴𝑜𝑝) ∗ 1000

ln(A) = −144.17 + 357.32 ∗ A𝑜𝑝 − 232.69 ∗ (A𝑜𝑝)2

A𝑜𝑝 =𝛾𝑆𝑖𝑂2 ∗ 𝑀𝑆𝑖𝑂2 + 𝛾𝐴𝑙2𝑂3 ∗ 𝑀𝐴𝑙2𝑂3 + 𝛾𝐶𝑎𝑂 ∗ 𝑀𝐶𝑎𝑂 + 𝛾𝑀𝑔𝑂 ∗ 𝑀𝑀𝑔𝑂

2 ∗ 𝑀𝑆𝑖𝑂2 + 3 ∗ 𝑀𝐴𝑙2𝑂3 + 𝑀𝐶𝑎𝑂 + 𝑀𝑀𝑔𝑂

Where η is the viscosity in Pa.s, T is the temperature in K, Mi is the molar

composition of slag system and all other parameters are shown in Table 2.20.

Table 2.20 Model parameters of NPL model [138]

SiO2 Al2O3 CaO MgO

Optical Basicity 0.48 0.6 1 0.78

64

2.4.9 Shankar Model

Based on Mills work on the optical basicity, Shankar did a doctoral thesis work on the

studies on high alumina blast furnace slags, which investigate the viscosities data and

improve the model prediction accuracy on blast furnace slag system [141]. The model

equations were shown as Equation 2-17. Shankar has different calculations on the AOP

comparing to the NPL model. The basicity of basic oxide and acid oxide were

normalized first; then calculated the slag basicity. The model predictions report

satisfactory agreement with experimental data.

Equation 2-17. Shankar model equations [141]

η = 𝐴 ∗ exp (1000 ∗ 𝐸

𝑇)

ln(A) = −0.3068 ∗ A𝑜𝑝 − 6.7374

B = −9.897 ∗ A𝑜𝑝 + 31.347

A𝑜𝑝 = (𝛾𝐶𝑎𝑂 ∗ 𝑀𝐶𝑎𝑂 + 𝛾𝑀𝑔𝑂 ∗ 𝑀𝑀𝑔𝑂

𝑀𝐶𝑎𝑂 + 𝑀𝑀𝑔𝑂)/ (

𝛾𝑆𝑖𝑂2 ∗ 𝑀𝑆𝑖𝑂2 + 𝛾𝐴𝑙2𝑂3 ∗ 𝑀𝐴𝑙2𝑂3

2 ∗ 𝑀𝑆𝑖𝑂2 + 3 ∗ 𝑀𝐴𝑙2𝑂3)

Where η is the viscosity of poise, T is the temperature in K, Mi is the molar

composition of slag system and all other optical basicity parameters are the same as

Table 2.20 shown.

2.4.10 Hu Model

Hu did a similar work as Shankar that optimized the Mill’s model towards the blast

furnace slag field [142]. Comparing the model from Mills and Shankar, Hu consider

the alumina charge compensation effect by the CaO, which is noted from his equation.

However, the equation structure can only apply on the MCaO>MAl2O3 condition, which

is a typical blast furnace composition range. The model prediction fits well with

experiment data in the SiO2-Al2O3-CaO, CaO-MgO-Al2O3-SiO2 and CaO-MgO-

65

Al2O3-SiO2-TiO2 system, with the mean deviation less than 25%. The model

equations were shown as Equation 2-18.

Equation 2-18. Hu model equations [142]

η = 𝐴 ∗ exp (1000 ∗ 𝐸

𝑇)

ln(A) = −0.3068 ∗ A𝑜𝑝 − 6.7374

B = −9.897 ∗ A𝑜𝑝 + 31.347

A𝑐𝑜𝑟𝑟 =0.48 ∗ 2 ∗ 𝑀𝑆𝑖𝑂2 + 0.6 ∗ 3 ∗ 𝑀𝐴𝑙2𝑂3 + (𝑀𝐶𝑎𝑂 − 𝑀𝐴𝑙2𝑂3) + 0.78 ∗ 𝑀𝑀𝑔𝑂

2 ∗ 𝑀𝑆𝑖𝑂2 + 3 ∗ 𝑀𝐴𝑙2𝑂3 + (𝑀𝐶𝑎𝑂 − 𝑀𝐴𝑙2𝑂3) + 𝑀𝑀𝑔𝑂

Where η is the viscosity of poise, T is the temperature in K, Mi is the molar


Table 2.20 shown.

2.4.11 Shu Model

There are two versions of Shu’s viscosity model, which published at 2009 and 2015

[143, 144]. In the present study, only the latest version (2015) were reviewed and

evaluated. Shu pointed that viscosity of CaO-MgO-Al2O3-SiO2 quaternary system is

composed of two sub ternary systems ideal mixing, which is SiO2-Al2O3-CaO and

SiO2-Al2O3-MgO. This assumption has benefits that ternary system involved

parameters and consideration are less than the quaternary system. For example, Ca

and Mg cations are required to charge compensate (AlO4)5-

structure. This assumption

avoids the consideration of the priority of Ca and Mg cations with AlO4. The

normalized molar fraction formula is used to combine two sub-ternary systems to a

quaternary variable, and then use Arrhenius equation to calculate the final viscosity.

Shu’s model considers the equilibrium between three types oxygen: O (bridging

oxygen), O- (non-bridging oxygen) and O

2- (free oxygen). Shu utilizes the Ottonello’s

66

work on the equilibrium constant K, which established a link between the optical

basicity and silicate polymerization [144]. A good agreement between calculated and

measured viscosity with a mean deviation of less than 25% was achieved.

Equation 2-19. Shu model equations [143, 144]

lnη = 𝑙𝑛𝐴 + 𝐸/𝑅𝑇

ln(𝐴) = 𝑚 ∗𝐸

𝑅+ 𝑛

E = 𝑋𝐴𝑙𝐸𝐴𝑙 + (1 − 𝑋𝐴𝑙)(𝑋𝑂2−𝐸𝑂2−𝑋𝑂−(𝑦𝑆𝑖𝐸𝑂− − (𝑆𝑖 − 𝑂−) + 𝑦𝐴𝑙𝐸𝑂− − (𝐴𝑙 − 𝑂−))

+ 𝑋𝑂0 ∗ (𝑦𝑆𝑖𝐸𝑂0(𝑆𝑖 − 𝑂0) + 𝑦𝐴𝑙𝐸𝑂0(𝐴𝑙 − 𝑂0)))

Where η is the viscosity of poise, T is the temperature in K, Xi is the molar

composition of slag system and E parameters shown in publication [143, 144].

2.4.12 Zhang Model

Zhang proposed a mathematical model to describe the viscosity behavior of the

multicomponent system, which is based on different oxygen ions present in molten

slag [145]. The three oxygen ions are bridging oxygen [O], non-bridging oxygen [O-],

and free oxygen [O2-

]. With the consideration of possible structural units, Zhang

specifies the oxygen ions between Al, Ca and Mg cations. For example, the charge

compensated oxygen between Ca and Al etc. The concentrations of these different

oxygen ions are calculated on the basis of Zhang’s assumptions, then, Zhang uses

Arrhenius type equation to calculate the slag viscosity and reported an outstanding

agreement with experimental data. The utilized equation and model parameters were

included in the Equation 2-20 and Table 2.21 respectively. As shown in Table 2.21

and Table 2.22, the major features of Zhang’s model are the assumptions based

calculations. The calculated structural units would be utilized to determine the

67

activation energy of that composition slag, and hence determine the viscosity at fixed

temperature.

Equation 2-20. Zhang model equations [145]

lnη = 𝑙𝑛𝐴 + 𝐸/𝑅𝑇

Where η is the viscosity of poise, E is the activation energy term, T is the temperature

in K, R is the gas constant

lnA = k(E − 572516) − 17.47

k = ∑ (𝑥𝑖𝑘𝑖)/ ∑ (𝑥𝑖)

𝑖,𝑖≠𝑆𝑖𝑂2𝑖,𝑖≠𝑆𝑖𝑂2

E =572516 ∗ 2

𝑛𝑂𝑆𝑖+ ∑ 𝑎2 ∗ 𝑛𝑂−

Where 𝑛𝑂𝑆𝑖 is the number of oxygens bridging with silicate, the 𝑛𝑂− is the number of

other types of oxygen except bridging oxygens 𝑛𝑂𝑆𝑖. The calculation of these

parameters were shown in the Table 2.22

Table 2.21 The model parameters used to calculate E [145]

kMg aMg aSiMg

aAl,Mg aMg

Al,Mg

-2.106*10-5

15.54 6.908 5.606 3.975

kCa aCa aSiCa

aAl,Ca aMg

Al,Mg

-2.088*10-5

17.34 7.422 4.996 7.115

kAl aAl

aMg

Al,Ca

-2.594*10-5

5.671 8.334

68

Table 2.22 All possible condition in the CaO-MgO-Al2O3-SiO2 system, only the

condition 1 equations were included. The equations for other conditions is not

included due to text limitation [145].

Condition

I. x𝐶𝑎𝑂 + x𝑀𝑔𝑂 < x𝐴𝑙2𝑂3 η𝑂𝑆𝑖= 2𝑥𝑆𝑖𝑂2

η𝑂𝐴𝑙= 3(𝑥𝐴𝑙2𝑂3

− x𝐶𝑎𝑂 − x𝑀𝑔𝑂)

η𝑂𝐴𝑙,𝐶𝑎= 4𝑥𝐶𝑎𝑂

η𝑂𝑆𝑖,𝑀𝑔= 4𝑥𝑀𝑔𝑂

II. x𝐶𝑎𝑂 < x𝐴𝑙2𝑂3, x𝐶𝑎𝑂 + x𝑀𝑔𝑂 < x𝐴𝑙2𝑂3

and x𝐶𝑎𝑂 + x𝑀𝑔𝑂 − x𝐴𝑙2𝑂3< 2(x𝑆𝑖𝑂2

+

2x𝐴𝑙2𝑂3)

[145, 146]

III. x𝐶𝑎𝑂 > x𝐴𝑙2𝑂3and x𝐶𝑎𝑂 + x𝑀𝑔𝑂 −

x𝐴𝑙2𝑂3< 2(x𝑆𝑖𝑂2

+ 2x𝐴𝑙2𝑂3)

[145, 146]

IV. x𝐶𝑎𝑂 > x𝐴𝑙2𝑂3and x𝐶𝑎𝑂 + x𝑀𝑔𝑂 −

x𝐴𝑙2𝑂3> 2(x𝑆𝑖𝑂2

+ 2x𝐴𝑙2𝑂3)

[145, 146]

V. x𝐶𝑎𝑂 < x𝐴𝑙2𝑂3and x𝐶𝑎𝑂 + x𝑀𝑔𝑂 −

x𝐴𝑙2𝑂3> 2(x𝑆𝑖𝑂2

+ 2x𝐴𝑙2𝑂3)

[145, 146]

2.4.13 Gan Model

Gan developed blast furnace viscosity model based on Vogel-Fulcher-Tammann

Equation 2-21, which has successfully applied to magmatic liquids before [147]. It is

a linear relation between the slag composition and model parameter (B, C). Gan

reported that model can accurately predict the viscosity of blast furnace slag with a

relative average error of 0.211. A slight modification of this model can also predict

the glass transition temperature of blast furnace slag satisfactorily.

Equation 2-21. Gan model equations, A is -3.1, the parameters of bi and ci were

shown in Table 2.23 [147]

η = 𝐴 +𝐵

𝑇 − 𝐶

69

B = ∑ 𝑏𝑖𝑥𝑖

C = ∑ 𝑐𝑖𝑥𝑖

Where η is the viscosity in Pa.s, T is the temperature in K, Xi are the molar

composition of slag system

Table 2.23 Model parameters of Gan model [147]

bi ci

SiO2 3308.42 1019.48

Al2O3 5490.72 725.95

CaO 751.19 985.23

MgO 1944.87 556.66

2.4.14 Tang Model

Tang proposed viscosity model utilizing a ratio of non-bridging oxygen to tetrahedral

metal (NBO/T) [148] as Equation 2-22 shown. Tang’s expression is similar to Iida’s

basicity equation with additional concerning of alumina-silicate structure. In “round

robin project”, the model predictions have an outstanding agreement with

experimental data, which reported smaller deviations than Iida model in CaO-MgO-

Al2O3-SiO2-R2O (K2O or Na2O) system.

Equation 2-22. Tang model equations [148]

η = exp (−9.4 −43.63

(3.75 +𝑁𝐵𝑂

𝑇 )+

150450

(3.75 +𝑁𝐵𝑂

𝑇 ) ∗ 𝑇)

𝑁𝐵𝑂

𝑇=

2 ∗ (𝑎𝑀𝑔𝑂 ∗ 𝑋𝑀𝑔𝑂 + 𝑎𝐶𝑎𝑂 ∗ (𝑋𝐶𝑎𝑂 − 𝑋𝐴𝑙2𝑂3))

2 ∗ 0.427 ∗ 𝑏𝐴𝑙2𝑂3 ∗ 𝑋𝐴𝑙2𝑂3 + 𝑋𝑆𝑖𝑂2

70

Where η is the viscosity in Pa.s, T is the temperature in K, Xi are the molar

composition of slag system and all other parameters are given by Shankar, other

model parameters are shown in Table 2.24

Table 2.24 Model parameters of Tang model [148]

ai bi

Ca 1 1

Mg 0.86 0.47

2.4.15 Ray Model

Based on the Urbain model, Ray proposed a new mathematical model, which is

capable of calculating the viscosity based on slag composition, temperature and

optical basicity [149] as Equation 2-23 shown. The model proposed is applicable to

homogeneous fluid melts only. The mathematical equations of Ray model are similar

to Mill model, which were shown as below:

Equation 2-23. Ray model equations [149]

η = 𝐴 ∗ exp (𝐵

𝑇)

B = 297.14 ∗ (A𝑜𝑝)2 − 466.69 ∗ A𝑜𝑝 + 196.22

ln(A) = −0.2056 ∗ B − 12.492

A𝑜𝑝 =𝛾𝑆𝑖𝑂2 ∗ 𝑀𝑆𝑖𝑂2 + 𝛾𝐴𝑙2𝑂3 ∗ 𝑀𝐴𝑙2𝑂3 + 𝛾𝐶𝑎𝑂 ∗ 𝑀𝐶𝑎𝑂 + 𝛾𝑀𝑔𝑂 ∗ 𝑀𝑀𝑔𝑂

2 ∗ 𝑀𝑆𝑖𝑂2 + 3 ∗ 𝑀𝐴𝑙2𝑂3 + 𝑀𝐶𝑎𝑂 + 𝑀𝑀𝑔𝑂

Where η is the viscosity of Poise, T is the temperature in K, Mi is the molar


Table 2.20 shown.

71

2.4.16 Li Model

Li proposed a novel viscosity model based on the flow mechanism involving the

concept of “cut-off” points proposed by Nakamoto [150]. The non-bridging oxygen

and free oxygen have large mobility because there are “cut-off” points near non-

bridging oxygen linkage Si-O-Ca and free oxygen. These “cut-off” points constantly

move and break the networks to produce new “cut-off” points when shear stress is

applied to the silicate melts. Thus, the movement of “cut-off” points results in viscous

flow. The concept of “cut-off” from Li and Nakamoto is similar to the “hole” theory

in the other silicate melts structure.

The model equations and parameters have been summarized in the Equation 2-24 and

Table 2.25.

Equation 2-24 Li model equations [150]

η = 𝐴𝑊 ∗ exp (𝐸

𝑅𝑇)

ln(𝐴𝑊) = 𝑎 + 𝑏 ∗ 𝐸

a =∑ 𝑎𝑖𝑥𝑖

∑ 𝑥𝑖

b =∑ 𝑏𝑖𝑥𝑖

∑ 𝑥𝑖

Where η is the viscosity of Poise, A and B is the parameters calculating from equation,

T is the temperature in K

Table 2.25 Model parameters of Li model [150]

A b

CaO-SiO2 -5.5781 -0.0000196

MgO-SiO2 -5.4658 -0.0000198

Al2O3-SiO2 -2.6592 -0.0000248

72

2.4.17 Quasi-Chemical Viscosity Model

Alex, Suzuki and Jak developed multicomponent slag viscosity model, which is called

quasi-chemical viscosity model (QCV) [151], as Equation 2-25 shown. QCV is based

on Erying liquid viscosity model, which assumes molten slag has quasi-crystalline

structure. In molten slag, the molecules oscillate from equilibrium position to a

neighboring one when their energy momentarily is equal or larger than the height of

the potential barrier. Therefore, QCV model links the oscillation molecules (also

called bond fraction) to slag viscosity. The potential oscillated molecules are

subdivided into cationic molecular structures (also called bond fraction). For example,

bond fraction parameters of alumina include Al-O-Al, Al-O-Si, Al-O-Mg and Al-O-

Ca. These bond fractions of each metal oxide can only be calculated from FactSage

software. In addition, second nearest neighbor bond (SNNB), which defines as the

impact from neighboring structure, is introduced to improve the model prediction

accuracy. As shown, QCV model includes calculations of each minor structure of four

aspects, which are mass, volume, and activation and vaporization energy term.

Equation 2-25. QCV model equations [151]

η = 2 ∗𝑅𝑇

∆𝐸𝑉∗

(2𝜋𝑘𝑚𝑆𝑈𝑇)0.5

𝑣𝑆𝑈

23

exp (𝐸𝑎

𝑅𝑇)

Factsage model links the viscosities of silicate melts to their thermodynamic

properties, which is described by the quasi-chemical theory. It utilized Q-pairs

(similar as a bond fraction in QCV model) to determine the E parameters and hence

viscosity. Therefore, the QCV models highly rely on the FactSage software to

calculate the critical parameters Q-pair. When FactSage updated from 6.2 to 6.4, the

model parameters require optimization to suit the changes of Q-pair.

73

2.4.18 Factsage 7.0

Factsage is one of the largest fully integrated database computing systems in the

chemical thermodynamics field of pyro-metallurgy study, which focus on the study of

thermodynamic prediction, such as equilibrium, viscosity, and chemical reaction.

Viscosity is one of the features of Factsage and the latest version is 7.0. Although the

mathematical formulas for Factsage are uncertain, it is still a useful and convenient

tool for viscosity prediction with input of temperature and slag composition as

Equation 2-26, which covered most of the slag system and temperature ranges.

Equation 2-26. Factsage model requirements

η = 𝑖𝑛𝑝𝑢𝑡 (𝑠𝑙𝑎𝑔 𝑐𝑜𝑚𝑝𝑜𝑠𝑖𝑡𝑖𝑜𝑛, 𝑇𝑒𝑚𝑝𝑒𝑟𝑎𝑡𝑢𝑟𝑒)

Where η is the slag viscosity, the input is the required information from user

2.4.19 Summary

Abundant mathematical models were developed to predict the viscosity of the molten

slag. In the present study, altogether 20 models, which is capable of predicting the

CaO-MgO-Al2O3-SiO2 system, were critically reviewed.

In summary, there are several common features within 18 models:

1. Most of the model utilize Arrhenius type equation to express and calculated slag

viscosity. Arrhenius equation is a formula for the temperature dependence of reaction

rates. Viscosity, as physical properties, was reported an outstanding agreement using

Arrhenius-type equation (Equation 2-27).

Equation 2-27. Arrhenius equation

η = 𝐴 ∗ exp (𝐸

𝑇)

74

Where η is the viscosity of Poise, A is the pre-exponential factor and B is the

activation energy of reaction, T is the temperature in K

2. Another interesting feature is the linear correlation between pre-exponential factor

A and activation energy B. From the publications different authors in various systems,

there is a strong linear relationship between A and B, which was utilized in the model

development. Fundamentally, in the Arrhenius equation, the A was regarded as a

frequency factor, which indicated the rate of collision between reactants. B is

activation energy the energy gap required to initial chemical reaction. The linear

relationship was never reported between A and B in reaction kinetics field. As

Equation 2-28 shown, the linear relationship between A and B was widely utilized

and demonstrate a linear relationship at existing viscosity data, including Hu, Shankar,

Urbain and Shu model [131, 142, 143].

Equation 2-28 the linear correlation between ln(A) and b

ln(A) = m ∗ b + n

Where A and B are the parameters required for Arrhenius model calculation, m and b

is generally given by authors

It is widely accepted that molten slag viscosity is determined by its internal structure.

In CaO-MgO-Al2O3-SiO2 system, (SiO4) tetrahedral forms the slag network, hence

increases viscosity. The CaO and MgO perform as network modifiers, which reduce

the slag viscosity. Al3+

can form (AlO4)-

tetrahedral structure similar to SiO4 (network

former). However, AlO45-

requires Mg and Ca cations to balance the electrical charge.

With an insufficient amount of Ca and Mg cations, AlO45-

tetrahedral structure will

break and behavior as network modifier (same as Mg2+

and Ca2+

).

75

The reviewed models can be categorized based on model structure, parameters, and

consideration of the silicate structures. In different stages of the viscosity

development, understanding of alumina-silicate structure was different:

(I) Al2O3 as an amorphous oxide was not considered in model development,

including Gan models.

(II) Consider Al2O3 as network former and introduce into the viscosity model. This

includes Urbain, Riboud, Iida, Mill, Shankar, Hu, Ray, Tang, Li, Suzuki and

Factsage, models.

(III) If basic oxides e.g. CaO are insufficient, the excess Al2O3 will behavior as basic

oxides. This was considered by Shu and Zhang models.

In the pyro-metallurgy field, the fundmental equation from other field were often

utilzed for the viscosity model development. The most popular equation was the

Arrhenius-type equation and its modified equations, which was utilized by Urban,

Mill, Shankar, Hu, Li, Zhang, Li, Ray, Riboud, and Shu (10 authors, Equation 2-29).

Equation 2-29 General form of Arrhenius-type equation

η = A ∗ T𝑋 ∗ 𝑒𝐸𝐴𝑅𝑇

Where η is viscosity in (Pa.s), T is temperature in K; and A is pre-exponential factor,

R is gas constant, X can be 0 (Ray, Shu, Mills, Shankar, Zhang, and Li), 0.5 (Suzuki)

and 1 (Riboud, Hu, and Urbain) from different researchers.

Vogel-Fulcher-Tammann (VFT) is an equation for glass-forming liquid (Equation

2-30), which was firstly proposed by Gan to predict slag viscosity of molten slag of

the CaO-MgO-Al2O3-SiO2 system.

Equation 2-30 VFT equation

log(η) = A +𝐵

𝑇 − 𝐶

76

Where η is viscosity in (Pa.s), T is the temperature in K; and A, B, C are model

parameters.

Another general equation is the basicity calculation of slag, which is the ratio of basic

oxide to acidic oxide. Researchers proposed different mathematical formulas to

correlate the slag structures with compositions. Urbain uses a weight ratio of

(WCaO+WMgO)/ (WAl2O3) to describe the basicity of slag and predict viscosity.

Afterward, Iida and Mills proposed viscosity models using the ratio of (WCaO+WMgO)/

(WSiO2+WAl2O3), with the multiplication of basicity of each oxide. Based on optical

basicity and Mills model, Shankar Ray and Hu revised the model structures and

parameters to improve the precision and accuracy on blast furnace slags containing

minor elements. Shu and Zhang's models established viscosity model with

consideration of three type’s oxygen O, O- and O

-2. However, the calculation of

oxygen concentration is a lack of theory support and relies on assumption. The

features of the existing viscosity models are summarized in Table 2.26 and Table 2.27.

14 structural models were reviewed are evaluated in the present study using the

accepted viscosity database of CaO-MgO-Al2O3-SiO2 slag system. Equation 2-31 is

used to calculate the difference between the measured and the calculated viscosity

values. The evaluation results have been summarized in Table 2.26 and Table 2.27.

Equation 2-31 Error deviation calculation

Δ =1

𝑛∗ ∑ |

𝜂𝐶𝑎𝑙𝑐 − 𝜂𝐸𝑥𝑝

𝜂𝐸𝑥𝑝| ∗ 100%

Where Δthe mean deviation, n is is the total number of simulations, ηCalc is the model

viscosity and ηExp is the experimental viscosity.

77

Table 2.26 Summary of reviewed viscosity model in CaO-MgO-Al2O3-SiO2 system

Sources Structure Related Equation Model Features

Error

Deviation

(%)

Urbain [131] 𝑊𝐶𝑎𝑂 + 𝑊𝑀𝑔𝑂

𝑊𝐴𝑙2𝑂3

Based on Frenkel-Weymann liquid viscosity model, Urbain

theoretically approved the linear correlation between A and B in

the Arrhenius-type equation.

30.2

Riboud [133] A = e(𝑎∗(𝑀𝐶𝑎𝑂+𝑀𝑀𝑔𝑂)−𝑏∗𝑀𝐴𝑙2𝑂3+𝑐)

B = 𝑎 ∗ (𝑀𝐶𝑎𝑂 + 𝑀𝑀𝑔𝑂) − 𝑏 ∗ 𝑀𝐴𝑙2𝑂3 + 𝑐

Based on Urbain model, Riboud simplify the model equations and

optimize the model parameters using viscosity data of blast

furnace slag

61.0

Iida [136,

137]

𝑊𝐶𝑎𝑂 ∗ 𝑎 + 𝑊𝑀𝑔𝑂 ∗ 𝑏

𝑊𝐴𝑙2𝑂3 ∗ 𝑐 + 𝑊𝑆𝑖𝑂2 ∗ 𝑑

Iida’s model was developed based on slag basicity and own

optimized parameters. 68.6

Mill [138] 𝑀𝐶𝑎𝑂 ∗ 𝑎 + 𝑀𝑀𝑔𝑂 ∗ 𝑏

𝑀𝐴𝑙2𝑂3 ∗ 𝑐 + 𝑀𝑆𝑖𝑂2 ∗ 𝑑

Mill’s model was developed based on the oxides’ optical basicity,

which was reported by Duffy and Ingram 70.4

Shankar

[141]

𝑊𝐶𝑎𝑂 ∗ 𝑎 + 𝑊𝑀𝑔𝑂 ∗ 𝑏𝑊𝐶𝑎𝑂 + 𝑊𝑀𝑔𝑂

𝑀𝐴𝑙2𝑂3 ∗ 𝑐 + 𝑀𝑆𝑖𝑂2 ∗ 𝑑𝑀𝐴𝑙2𝑂3 + 𝑀𝑆𝑖𝑂2

Shankar optimized the model parameters and equation based on

Mill’s work. 55.2

78

Ray [149] 𝑀𝐶𝑎𝑂 ∗ 𝑎 + 𝑀𝑀𝑔𝑂 ∗ 𝑏

𝑀𝐴𝑙2𝑂3 ∗ 𝑐 + 𝑀𝑆𝑖𝑂2 ∗ 𝑑 Ray optimized the model parameters based on Mill’s work. 51.5

Hu [142] 𝑀𝐶𝑎𝑂 − 𝑀𝐴𝑙2𝑂3 + 𝑀𝑀𝑔𝑂 ∗ 𝑏 + 2𝑀𝑆𝑖𝑂2 ∗ 𝑐

𝑀𝑀𝑔𝑂 + 𝑀𝐶𝑎𝑂 − 𝑀𝐴𝑙2𝑂3 + 𝑀𝐴𝑙2𝑂3 ∗ 𝑐 + 2𝑀𝑆𝑖𝑂2

Hu also optimized the model parameters and equations based on

Mill’s work 44.3

Gan [147]

B = ∑ 𝑏𝑀𝑂𝑀𝑀𝑂

C = ∑ 𝑐𝑀𝑂𝑀𝑀𝑂

Gan first proposed Vogel-Fulcher-Tammann-type equation in

CaO-MgO-Al2O3-SiO2 field, which can also predict the glass

transition temperature the blast furnace slag with slight

modification.

54.1

Tang [148] 𝑁𝑜𝑛 − 𝑏𝑟𝑑𝑔𝑖𝑛𝑔 𝑜𝑥𝑦𝑔𝑒𝑛

𝑆𝑖𝑂4

Tang proposed the viscosity model using the ratio of non-bridging

oxygen to silica content. 63.9

QCV [151]

E𝑎 = E𝑎,𝑆𝑖−𝑆𝑖𝑀𝑆𝑖−𝑆𝑖 + E𝑎,𝑆𝑖−𝑀𝑒𝑀𝑆𝑖−𝑀𝑒

+ E𝑎,𝑀𝑒−𝑀𝑒𝑀𝑀𝑒−𝑀𝑒

Suzuki developed the viscosity model based on a bond fraction,

which was calculated by Factsage software. Suzuki’s model

contains large number of equations and parameters (>50 equations

and parameters for CaO-MgO-Al2O3-SiO2 quaternary system,

more for higher order system)

35.1

FactSage N/A N/A 37.7

Shu [143, E = E𝑆𝑖𝑂2𝑀𝑆𝑖𝑂2 + E𝑀2𝑆𝑖𝑂4𝑀𝑀2𝑆𝑖𝑂4 + E𝑀𝑜𝑀𝑀𝑜 Shu developed the viscosity models based on compositions of 42.4

79

144] three types of oxygen, which was calculated from optical basicity

values.

Zhang [145]

E𝑎 = E𝑎,𝑏𝑟𝑖𝑑𝑔𝑖𝑛𝑔𝑀𝑏𝑟𝑖𝑑𝑔𝑖𝑛𝑔 + E𝑎,𝑛𝑜𝑛−𝑏𝑟𝑖𝑑𝑔𝑖𝑛𝑔

𝑀𝑛𝑜𝑛−𝑏𝑟𝑖𝑑𝑔𝑖𝑛𝑔 + E𝑎,𝑓𝑟𝑒𝑒𝑀𝑓𝑟𝑒𝑒

Zhang developed the viscosity models based on compositions of

three types of oxygen, which was calculated from assumptions of

[AlO4] binding with Ca2+

and Mg2+

in CaO-MgO-Al2O3-SiO2

system.

28.5

Table 2.27 Summary of applicable oxides of existing viscosity model

Sources Application

Bottinga [126]

SiO2, Al2O3, CaO, MgO, TiO2, FeO, MnO, SrO, BaO,

Li2O, Na2O and K2O

Giordano [128]

SiO2, Al2O3, CaO, MgO, Na2O and K2O

Gupta

SiO2, Al2O3, CaO, MgO, Na2O, K2O, MnO and FeO

Neutral Network

[127]

SiO2, Al2O3, CaO and MgO

Urbain [131] SiO2, Al2O3, CaO, MgO, B2O3, MnO, FeO and PbO

80

Riboud [133] SiO2, Al2O3, CaO and MgO

Iida [136, 137] SiO2, Al2O3, CaO and MgO

Mill [138] SiO2, Al2O3, CaO, MgO, Na2O, TiO2, B2O3, MnO,

FeO, PbO and CaF2

Shankar [141] SiO2, Al2O3, CaO, MgO and TiO2

Ray [149] SiO2, Al2O3, CaO, MgO and TiO2

Hu [142] SiO2, Al2O3, CaO and MgO

Gan [147] SiO2, Al2O3, CaO, MgO, N2O and K2O

Tang [148] SiO2, Al2O3, CaO, MgO, N2O, K2O, FeO and Fe2O3

QCV [151] SiO2, Al2O3, B2O3, MgO, CaO, MnO, FeO, ZnO and

CuO

FactSage All oxides

Shu [143, 144] SiO2, Al2O3, CaO and MgO

81

2.5 The viscosity study review of suspension system

The viscosity of suspensions is of interest in many disciplines of engineering, for example,

food science, wastewater treatment and etc. The suspension viscosity ηsus primarily depends

on (1) the solid fraction, (2) shape and size of particles, and (3) the suspending Newtonian

liquid, which will be reviewed in the section 2.5.1 and 2.5.2 respectively.

A large number of studies have been carried experimentally and theoretically at room

temperature condition. There is a research gap that the solid impact on suspension was rarely

studied in a high-temperature region. It is known that the precipitation of solid particles in

molten slag was commonly observed in iron, steel, copper and other pyrometallurgy

processes. It is necessary to explore and compare the suspension viscosity by the systematic

variation of the parameters at both room and smelting temperature conditions. Table 2.28

summarized the experiment measurements of suspension viscosity at different systems.

Table 2.28 The brief review of viscosity study of suspension system at different system,

viscosity and temperature range, note: the relative viscosity means the ratio of suspension

viscosity to liquid viscosity

Author Solid/Liquid System Viscosity Range

(Pa.s)

Temperature Range

(oC)

Bibbo [152] Fiber

Water

Relative Viscosity

0.5-10

25

Chong [153] Glass beads

Polyisobutylene (PIB)

10-500 25

Darton [154] Silica sand

Water

0.1-3 20

Fan [155] Fiber

Water

Relative Viscosity

0.4-2

25

https://en.wikipedia.org/wiki/Eta_(letter)

82

Joung [156] Fiber

Water

Relative Viscosity

0.5-3.7

25

Kwon [157] Magnetic particle

Ethylene glycol

0.02-0.6 25

Konjin [158] Glycerine

polymethylmethacrylate

0.1-2.3 25

Marshall [159] Silica sols

Cis/trans-

decahydronaphthalene,

(Decalin)

2-3.5 200

Namburu [160] SiO2 nanoparticle

60% ethyleneglycol 40%

water

0.004-0.3 -35-50

Tsuchiya [161] Glass beads

Water

0.5-10 20

Wu [9] Paraffin

Oil

0.09-0.47 25

CaO-MgO-Al2O3-SiO2 0.2-0.5 1300-1400

Lejeune [162] CaO-MgO-Al2O3-SiO2 1.4-5 830-950

Wright [163] CaO-MgO-Al2O3-SiO2 2-7.5 1400-1500

2.5.1 Effects of liquid viscosity & Solid Fraction

Liquid viscosity and solid fraction are the two most critical factors in the experimental study

of suspension viscosity, which was also approved in the model simulation work. Einstein first

83

proposed a mathematical expression to predict the suspension viscosity ηsus using liquid

viscosity ηLiq and solid fraction f. The mathematical expression was accepted and optimized

by other researchers to improve the prediction accuracy of Einstein Model [164]. From the

model view, the mathematical expression η𝑠𝑢𝑠 = η𝑙𝑖𝑞 ∗ η𝑟𝑒𝑙𝑎 were utilized for the model

development of suspension viscosity prediction, where nrela is expressed by solid fraction as


Equation 2-32 Definition of relative viscosity

η𝑠𝑢𝑠

η𝑙𝑖𝑞= η𝑟𝑒𝑙𝑎 = f(𝑓)

Where η𝑠𝑢𝑠 is suspension viscosity, η𝑙𝑖𝑞 is the liquid viscosity. f (f) is a mathematical

function of solid fraction.

From the existing viscosity results, it is accepted that both liquid viscosity and solid fraction

has a positive proportional impact on the suspension viscosity at a temperature ranging from -

40 to 1500 oC. When a force applied, the shear stress of liquid is enlarged when the solid

exist within liquid comparing to the pure liquid condition. As

Figure 2.25 shown, with the appearance of the solid particle, the smooth molecular

distribution of fully liquid was converted to the rigid distribution of solid/liquid system;

hence increased the gradient (viscosity). Also, the increase in viscosity with solids

concentrations was attributed to the increased frequency of particle-particle interactions.

Figure 2.25 The shear stress enlarged from fully liquid system to solid/liquid system











84

For the solid fraction ranging from 0-1, the solid proportion and liquid viscosity have a

positive proportional impact on the suspension viscosity. In the low melt fraction regime, the

solid particles have a predominant role until the solid-like behavior is exhibited as solid

fraction achieving 1. As Figure 2.26 shown, with the increasing of solid particles, the

viscosity moderately increases but when a critical solid content is reached, the viscosity

increases so rapidly that over a short range. Upon critical point, the viscosity slowly increased,

which is known as solid-like behavior.

Figure 2.26 Viscosity deduced from data of van der Molten and Paterson (1979) [165]at high

solid fraction (circles) and from data of Mg3Al2Si3O12 by Lejeune (triangles) [162] and other

values at low solid fraction (squares) by Thomas [166]

2.5.2 Effects of Particle Size

There is a contradiction discussion about the impact of particle size on the suspension

viscosity. As Figure 2.27 shown, Wu construct a series study of paraffin/silicon oil system

under room temperature condition. The particle size ranges from 150 um to 450 um reported

similar results, which is only slightly derivate 1.2% [9]. Konijn constructs viscosity

measurement of glycerine/polymethylmethacrylate system and also reported that the particle

size did not impact on the suspension viscosity [167].

85

Figure 2.27 Experiment data of different particle size vs model prediction [167]

However, in Gust’s study, utilizing silica sand/water system, he proposed that the apparent

viscosity increased with particle size at the different pseudo shear rate [168]. The particles of

greater size possess more inertia such that on interaction with rotational bob, which will

momently stop and accelerate during rotation. In both these stages, their inertia affects the

amount of energy required. This dissipation of energy appears as “extra viscosity”.

In Bruijn's study of glycerine and polymethylmethacrylate system, for particles with

diameters less than 1 to 10 microns, colloid-chemical forces become important causing that

the relative viscosity increase as particle size decreasing [169]. For particles larger than 1 to

10 microns, de Bruijn believes that inertial effects due to the restoration of particle rotation

after collision result in an additional energy dissipation and consequent that viscosity

increased with increasing particle diameter, which reports similar conclusion as Gust study

[169].

Most of the viscosity models assumed that the particle shape is sphere for the estimation of

volume impact of solid particle. However, the experimental results demonstrated that

different particle shape could have significantly impact on the suspension viscosity. Nawab

observed experimentally that Nylon fibre suspensions could produce a measured viscosity

three times of the theoretical predictions [170]. This difference might be a result of fibre

curvature. By comparison of suspension viscosity of different particle shapes, at same

condition, it can be ranked that spherical particle reported the smallest suspension viscosity

[170].

86

2.5.3 The review of viscosity model of suspension system

On 1905, Einstein proposed the mathematical equations to estimate the viscosity of the

suspension system, which related the viscosity of the two-phase mixture to the volume

fraction of solid particles and liquid viscosity [173]. The Einstein model was developed using

Stoke law under the assumption of no interaction between the solid particles. Also, he

assumed that at very low particle fraction, the energy dissipation during laminar shear flow

increase due to the perturbation of the streamline by particles. Because the interactions

between solid particles are not considered, the equation can only be applied to the dilute

solution system [173].

Although Einstein model has a limited prediction range, the basic mathematical expression of

viscosity model of suspension system was accepted and utilized by other researchers, which

the suspension viscosity dependent on a constant liquid viscosity and solid volume fraction.

Other researchers accepted the basic expression of relative viscosity [η𝑠𝑢𝑠

η𝑙𝑖𝑞= η𝑟𝑒𝑙𝑎 ] and

developed own mathematical models to express the relative viscosity with high particle

fractions. There are two major branches of model development: 1) Extension of Einstein

model and 2) Cell model theory.

It is known that Einstein model assumed that no interaction occurred between solid particles.

Part of researchers focuses on the study by considering the possible interaction between two

or more particles interactions and derives the mathematical equations to predict the

suspension viscosity with a high solid fraction. For example, KD assume three flow pattern of

nearby particles including rotating independently, rotate as dumb-bell and rigid flow pattern;

hence derive the equation.

The development of Cell model based on the assumption that solid sphere of radius of Ro is

surrounded by liquid out to a radius R as shown in Figure 2.28. Suitable boundary conditions

and Stoke equation were applied at this outer boundary layer. For example, Brady assumed

that the velocity field on the outer sphere is precisely that of externally imposed flow [171].

Happel assumes that the shear stresses on the outer sphere are those of the imposed flow

[172].

87

Figure 2.28. The description of interaction between solid sphere and fluid particle

In the present study, altogether 11 models were collected and evaluated using experimental

data. The model features and its equations were summarized in Table 2.29 below.

88

Table 2.29. Summary of 10 different viscosity model, f is the solid fraction within suspension

Model Features Model Equation

Einstein [173] Einstein model is suitable for diluted sphere particles suspension under the assumption of

no interaction between solid particles.

η𝑠𝑢𝑠

η𝑙𝑖𝑞= η𝑟𝑒𝑙𝑎 = (1 +

5

2𝑓)

Kunitz [174] Kunitz modifies Einstein model in one of the deviation steps and empirical optimal the

parameters from (1-f)2 to (1-f)

4.

η𝑟𝑒𝑙𝑎 =1 + 0.5𝑓

(1 − 𝑓)4

Krieger-Dougherty

[175]

Assume three flow pattern of nearby particles including rotate independently, rotate as

dumb-bell and rigid flow pattern; hence derive the equation. η𝑟𝑒𝑙𝑎 = (1 −

𝑓

0.62)

−2.5∗0.62

Probstein [176]

A polydisperse suspension with a particle size distribution from submicrometer to

hundreds of micrometers is simulated and treated as bimodal. η𝑟𝑒𝑙𝑎 = (

1 − 1.351𝑓

1 − 0.39𝑓)

−2.493

Toda [177]

Based on Einstein theory, Toda model further derives the equation on the calculation of

dissipation of mechanical energy into heat in the dispersion. η𝑟𝑒𝑙𝑎 =

1 + 0.5𝑓 ∗ (1 + 0.6𝑓) − 𝑓

(1 − (1 + 0.6𝑓) ∗ 𝑓)2(1 − 𝑓)

Happel [178]

Based on the cell model theory, Happel assumes that the shear stresses on the outer sphere

are those of the imposed flow; then derive the equations on the steady-state Stokes-Navier

equations of motion omitting inertia terms.

η𝑟𝑒𝑙𝑎

= (1

+𝑓 (22 ∗ 𝑓

73 + 55 − 42 ∗ 𝑓

23)

10 ∗ (1 − 𝑓103 − 25 ∗ 𝑓 ∗ (1 − 𝑓

43))

Thomas [179]

Thomas model largely concerned with the transport characteristics of non-Newtonian

suspensions (sphere particle) by consideration of inertial force and measuring instrument

wall effects.

Thomas model reported an average 25% deviations for sets of existing viscosity data

η𝑟𝑒𝑙𝑎 = 1 + 2.5 ∗ f + 10.05 ∗ f 2

+ 0.00273 ∗ e16.6𝑓

89

using different size sphere particles and containers.

Roscoe [180]

Einstein expression is re-evaluated and optimized to improve the prediction of existing

viscosity data.

Roscoe model reported a good agreement with different sizes of sphere particles

suspension, which ranges from 10-40 solid%.

η𝑟𝑒𝑙𝑎 = (1 − 𝑓)−2.5

Mooney [181]

Mooney developed a model based on Einstein approach and reported a good agreement

with experimental data. η𝑟𝑒𝑙𝑎 = e

2.5𝑓1−0.75𝑓

Batchelor [182]

Cell model theory η𝑟𝑒𝑙𝑎 = (1 +

5

2𝑓 + 7.6 ∗ 𝑓2)

Bergenholtz [183]

Cell model theory η𝑟𝑒𝑙𝑎 = (1 +

5

2𝑓 + 5.92 ∗ 𝑓2)

90

Chapter 3 : Experiment Methodology

This chapter describes the experimental methodology utilized in the present study, which

include:

1. High-temperature viscosity measurements for fully liquid slag, which is established

by the Dr. Chen

2. Room temperature viscosity measurements for suspension, which ranges from 0-30

wt% solid.

3. The Raman spectroscopy study

3.1 High-Temperature Viscosity Measurement

The viscosity measurement techniques of high-temperature viscosity measurements have

been detailed studied by Dr. Chen in his Ph.D. Thesis [184]. A digital rotational rheometer

(model LVDV III Ultra; Brookfield Engineering Laboratories, Middle-boro, MA) controlled

by a personal computer was used in the current study. The acquisition of the torque measured

by the rheometer was simultaneously collected by Rheocalc software provided by Brookfield

Engineering Laboratories. A Pyrox furnace with lanthanum chromite heating elements

(maximum temperature 1923 K (1650 oC) was employed. The rheometer placed on a

movable platform was enclosed in a gas-tight steel chamber. There were two independent gas

flow circuits (one through the chamber, and another through the furnace) to suppress heat to

the chamber and protect the rheometer from high temperature. The rheometer rotated co-

axially the alumina driving shaft with the cylindrical spindle. The schematic diagram of

experimental set up is shown in the Figure 3.1.

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Figure 3.1 Schematic diagram of furnace for viscosity measurement at high temperature

Figure 3.2 provide dimensional details of the cylindrical crucible and spindle used during

viscosity measurements. The viscosity measurements included 3 major steps: 1. the

calibration of one set of equipment under room temperature, including Al2O3 rod, crucible

and spindles, 2. High temperature viscosity measurement using the calibrated equipment and

3: elemental analysis of quenched sample using EPMA.

Figure 3.2 Schematic diagram of crucible and spindle

92

3.2 Room Temperature Viscosity Measurement

The viscosity of suspension was measured using rotational viscometer as Figure 3.3. The

viscosities of solid-containing liquid at room temperature are measured by A Brookfield

digital rotational rheometer (model LVDV III Ultra) controlled by a PC with the standard

spindle provided by the same company. The acquisition of the torque measured by the

rheometer can be simultaneously collected by Rheocalc software provided by Brookfield

Company. A thermostatic water bath will be used to control and maintain the temperatures at

low-temperature ranges from 10 – 40 oC. A transparent crucible will be submerged in the

water

Figure 3.3 Schematic diagram of viscosity study at room temperature

3.3 Raman Spectroscopy Study

The Raman spectroscopy study was carried into two steps, the first step is to obtain the

quenched sample, which is completed using phase equilibrium experiment. The phase

equilibrium experiments were carried out in the vertical tube furnace by stabilizing the

synthetic sample in the hot zone for a period of time at Ar gas atmosphere. After the sample

achieves equilibrium, it will be quenched directly into the water bucket, which maintains the

high-temperature structure for Ramen analysis. The quenched sample will be crashed and

mounted to stabilize in the resin for Raman analysis.

93

The photograph of the furnace below is vertical tube furnace. The schematic diagram is

shown in Figure 3.4. The detailed description of the experimental procedures and conditions

were demonstrated in the “Chapter 6: Structural studies of Silicate using Raman

Spectroscopy”.

Figure 3.4 (a) left, a photograph of phase equilibrium experiment. (b) Right, a schematic

diagram of a vertical tube furnace

94

Chapter 4 : Viscosity Model Development in CaO-MgO-Al2O3-SiO2 System Based

on Urbain Model

The Urbain model was optimized in the present study by introducing the concept of optical

basicity to describe the correlation between slag composition and viscosity. The optimized

version significantly improves the prediction accuracy of CaO-MgO-Al2O3-SiO2 system of

blast furnace slag; also the parameters in the present model are 14 comparing to 22

parameters in the Urbain model (1987 version).

In chapter 4, the optimized Urbain model was presented in section 4.1. In addition, the

optimized model can be extended to calculate the viscosity of blast furnace slag including 8

common minor elements, including Fe, Ti, F, S, Na, K, B and Mn, which was reported in

section 4.2.

4.1 CaO-MgO-Al2O3-SiO2 system in blast furnace composition range

4.1.1 Introduction

Development of a reliable viscosity model for the CaO-MgO-Al2O3-SiO2 systems over a

wide range of compositions and temperatures is important for iron and steel making

processes. A blast furnace (BF) slag with proper viscosity leads to (a) fluent flowing in the

tapping process, (b) easy separation from hot metal and coke, (c) efficient desulphurisation

process and (d) less accretion formation on the BF wall [1]. High-temperature viscosity

measurement is practically difficult and, costing considerable time and money. Therefore, it

is necessary to establish a reliable model to predict slag viscosity to provide accurate

information for efficient blast furnace operation.

A number of viscosity models have been developed to predict the viscosity in the CaO-MgO-

Al2O3-SiO2 (typical BF slag components) system over the last decades as reviewed in Section

2.4. These viscosity models can be generally classified into two groups, empirical models,

and structural models. The empirical models correlate slag viscosity as a function of

temperatures and bulk compositions directly using experimental data. The structural models

consider the profound internal structure of silicate melts, which are more accurate and

flexible than empirical models. Urbain model is one of the structural viscosity models for

viscosity prediction covering a wide range of multi-component system. Several authors

95

chosen Urbain model for optimization due to its flexibility. Riboud and Forsbacka optimized

the Urbain model for mould fluxes and coal ash slag respectively, which both reported an

outstanding agreement with that slag system [134, 135]. Urbain proposed the model on 1981

for viscosity prediction of complex slag system, including CaO, MgO, FeO, SiO2, K2O and

etc [132]. From 1981-1990, Urbain focus on the viscosity experiment study of CaO-MgO-

Al2O3-SiO2 slag system and published the outcomes [60, 185]. Later on 1987, Urbain modify

the model equations and parameters for CaO-MgO-Al2O3-SiO2 system, which were

demonstrated in Section 2.4.7 [131]. The 1987 version of Urbain model demonstrated

superior performance on the CaO-MgO-Al2O3-SiO2 slag system. In the present study, due to

high flexibility, the Urbain model (1987 version) was selected as basement to developed a

new viscosity model for the CaO-MgO-Al2O3-SiO2 system in the blast furnace slag

composition range [131].

4.1.2 Experimental Data Used for Model Development

Accurate viscosity data are essential for successful development of a reliable viscosity model.

The viscosity measurements in the CaO-MgO-Al2O3-SiO2 system have been collected from

37 publications and critically reviewed in the Section 2.3. These data covers the composition

ranges of 10-67 wt% SiO2, 1-40 wt% Al2O3, 1-60 wt% CaO and 1-38 wt% MgO. The

reliability of viscosity data directly impacts on the model prediction performance. The quality

of data was carefully examined. Three sequential steps were undertaken to evaluate the data:

a) Review experimental techniques, b) Check data self-consistency, and c) Cross reference

comparisons. The evaluation details and examples have been demonstrated in the Section 2.3.

1760 out of 3125 viscosity data in the CaO-MgO-Al2O3-SiO2 system were accepted for

model development in the present study.

4.1.3 Silicate Melt Structure

The viscosity of molten slag is closely related to its structure, which is dependent on its

composition and temperature. The final blast furnace slag has four major components, SiO2,

Al2O3, CaO and MgO that can be categorized into three groups, acidic oxide (SiO2), basic

oxide (CaO and MgO) and amphoteric oxide (Al2O3). SiO2 forms a network structure through

(SiO4)4-

tetrahedral units to increase viscosity. The basic oxides Ca2+

and Mg2+

tend to break

the network and reduce slag viscosity.

Al2O3 can behave as either an acidic oxide or basic oxide depending on the concentrations of

other components. If sufficient basic oxides Ca2+

and Mg2+

are present to balance the (AlO4)5-

96

charges, the Al2O3 acts as an acidic oxide, which is incorporated into the silicate network as

(AlO4)5-

form. In the case of insufficient basic oxides, Al2O3 will behave the same as Ca2+

or

Mg2+

to break the (SiO4)4-

network. In typical BF composition ranges, where

(CaO+MgO)/SiO2 is high, the Al2O3 component is considered to act as an acidic oxide and

requires charge compensation of CaO and MgO.

4.1.4 Description of Model

The Urbain model is a structure-based model for the slag viscosity prediction, which has been

optimized for other multi-component systems by various researchers. Urbain firstly proposed

the model on 1981 and modified it to improve the performance in CaO-MgO-Al2O3-SiO2

system on 1987. As comparison in the literature review, the Urbain model (1987) version is

more suitable for the viscosity prediction of CaO-MgO-Al2O3-SiO2 system. Present study

select the Urbain model (1987 version) as a basement for the model development due to its

high flexibility. The comparisons of two Urbain models were introduced in the Section 2.4.7.

Viscosity is generally a function of temperature and chemical composition of molten slag.

Urbain considered Weymann’s expression of the temperature dependence of viscosity, which

is the modified Arrhenius-type equation [186] (Equation 4-1).

Equation 4-1 Arrhenius-type equation

η = A ∗ T ∗ exp (1000𝐵

𝑇)

Where η is viscosity in Pa.s, T is the absolute temperature (K), A is the pre-exponent factor

and B represents the integral activation energy.

In the modelling study by Urbain, the pre-exponent factor A and activation energy B was

reported to have a relationship as Equation 4-2 shown. The linear correlation were accepted

and utilized in other researchers’ viscosity models, such as the Shankar [32], Shu [187] and

Hu [142]. In the current study, a similar relationship between ln(A) and B is confirmed for

the CaO-MgO-Al2O3-SiO2 system using the accepted viscosity data. ln(A) and B has a strong

linear correlation (R2=0.948) and is used in the construction of current viscosity model. The

values of m and n in the present model are determined to be 0.501 and 7.681 respectively

optimized from the evaluated measurements in the CaO-MgO-Al2O3-SiO2 system (Section

2.3).

97

Equation 4-2 the linear relationship between A and B

𝑙𝑛𝐴 = −𝑚𝐵 − 𝑛

Where A the pre-exponential factor and B is the activation energy from Equation 4-3. m and

n is the model parameters are 0.501 and 7.681 respectively.

They are close to that reported by Hu (0.508 and 7.28) but different from that reported by

Urbain (0.29 and 11.57) [142]. Because, both Urbain and present study utilized the equation

ln(n/T)=ln(A)+1000B/T to determine the value of B; however Hu model utilized the

ln(n)=ln(A)+1000B/T. Both equations reported the linear relationship as Figure 4.1 shown.

𝑙𝑛𝐴 = −𝑚𝐵 − 𝑛

Figure 4.1 The linear relationship between EA and ln(A)

4.1.5 Expressions of Activation Energy

In the tradition Arrhenius equation, B is defined as the term “activation energy”. It is known

that the viscous flow is driven by thermally activated process. According to the network

theory, there are silicate network, broken network and free-moving components in the molten

slag. The activation energy term described the sum of required energy for these components

movement, which overcome the potential barrier to reach another equilibrium positions. In

the present study, the integral activation energy can be expressed as Equation 4-3 shown. The

contribution of the broken and free-moving components were individually calculated and

98

normalized based on molar composition. The contribution of silicate network is constant,

which is derived from the pure silica.

Equation 4-3 Parameter B calculation

𝐵 =𝑀𝐶𝑎𝑂 ∗ 𝐵𝐶𝑎𝑂 + 𝑀𝑀𝑔𝑂 ∗ 𝐵𝑀𝑔𝑂 + 𝑀𝐴𝑙2𝑂3

∗ 𝐵𝐴𝑙2𝑂3

𝑀𝐶𝑎𝑂 + 𝑀𝑀𝑔𝑂 + 𝑀𝐴𝑙2𝑂3

+ 𝐵𝑆𝑖0

Where M is a molar fraction of oxide, Bi is partial activation energy calculated by Equation

4-4 to Equation 4-6. A constant value of 63.98 is used for𝐵𝑆𝑖0 , which is derived from the pure

SiO2.

The partial activation energy Bi of each oxide is expressed as the third order polynomial

equation Equation 4-4 shown.

Equation 4-4 Partial activation energy Bi calculation, for Equation 4-3

𝐵𝐶𝑎 = 𝐵𝐶𝑎1 + 𝐵𝐶𝑎

2 ∗ 𝑁 + 𝐵𝐶𝑎3 ∗ 𝑁2

𝐵𝑀𝑔 = 𝐵𝑀𝑔1 + 𝐵𝑀𝑔

2 ∗ 𝑁 + 𝐵𝑀𝑔3 ∗ 𝑁2

𝐵𝐴𝑙 = 𝐵𝐴𝑙1 + 𝐵𝐴𝑙

2 ∗ 𝑁 + 𝐵𝐴𝑙3 ∗ 𝑁2

Where N represents the effective optical basicity of the slag and Bi1, Bi

2 and Bi

3 are model

parameters of each metal oxide.

The parameters B1, B

2 and B

3 for the present model were optimized from the viscosity

measurements as shown in Table 4.1. The parameter optimizations were constructed from

calculated activation energy and molar composition of oxides. The activation energy B and

pre-exponential factor A can be determined from plotting ln (η

𝑇) = ln(A) +

1000B

T. With

known B and Equation 4-3, the range of BCaO, BMgO, BAl2O3 and BSiO2 can be estimated within

a certain range for all compositions, which are BCaO= (-30)~ (-250), BMgO= (-45)~(-180),

BAl2O3= (-15)~(+10) and BSiO2= around 60. It can be noted that at low basic oxide conditions,

the Al2O3 has a negative contribution on the silicate network due to its amphoteric property.

The parameters of B1, B

2 and B

3 were \optimized based on the oxide contribution ranges.

99

The experiment measurements confirmed that CaO and MgO negatively contributed to the

activation energies, which represent the network breaking and reduce the slag viscosity. In

contrast, the Al2O3 and SiO2 positively contributed to the activation energy, which represents

the network-forming effect and improve the slag viscosity.

Table 4.1 Parameters B used in Equation 4-4

B CaO MgO Al2O3

1 -35.7 -46.9 0.5

2 6.76 20.16 2.32

3 -70.2 -60.1 -3.32

The effective optical basicity of the slag N can be calculated by Equation 4-5 using the

optical basicity of CaO, MgO, Al2O3, (SiO4)4-

and (AlO4)5-

. The optical basicity of each

component represents their ability for network-breaking or network-forming. The values of

optical basicity of CaO, MgO, and Al2O3 are adopted from Duffy. The new parameters ΛiOpt

,

which represent the optical basicity of (SiO4)4-

and (AlO4)5-

were derived from the viscosity

data. The optical basicity values were shown in Table 4.2.

Equation 4-5 Slag basicity N calculation, for Equation 4-4

𝑁 =Λ𝐶𝑎𝑂 ∗ 𝑀𝐶𝑎𝑂 + Λ𝑀𝑔𝑂 ∗ 𝑀𝑀𝑔𝑂 − Λ𝐴𝑙2𝑂3

∗ 𝑀𝐴𝑙2𝑂3

Λ(𝐴𝑙𝑂4)5−𝑂𝑝𝑡 ∗ 𝑀(𝐴𝑙𝑂4)5− + Λ

(𝑆𝑖𝑂4)4−𝑂𝑝𝑡 ∗ 𝑀(𝑆𝑖𝑂4)4−

Where M is a molar fraction of metal oxide, Λi is the effectiveness of basic oxides and ΛiOpt

is the effectiveness of acidic oxide. Note: MAlO4 = 2*MAl2O3.

Table 4.2 Model parameters N

CaO MgO Al2O3

100

Λ 1 0.78 0.6

(SiO4)4-

(AlO4)5-

ΛOpt

2.789

0.295

4.1.6 Model Performances

The revised Urbain model has been constructed in the present study to predict the viscosity

for BF slags. This optimized model has a reduced number of equations (from 14 to 7) and

parameters (from 22 to 14) compared to the Urbain model (1987 version). The prediction

performance was evaluated by comparison of other models using the accepted viscosity

measurements in the CaO-MgO-Al2O3-SiO2 slag system.

In order to provide a full view of the comparison, the evaluation of the model performance

was carried out for two different composition ranges: a) all data in the CaO-MgO-Al2O3-SiO2

system; b) data in the typical BF slag composition range 30-40 wt% SiO2, 10-20 wt% Al2O3,

30-45 wt% CaO and 5-10 wt% MgO. Each viscosity model was examined and compared

using the above data classifications to test its accuracy.

The mean deviation Δ is calculated using Equation 4-6 described as follows.

Equation 4-6 the viscosity prediction deviation calculation

Δ =1

𝑛∗ ∑ |

𝜂𝐶𝑎𝑙𝑐 − 𝜂𝐸𝑥𝑝

𝜂𝐸𝑥𝑝| ∗ 100%

Where Δ the mean deviation, n is is the total number of simulations, ηCalc is the model


The results for model comparison are shown in

Figure 4.2. It can be seen that the present model has the lowest deviation in both composition

ranges, with 29.5% in the full composition range and 13.5% in the BF slag composition range.

The relative deviations reported by other models are all above 30% in the full composition

range and 20% in the BF slag composition range.

101

Figure 4.2 Comparison of the current viscosity model with others

A detailed comparison of the viscosity model performance is constructed using the three most

accurate models: present model, Zhang model [188] and Urbain model [131] in the viscosity

range 0 - 1 Pa.s, which is typical for BF slags. As Figure 4.3 shown, the present model has

superior performance than both Zhang and Urbain models. The mean deviation is an average

of the absolute deviation which may underestimate the model prediction accuracy. For the

viscosity measurements between 0-1 Pa.s, as Figure 4.3 shown, the mean deviation is 12.5%,

16.4% and 16.3% for the present model, Zhang model, and Urbain model respectively.

However, for a given experimental viscosity, the maximum predicted deviations can be 0.3

Pa.s for Urbain model, 0.37 Pa.s for Zhang model that are much higher than the present

model (0.06 Pa.s).

102

Figure 4.3 Three model performance for 0 - 1 Pa.s, mean deviation for three models: present

model 12.5%, Zhang model 16.4% and Urbain model (1987 version) 16.3% [131, 188]

4.1.7 Industrial Applications

Examples of the applications in the prediction of BF slag viscosity are shown in this section

using the present viscosity model. Figure 4.4 shows the effect of MgO on the viscosity of BF

slag at 15 wt% Al2O3 and 1500 °C. It can be seen that the calculated viscosities by the present

model agree very well with Machin’s measurements. At a given CaO/SiO2 ratio and Al2O3

concentration, replace of (CaO+SiO2) by MgO decreases the slag viscosity. On the other

hand, the BF slag viscosity increases with decreasing MgO. In the ironmaking process,

sulphur removal of hot metal directly related to the slag viscosity. The higher viscosity of the

slag could increase the sulphur content in the hot metal. To balance the viscosity raised by

decreasing MgO, the CaO/SiO2 ratio in the slag can increase according to the predictions

shown in Figure 4.4. It also can be seen that at CaO/SiO2 ratio of 1.30, 15 wt% Al2O3 and

1500 °C, the viscosities of the BF slag are below 0.5 Pa.s even the MgO concentration in the

slag is as low as 2 wt%. This indicates that low MgO in slag does not have a significant effect

on slag tapping.

103

Figure 4.4 Effect of MgO on viscosity of BF slag at 15 wt% Al2O3 and 1500 °C predicted by

the present model with comparisons to the experimental data [74]

Figure 4.5 shows the effects of Al2O3 concentration and temperature on slag viscosity at 40

wt% SiO2 and 10 wt% MgO. It can be seen that the calculated viscosities by the present

model agree very well with the reported measurements. At fixed SiO2 concentration and

temperature, the viscosity increases with increasing Al2O3 concentration and the increment is

more significant at lower temperatures. For example, the viscosity is increased by

approximately 0.4 Pa.s at 1500 oC and 0.65 Pa.s at 1450

oC when the Al2O3 concentration in

the slag is increased from 10 to 20 wt%. On the other hand, the viscosity is more sensitive to

temperature for the slag containing higher Al2O3. Decrease of temperature from 1500 to

1450oC increases the viscosity by 0.1 Pa.s for 10 wt% Al2O3 slag and 0.35 Pa.s for 20 wt%

Al2O3 slag. This indicates that increased Al2O3 concentration in BF slag not only increases

viscosity directly but also decreases the thermal stability of the slag.

104

Figure 4.5 Effects of Al2O3 concentration and temperature on slag viscosity at 40 wt% SiO2

and 10 wt% MgO predicted by the present model with comparisons to the experimental data

of Gultyai [83], Hofmann [22] and Machin [68]

4.1.8 Conclusions

A novel viscosity model has been developed based on Urbain model (1987 version) in the

CaO-MgO-Al2O3-SiO2 system. The present model improved the viscosity prediction for the

blast furnace slag. The present model shows superior performance to the existing viscosity

models, which reduce the prediction deviation from 22% (Urbain model) to 14% (present

model). Also, the parameters in the present model are 14 compared to 22 in the original

Urbain model. Present model can provide accurate viscosity prediction of CaO-MgO-Al2O3-

SiO2 system, which occupied 97% of blast furnace slag. In recent study, the impact of minor

element was addressed, which report the significant impact on the final slag viscosity. The

present model was further investigated and developed for the viscosity prediction of minor

element within the blast furnace slag, which would be demonstrated in the Section 4.2.4.2

CaO-MgO-Al2O3-SiO2 system containing 8 minor elements

4.2.1 Introduction

Slag viscosity is one of the important properties in ironmaking process, which significantly

influences operation and fuel efficiency. Viscosities of the CaO-MgO-Al2O3-SiO2 system (97

wt% of slag) have been well studied in last decades. Because of gradual consumption of high-

grade iron ore, in view of operation cost and energy efficiency, the low-grade materials and

pulverized coal injection were used in the blast furnace (BF) operation. This results in

105

increases of impurities, such as Na2O, K2O, MnO and TiO2 in the slags. CaF2 and B2O3 are

fluxes used in BF maintenance stage to remove the accretion formed inside the furnace wall,

which will also affect the final slag composition. A typical blast furnace slag compositions

including minor elements are summarized in Table 4.3.

Table 4.3 Summary of typical BF composition range

In the present study, the impacts of 8 minor elements on slag viscosity were individually and

systemically studied. Previous viscosity data relevant to the BF slag with minor elements

were also collected and reviewed. A series of viscosity measurements of 6 minor elements

(Na2O, K2O, S, MnO, FeO, TiO2, CaF2 and B2O3) was conducted at the University Of

Queensland (UQ). The viscosity model was developed for the prediction of CaO-MgO-

Al2O3-SiO2 slag system containing minor elements.

4.2.2 Experimental Methodology

A series of high-temperature viscosity measurements were carried out to investigate the

effects of TiO2, MnO, FeO, B2O3, CaS, CaF2 on the BF slag. The apparatus and

methodologies of the viscosity measurements have been reported in previous studies [13] and

section 3.1. The viscosity measurements were carried out from high temperature to low

temperature in 50 °C interval. The sample was kept for long enough time after temperature

decreasing to achieve the equilibrium. The lowest measuring temperatures of the slags were

predicted by FactSage 6.2 to ensure the molten slag status. After measurements have been

Component Composition (wt%)

SiO2 30-40

Al2O3 15-20

CaO 35-45

MgO 5-10

CaO/SiO2 1-1.2

F, S, MnO, FeO, B2O3, Na2O, K2O, TiO2 0-3

106

completed, the sample was directly quenched into the water to convert the liquid into the

glass. The quenched samples were sectioned, mounted, polished and elementally analyzed by

electron probe X-ray micro-analysis (EPMA). In the present study, S is recalculated to CaS,

and F is recalculated to CaF2 for presentation purpose. The samples containing B2O3 and CaS

were also sent for Inductively Coupled Plasma (ICP) analysis. The compositions of B2O3 and

CaS measured by ICP were very close to those measured by EPMA.

4.2.3 Viscosity Database

4.2.3.1 Collected Reference

The viscosity database was established by collecting reliable viscosity measurements from

literature and present measurements. After a critical literature review, very limited viscosity

data in systems of CaO-MgO-Al2O3-SiO2-B2O3 and CaO-MgO-Al2O3-SiO2-Na2O (K2O)

were found, which were reviewed in the Section 2.3.5. More researchers studied the impact

of FeO and TiO2 additives on BF slag viscosity, which were reported in the section 2.4.5.

Only one publication in each system was collected for MnO, Na2O, and K2O containing BF

slag system. According to the measurement techniques and conditions, the viscosity data

were carefully examined and evaluated. For example, the data obtained at a temperature

significantly below the liquidus temperature (e.g. 50 °C), which is not accepted in the present

study.

4.2.3.2 Minor Element Impact

In the CaO-MgO-Al2O3-SiO2 slag system, the role of four major components CaO, MgO,

Al2O3 and SiO2 had been explained before in the Section 4.1.3. The viscosity of molten slag

is closely related to its structure, which is dependent on its composition and temperature. The

final BF slag has four major components, SiO2, Al2O3, CaO and MgO that can be categorized

into three groups, acidic oxide (SiO2), basic oxide (CaO and MgO) and amphoteric oxide

(Al2O3). SiO2 forms a network structure through (SiO4)4-

tetrahedral units to increase

viscosity. The basic oxides Ca2+

and Mg2+

tend to break the network and reduce slag

viscosity.

The silicate structure is composed of connected silicate, broken network and free-moving

component. According to the network theory, the minor elements can be classified into 3

categories: network former, network modifier and amphoteric oxide. The elements of F, S,

Na, Fe, Mn belong to the network modify group, which reduce the slag viscosity. According

to Kim’s viscosity study of K2O containing system, K2O is the network former, which

107

increased the slag viscosity within composition range 1-10 wt%. In terms of the viscosity

impact of TiO2, there are two contradictive opinions. Liao believed that the TiO2 has a similar

structural unit as SiO2, which positively increase the slag viscosity (TiO2>20wt%) [119].

When the TiO2 concentration decreased, in Park’s viscosity measurement, it has been found

the addition of TiO2 reduce the slag viscosity of blast furnace type slag [121].

4.2.4 Result & Discussion

4.2.4.1 Comparisons of viscosities

The viscosities of 8 synthetic slags with minor elements (B2O3, F, S, MnO, FeO, Na2O, K2O,

and TiO2) were measured. The viscosity data from both present study and literatures

indicated that the additions of minor elements B2O3, F, S, MnO, FeO, TiO2 and Na2O reduce

the viscosity. In addition, the viscosity reduction effect of CaF2 additive is stronger than other

minor elements. Kim et al reported that addition of K2O in CaO-MgO-Al2O3-SiO2 system

increased the viscosity.

Figure 4.6 shows the comparison between the present viscosity measurements and data from

Liao et al [119] and Park [120] in the close composition in the CaO-MgO-Al2O3-SiO2-TiO2

system. It can be seen that the present measurements generally agree with Park’s data. The

comparison of viscosity data at a different TiO2 concentration in close CaO/SiO2 ratio, Al2O3

content, and MgO content shows that the addition of TiO2 into the system keeps decreasing

the viscosity.

Figure 4.6 Comparison of viscosities for CaO-MgO-Al2O3-SiO2-TiO2 slag by Park [120] and

Liao [119]

108

4.2.4.2 Viscosity Model Description

A viscosity model on CaO-MgO-Al2O3-SiO2 system has been proposed by the present

authors in the Section 4.1. In the present study, the model is extended to predict the effects of

Na2O, K2O, MnO, FeO, TiO2, B2O3, CaF2 and CaS additions on the viscosity of blast furnace

slags.

The details of model developments had been introduced in the Section 4.1. The following

section will focus on the extension part of addition of minor element. The temperature

dependence of viscosity can be described by the Arrhenius-like equation as shown in

Equation 4-7.

Equation 4-7 the modified equation from Frenkel-Weymann equation (Equation 4-1)

η = A ∗ T ∗ exp (EA

𝑇)

Where η is viscosity in Pa.s, T is the temperature in K, EA is viscous activation energy in

kJ/mol, and A is the pre-exponential factor.

𝑙𝑛𝐴 = −𝑚 ∗ EA − 𝑛

Where A the pre-exponential factor and B is the activation energy from Equation 4-3. m and

n is the model parameters are 0.501 and 7.681 respectively.

This correlation has been widely used by many researchers in the development of viscosity

models, such as the Shankar, Shu, and Hu. The values of m and n in the present model are

determined to be 0.501 and 7.681 respectively, which is the same as shown in section 4.1.4.

As shown in Equation 4-8, the activation energy B in the present model is expressed by the

sum of all metal oxides multiplied with their partial activation energies Ei (i =SiO2, FeO, CaO,

MgO, Al2O3, CaF2, B2O3, TiO2, Na2O, K2O, MnO, and CaS).

Equation 4-8 Activation energy equation

EA = ∑(Mi *Ei)

Where Mi and Ei are molar fractions and partial energy of each metals oxides respectively.

109

Please note, the equation and parameters of SiO2, CaO, MgO, and Al2O3 were reported in the

section 4.1.4 before. In Equation 4-9, the partial activation energy Ei of each metallic oxide

can be expressed using the following polynomial equation. The model parameters were

reported in Table 4.4.

Equation 4-9 Partial activation energy Ei calculation, for Equation 4-8

Ei = Ei0 + Ei

1*B + Ei2*B２

Where B is optical basicity ratio, Bi0, Bi

1 and Bi

2 are model parameters of each metal oxide.

From the experiment measurements, the contributions of minor elements could be estimated

within a range using the calculated activation energy and its molar composition. And Bi1-3

can

be determined, which is summarized in the Table 4-4. A large negative numbers were

reported for the model parameters of CaF2 and B2O3, which significantly reduce the slag

viscosity. In contrast, the K2O positively contributed to the activation energy, which

represents the network-forming effect and improve the slag viscosity.

Table 4.4 Model parameters to calculate Ei of each minor element, the parameters of SiO2,

CaO, MgO, and Al2O3 were reported in the section 4.1.4 before

E CaF2 FeO TiO2 B2O3

CaS MnO Na2O K2O

1 -832.48 -279.62 -94.56 -263.07 -80.65 -43.77 -29.66 34.94

2 1752.92 1224.44 142.54 10.01 1.75 4.22 2.50 -1.10

3 -14.06 59.91 117.53 10.00 43.24 1.03 1.64 -6.52

As Equation 4-10 shown, the structural of different silica composition is indicated by

parameter basicity B, which was calculated using optical basicity and molar composition of

oxide.

Equation 4-10 Slag basicity B calculation, for Equation 4-9

B =∑ Bi*Mi-BAl2O3MAl2O3i=Ca,Mg,andetc

∑ Ai*Mii=Si&Al

110

Where M is molar fraction of cations and anions, Bi is optical basicity of basic oxides (CaO,

MgO, Na2O, K2O, MnO, CaS, CaF2, MnO, B2O3, FeO, and TiO2) and Ai is optical basicity of

acidic oxide (SiO2 and Al2O3) from the optical basicity of Duffy as shown in Table 4.5.

Table 4.5 Optical basicity of oxide from Duffy

Optical

Basicity CaF2 FeO TiO2 B2O3

CaS MnO Na2O K2O

1.2 1 1 0.42 1 1 1.15 1.4

The present model performance is evaluated using Equation 4-6 by comparison between the

predicted viscosity and experimental data. In the present study, only the measurements

ranging within blast furnace slag composition were selected for evaluation, which is

CaO/SiO2=1-1.3, 1-10 wt.% MgO, 10-20 wt.% Al2O3 and 1-5 wt.% minor element. In

addition, the Urbain model (1981 version) was utilized as the comparison with present model.

The outcomes were summarized in Table 4.6. Present model reported a low deviation within

BF slag composition ranges comparing to the Urbain model (1981 version). From the

equations and parameters of the Urbain model, it did not encounter the CaF2 and B2O3 as a

strong network modify, which report a large deviations for these two components. Also,

Urbain model regarded the K2O as a network modify in the CaO-MgO-Al2O3-SiO2 system,

which did not obey the experimental measurements. In contrast, the Urbain model reported

the lowest deviation for MnO containing system, because Urbain modified its models for

CaO-MgO-Al2O3-SiO2-MnO system on 1987.

Table 4.6 Summary of model performance in BF slag composition range

BF slag with different minor

elements

Deviation (%)

Present Model Urbain Model

TiO2 14.5 25.8

B2O3 4.9 40.6

111

CaF2 8.6 50.4

CaS 4.2 38.2

MnO 6.8 15.5

FeO 12.6 23.4

Na2O 14.6 32

K2O 13 30

The performance of present model (Figure 4.7A) and Urbain (Figure 4.7B) model were

further investigated in the CaO-MgO-Al2O3-SiO2-“TiO2” system of the Shankar, Park and

present study measurements [41]. As Figure 4.7 shown, present retained consistent

performance from low to high viscosity regions. Urbain model reported the accurate

prediction and under-estimate the high viscosity slag.

Figure 4.7 the model prediction vs experimental results of CaO-MgO-Al2O3-SiO2-TiO2 slag

system of Park [120], Shankar [32] and present (A) left, present model and (B) right, Urbain

Model (1981 version) [132]

At the current stage, the present model could not provide accurate predictions beyond BF slag

composition range. Figure 4.8 demonstrates that the deviation of the predictions increases

with increasing FeO concentration. As shown in Figure 4.8, when FeO concentration is lower

than 10 wt%, the average predict deviation is around 15%. If the FeO content is increased to

112

30 wt% (copper slag composition range), the prediction deviation will be increased to 30%. It

indicated that the present model can only provide accurate viscosity information for BF slag

composition ranges.

Figure 4.8 Increase of prediction deviation in CaO-MgO-Al2O3-SiO2-FeO system with

increasing FeO concentration by Bills [64] , Gorbachev [189], Higgins [190] and present

study

4.2.4.3 Industrial Application

The viscosity reduction ability of 8 minor elements was compared through model prediction

at 1500 °C. The base composition is 35 wt% SiO2, 17.4 wt% Al2O3, 38.6 wt% CaO and MgO

9 wt%. The concentrations of SiO2, Al2O3, CaO and MgO proportionally decrease when the

concentration of additive increases. Except for K2O, other additives decrease the slag

viscosity. It can be seen from Figure 4.9 that, the ability of viscosity decrement by different

minor elements in BF slag systems can be ranked as: CaF2> B2O3 > CaS > Na2O > TiO2 >

MnO > FeO. Because of strong viscosity reduction ability, CaF2 and B2O3 minor element

were often used to remove accretions on the BF wall.

113

Figure 4.9 The comparison of viscosity reduction ability of 8 minor elements on BF slag

viscosity

There are two major routes to reduce the operation cost of BF ironmaking process: 1) reduce

MgO flux addition, 2) increase using high Al2O3 content iron ore. Both routes will tend to

increase the slag viscosity at current operation condition. The minor elements from low-grade

iron ore can effectively reduce BF slag viscosity. For example, due to abundant Ti-bearing

iron ore resources in western part of China, Ti-bearing iron ores were used and CaO-MgO-

Al2O3-SiO2-TiO2 slag was generated. The concentration of TiO2 in final slag can be 21-23 wt%

in Panzhihua Iron and Steel and 15-18 wt% in Hebei Iron & Steel Group. As Figure 4.10

shown, present model can provide an accurate prediction for typical slag compositions

containing TiO2 above 1450 oC and 0-20 wt% TiO2 containing slag. The TiO2 addition into

slag can reduce slag viscosity however due to inevitable precipitation of Ti(C, N) at high

temperature; the viscosity significantly increases and blast furnace operation with high TiO2

slag is still challenging.

114

Figure 4.10 Comparison of model prediction and Liao’s measurements [119]

4.2.5 Conclusions

In the present study, the impacts of 8 minor elements on BF slag viscosity were systemically

studied, which includes Na2O, K2O, FeO, B2O3, CaF2, CaS, TiO2, and MnO. It was found that

CaF2 has the most significant effect of BF slag viscosity reduction. Except for K2O, the other

7 additives decrease the slag viscosity.

An existing CaO-MgO-Al2O3-SiO2 viscosity model has been extended to predict the effects

of minor elements on the viscosity of BF slags using present and collected viscosity data. The

model reported the good agreements with the available experimental data within BF slag

composition range. For the slag of CaO-MgO-Al2O3-SiO2-“FeO” system (copper smelting

slag), the prediction deviation would increase at high concentration of “FeO” content. Further

experimental work will be required to improve the model performance.

115

Chapter 5 : Viscosity Model Development Based on Probability Theorem

In the existing viscosity models of the CaO-MgO-Al2O3-SiO2 system, few researchers

discussed the distribution of cations (Ca2+

or Mg2+

) in SiO4 and AlO4 network

structure. A new term probability was proposed to describe the probability of Ca2+

(or

Mg2+

) cations to connect with SiO4 and AlO4 tetrahedra unit by considering the ionic

electronegativity and radius.

The proposed model demonstrated superior performance in the viscosity prediction of

full composition range of CaO-MgO-Al2O3-SiO2 system; as well as its sub binary,

ternary system, blast furnace composition and ladle furnace range. In chapter 5, the

novel developed model was presented in Section 5.1. In addition, the present model

can be extended to calculate the viscosity of CaO-MgO-Al2O3-SiO2-“FeO”, which

was reported in Section 5.2.

5.1 CaO-MgO-Al2O3-SiO2 system in full composition range

5.1.1 Introduction

Slag viscosity is critically important to various pyrometallurgical operations, which is

necessary for process optimization and reducing the operating costs.

Critical data evaluation and model assessments have been carried out in Section 2.3.

3115 viscosity data in the CaO-MgO-Al2O3-SiO2 system, which covers wide

composition and temperature ranges, were collected and examined based on

experimental techniques, data consistency, and cross-reference comparisons. The data

related to the compositions of ironmaking and steelmaking slags were also selected

for evaluation.

Using the accepted data above, a new viscosity model is proposed for the CaO-MgO-

Al2O3-SiO2 system and the performance of this model is compared with other existing

models. In addition, the present model can also be used to predict the low orders

silicate systems containing CaO, MgO, and Al2O3.

5.1.2 Silicate melt structure

The viscosity of molten slag closely related to its structure, which is dependent on

composition and temperature. The components of the quaternary system CaO-MgO-

Al2O3-SiO2 can be categorized into three groups: acidic oxide (SiO2), basic oxide

116

(CaO and MgO) and amphoteric oxide (Al2O3). SiO2 forms a network structure

through (SiO4) tetrahedral units. The addition of basic oxide, either CaO or MgO, will

break the [SiO4] network. It is widely accepted that O2-

from basic oxides tends to

break the Si-O-Si bond in silicate network and forms Si-O- intermediate, which

require cations (Ca2+

or Mg2+

) charge compensation. Also, amphoteric oxide Al2O3

can form AlO4 unit to connect with the [SiO4] network, which requires cations (Ca2+

or Mg2+)

charge compensation as well. As shown in Figure 5.1, the insertion of O2-

into SiO4 network tends to break covalent bond between Si and [O] and Ca2+

will

compensate the O- charge. This intermediate Ca(Mg)-SiO4 structure unit has one free

positive charge, which is able to break another SiO4 or compensate the AlO4 charges.

Figure 5.1 Interaction among Ca2+

cations, silica and alumina

Al2O3 can behave as either acidic oxide or basic oxide depending on the

concentrations of basic oxides. If sufficient Ca2+

and Mg2+

cations are present to

balance the (AlO4)- charges, the Al2O3 acts as an acidic oxide which is incorporated

into the silicate network in tetrahedron coordination. In the case of insufficient basic

oxides, Al3+

will behave the same as Ca2+

or Mg2+

to break the (SiO4) network.

In CaO-MgO-Al2O3-SiO2 system, the major roles of Ca2+

/Mg2+

are to compensate the

Si-[O]- charge and [AlO4]

5-. Due to electrical force between charges, it is accepted

that when the Ca2+

/Mg2+

concentration is low, they have higher priority to balance the

AlO4 charges than breaking the Si-O covalent bond.

5.1.3 Pre-Exponential Factor A

The temperature dependence of viscosity can be described by the Arrhenius-type

equation (Equation 5-1).

117

Equation 5-1 Arrhenius type equation

η = A ∗ exp (1000 ∗ 𝐸𝐴

𝑇)

Where η is viscosity in Pa.s, T is the absolute temperature (K), A is the pre-

exponential factor, EA represents the integral activation energy in J/mol.

As shown in Equation 5-2, a linear relationship between pre-exponent factor A and

activation energy EA was proposed by Urbain [131]. The activation energy EA and

pre-exponential factor A can be determined by plotting ln(η) against 1/T under the

same composition.

Equation 5-2 the linear relationship between A and B

𝑙𝑛𝐴 = −𝑚 ∗ 𝐸𝐴 − 𝑛

Where A the pre-exponential factor and EA is the activation energy from Equation 4-3.

m and n is the model parameters are 0.4144 and 4.1485 respectively.

This linear correlation has been widely applied in different viscosity models, such as

the Shankar’s and Hu‘s model [141, 142]. In the present study, from 604

compositions of accepted viscosity data, the linear correlation is confirmed as shown

in Figure 5.2, ln(A) and EA has a linear relationship with R2=0.948, which will be

used in the construction of the present viscosity model. m and n values in Equation

5-2 are 0.4144 and 4.1485 respectively.

118

Figure 5.2 The linear relationship between EA and ln(A)

5.1.4 Network Modifier Probability

In the existing viscosity models of the CaO-MgO-Al2O3-SiO2 system, few researchers

discussed the distribution of cations (Ca2+

or Mg2+

) in SiO4 and AlO4 network

structure except Zhang model [188]. Zhang et al calculated the concentration of three

types oxygen (O2-

, O- and O

0) by several assumptions; for example, the full amount of

CaO first compensate the Al2O3 then break silicate network; then MgO will break the

rest of silicate network, which did not consider equilibrium condition within the

quaternary system.

With the study of silicate based mineralogy, Ramberg suggests that the silicate

structure (polymerized level of the SiO4 network) is dependent on basic oxide

concentrations, atomic radius and electronegativity [191]. In the present study, a new

term “probability (P)” is introduced to describe the probability of Ca2+

(or Mg2+

)

cations to connect with SiO4 and AlO4 tetrahedral unit. PCa and PMg. The Equation 5-3

are proposed to be the probability of Ca2+

or Mg2+

connecting to the Si-O network

respectively. Ca2+

and Mg2+

cations were also required for (AlO4)- charge

compensation. Therefore, the (1-PCa) are the probability of cations to connect with

AlO4. It is known that Ca2+

and Mg2+

have a higher priority to compensate the AlO4

charges. At low concentration of CaO/MgO, there is a high probability of

compensating the (AlO4)- charges. When the concentration of CaO/MgO increases,

the probability of breaking Si-O will raise.

119

Equation 5-3 the probability calculation of cations Ca and Mg for Equation 5-6

𝑃𝐶𝑎 =χ𝐶𝑎2+𝑀𝐶𝑎2+

χ(𝑆𝑖𝑂4)4− ∗ 𝑀(𝑆𝑖𝑂4)4− + χ(𝐴𝑙𝑂4)5− ∗ 𝑀(𝐴𝑙𝑂4)5−

𝑃𝑀𝑔 =χMg2+𝑀𝑀𝑔2+


Where M is a molar fraction of a metal oxide; X is electronegativity of structure units

in slag system.

The electronegativity of Ca2+

, Mg2+

, AlO4 and SiO4 units are determined using

Mulliken equation, as shown in Equation 5-4, which is derived from 1st ionization

energy and electron affinity of the atom. The values of electronegativity are shown in

Table 5.1.

Equation 5-4 Mulliken equation

χ =𝐼 + E

2

Where I is the ionization energy (kJ/mol) and E is electron affinity (kJ/mol)

Table 5.1 Electronegativity χ of basic oxide cations and network former units

Ca2+

Mg2+

(AlO4)

(SiO4)

Χ 3.07 3.82 6.674 6.985

5.1.5 Activation Energy EA

In Arrhenius equation, EA is defined as the integral activation energy of silicate slag,

which is composed of four metal oxides and can be expressed as Equation 5-5.

120

Equation 5-5 Activation energy calculation

𝐸𝐴 = 𝐸𝐶𝑎𝑂 + 𝐸𝑀𝑔𝑂 + 𝐸𝐴𝑙2𝑂3+ 𝐸𝑆𝑖𝑂2

Where Ei is activation energy of i component (i = SiO2, Al2O3, CaO, and MgO),

which is calculated from Equation 5-6.

In CaO-MgO-Al2O3-SiO2 system, as a network modifier, three structure units are

relevant to CaO including free oxygen O2-

, SiO4-Ca-SiO4, and SiO4-Ca-AlO4. As PCa

defined before, one Ca2+

cation has probability PCa to connect with one SiO4

tetrahedron. Therefore, the probability of SiO4-Ca-SiO4 and SiO4-Ca-AlO4 can be

assumed as PCa2 and PCa*(1-Pca) respectively. As Equation 5-5 shown, the integral

activation energy of CaO is calculated by the sum of energy contributions of each

structural unit multiplied by its probability. The 𝐸𝐶𝑎0 is the constant representing O

2-

from CaO. Because of similar properties, the calculation of MgO integral energy is

expressed in Equation 5-6.

As an amphoteric oxide, Al2O3 shows both negative and positive impacts on

activation energy. There are four possible structure units for aluminum cations, those

are, network modifies unit: O2-

, 3(SiO4)-Al and network former unit: AlO4-Ca-AlO4

and AlO4-Mg-AlO4. The charge balanced AlO4-Ca/Mg structure units give a positive

contribution to the integral activation energy. The (1-PCa) and (1-PCa) are used to

describe the probability of Ca2+

/Mg2+

participating on alumina network. One

Ca2+

/Mg2+

cation is able to balance two (AlO4) structure units; therefore the

probability order is assumed to be 2. 3(SiO4)-Al represents the network breaking the

effect of Al3+

cation; so it gives a negative contribution to the activation energy. The

probability of one alumina cation which is not charge compensated is (1-(1-PCa)*(1-

PMg)). The probability order is assumed to be 3, because of 3 SiO4 structure units. The

EAl0 is the constant representing free O

2- from Al2O3. However, due to charge

compensation, most of the O2-

contributes into AlO4 network, which reflects small

activation energy in Table 5.2.

Silica has only one structure unit SiO4. It has a positive impact on viscosity and

activation energy and the parameter related is a constant shown in Table 5.2.

121

The overall activation energy of all structure units is optimized from collected

viscosity data in the CaO-MgO-Al2O3-SiO2 system. From the parameters in Table 5.2,

it can be seen that the major structural unit in network breaking is Si-Ca(Mg)-Si. The

free O2-

and Si-Ca(Mg)-Al have less significant impacts on the activation energy. The

Al2O3 behaves almost the same as SiO2 in CaO-MgO-Al2O3-SiO2, which has strong

positive impact on activation energy. In addition, the CaO has higher priority to

compensate the AlO4 charges and lower priority for SiO4 charges, which is

demonstrated by the optimized parameters.

Equation 5-6 Partial activation energy calculation

𝐸𝐶𝑎 = 𝐸𝐶𝑎0 + 𝐸𝑆𝑖𝑂4−𝐶𝑎−𝑆𝑖𝑂4

∗ 𝑃𝐶𝑎2 + 𝐸𝑆𝑖𝑂4−𝐶𝑎−𝐴𝑙𝑂4

∗ 𝑃𝐶𝑎 ∗ (1 − 𝑃𝐶𝑎)

𝐸𝑀𝑔 = 𝐸0𝑀𝑔 + 𝐸𝑆𝑖𝑂4−𝑀𝑔−𝑆𝑖𝑂4

∗ 𝑃𝑀𝑔2 + 𝐸𝑆𝑖𝑂4−𝑀𝑔−𝐴𝑙𝑂4

∗ 𝑃𝑀𝑔 ∗ (1 − 𝑃𝑀𝑔)

𝐸𝐴𝑙 = 𝐸0𝐴𝑙 + 𝐸𝐴𝑙−3𝑆𝑖𝑂4

∗ [1 − (1 − 𝑃𝐶𝑎) ∗ (1 − 𝑃𝑀𝑔)]3

+ 𝐸𝐴𝑙𝑂4−𝐶𝑎−𝐴𝑙𝑂4

∗ (1 − 𝑃𝐶𝑎)2 + 𝐸𝐴𝑙𝑂4−𝑀𝑔−𝐴𝑙𝑂4∗ (1 − 𝑃𝑀𝑔)

2

𝐸𝑆𝑖2= 𝐸𝑆iO4

Where P represents the probability of Ca/Mg molecules breaking silicate network

defined in Equation 5-3, and E is parameters of structure units from Table 5.2


Al2O3-SiO2 system

Basic Oxide Acidic Oxide

Ca2+

Mg2+

SiO4 Al3+

-0.24

ECa0 -0.31 E0

Mg -0.24 ESiO4 7.21 E0

Al -0.53

ESiO4−Ca−SiO4 -7.38 ESiO4−Mg−SiO4

-9.09 EAlO4−Ca−AlO4 23.78

ESiO4−Ca−AlO4 -0.71 ESiO4−Mg−AlO4

-0.51 EAlO4−Mg−AlO4 15.83

122

5.1.6 Model Performance

The performance of the current model is evaluated by comparison with other models

using the viscosity data in the CaO-MgO-Al2O3-SiO2 system.

The mean deviation Δ is calculated using Equation 5-7.

Equation 5-7 Error deviation calculation

Δ =1

n∗ ∑ |

ηCalc − ηExp

ηExp| ∗ 100%

Where Δ is the mean deviation, n is the total number of data, ηCalc is the model


5.1.6.1 CaO-MgO-Al2O3-SiO2 system

The evaluation of the model performance was carried out for three different

composition ranges: (i) all viscosity data in the CaO-MgO-Al2O3-SiO2 system; (ii)

data in the blast furnace slag composition range 30-40 wt.% SiO2, 10-20 wt.% Al2O3,

30-45 wt.% CaO and 5-10 wt.% MgO and (iii) data in the ladle slag composition

range 10-25 wt.% SiO2, 20-30 wt.% Al2O3, 40-50 wt.% CaO and 5-10 wt.% MgO.

The results for model comparison are shown in Figure 5.3. It can be seen that the

present model performance very well in all composition ranges, with the mean

deviation 21.4% in the full composition, 12.5% in the BF slag composition and 15.5

in the ladle slag composition range.

123

Figure 5.3 The performance summary of viscosity models in, (i) full CaO-MgO-

Al2O3-SiO2 composition, (ii) BF slag composition and (iii): ladle slag composition

A detailed comparison is conducted using three most accurate models: present model,

Zhang model and Urbain model at the viscosity range of 0 - 5 Pa.s [131, 145]. It can

be seen from Figure 5.4, the present model has overall superior performance than both

Zhang and Urbain models. The mean deviation is 12.5%, 19.4% and 19.3% for the

present model, Zhang model, and Urbain model respectively. At high-value ranges

(>2 Pa.s), the present model prediction distributed on both sides of the experiment

viscosity; in contrast, the Urbain and Zhang model tend to underestimate the

experimental data. On the other hand, it is clear that all models shown in Figure 5.4

can predict viscosity more accurately at viscosity range below 2 Pa.s which is usually

enough for BF and steelmaking ladle slags.

124

Figure 5.4 Comparison between experimental viscosity and calculated viscosity by

present model (12.5% deviation), Zhang model (19.4 deviations) [145] and Urbain

model (19.3 % deviation) [131]

5.1.6.2 Viscosity Trend Prediction

The impacts of CaO and MgO on viscosity are investigated using model prediction

and experimental data. At fixed SiO2, Al2O3 and temperature (1500 °C), as shown in

Figure 5.5, the replacement of MgO by CaO content was evaluated under two

compositions: 1) high acidic oxide (44 wt.% SiO2, 15 wt.% Al2O3) and 2) low acidic

oxide (33 wt.% SiO2 and 5 wt.% Al2O3). In both conditions, through CaO

replacement, the slag viscosities decrease and decrement slope continuously reduced.

Because of charge compensation impact of SiO4 and AlO4 units, the viscosity

decrement is more sensitive at low acidic oxide concentrations. It is noted that at 44

wt% SiO2 and 15 wt% Al2O3, replacement of MgO by CaO first decreases and then

increase viscosity. The model predictions agree well with experimental data by

Gul’tyai and Hofmann [22, 65].

125

Figure 5.5 Comparisons between model predictions and Gul’tyai [65] and Hofmann

[22] results, 1500 °C in the system CaO-MgO-Al2O3-SiO2

5.1.6.3 Sub-Ternary & Sub-Binary System

The present model can also be used to predict the low-order silicate systems

containing CaO, MgO, and Al2O3. As shown in Figure 5.6, the linear relationship

between activation energy EA and pre-exponential factor B can also be applied for

lower-order systems with different m and n values (Equation 5-2). For each binary

and ternary system, the individual m and n values were used to minimize the

prediction deviation. The values of m, n and prediction deviation for each system are

summarized in Table 5.3 below. In the lower-order system, modifications were

required in Equation 5-5 to suit the actual system. For example, in SiO2-CaO system,

both EMg and EAl equals to 0 in SiO2-CaO system.

Table 5.3 The summary of model parameters in binary and ternary silicate system

containing CaO, MgO, and Al2O3.

m n Error

Deviation (%)

Database

SiO2-Al2O3-CaO 0.5953

2.668 24.2 Hofmann, Bills, Johannsen

Machin and Urbain

SiO2-Al2O3-MgO 0.3831

1.442 28.4 Johannse and Lyutikov

126

SiO2-CaO 0.5741

2.311 20.2 Bockris and Urbain

SiO2-MgO 0.4468

1.532 13.1 Bockris, Hofmann, and

Urbain

SiO2-Al2O3 0.5359

2.371 9 Bockris and Urbain

Figure 5.6 The linear relationship between EA and ln(A) for (A): SiO2-Al2O3-CaO and

SiO2-Al2O3-MgO system and

The experimental viscosity data for the systems of SiO2-Al2O3-CaO, SiO2-Al2O3-

MgO, SiO2-CaO, SiO2-MgO and SiO2-Al2O3 are compared with calculated values by

the present model. As shown in Figure 5.7 (A~E), the predicted viscosities by the

present model agree well with reported data. Higher error deviations are reported in

two ternary systems indicating that current model needs to be improved to better

describe the amphoteric behavior of Al2O3 in extreme conditions (very high Al2O3

concentration). Note that all available viscosity data in the ternary and binary systems

have been used without evaluation. Evaluated data would give a better performance of

the present model.

127

(A)

(B)

128

(C)

(D)

(E)

Figure 5.7 Comparisons between experiment viscosity and model prediction in the

systems (A) SiO2-Al2O3-CaO, (B) SiO2-Al2O3-MgO, (C) SiO2-CaO, (D) SiO2-MgO

and (E) SiO2-Al2O3

5.1.7 Industrial Application

5.1.7.1 Blast Furnace Slag

Examples of the industrial applications using the developed viscosity model are

demonstrated in this section. Figure 5.8 shows the effect of (WCaO/WSiO2) on the

viscosity of blast furnace slag at 15 wt% Al2O3 and various MgO concentrations at

129

1500 oC. It can be seen that predictions agree well with Kim, Machin and Gul’tyai’s

data. At a given Al2O3 and MgO concentration, the addition of CaO continuously

decreases the slag viscosity. Also, it indicates that at a given WCaO/WSiO2, the slag

viscosities decrease with increasing MgO concentration. The effect of MgO seems to

be more significant at low WCaO/WSiO2. MgO is usually added in the BF operation as

flux. Reduction of MgO can decrease the direct cost in material and also fuel

consumptions. It can be seen from Figure 5.8 that reduced MgO will increase the slag

viscosity. To keep the slag viscosity at a low-level, WCaO/WSiO2 needs to be increased.

However, liquidus temperature has to be controlled to avoid the formation of solid

phase at operating temperature.

Figure 5.8 Effects of WCaO/WSiO2 and MgO on slag viscosity at 1500 °C and 15 Al2O3

by the present model in comparisons with the data from Kim [122], Gul’tyai [83] and

Machin’s [74]

The present viscosity model can only predict viscosities for single liquid phase. It is

essential to make sure the slag is liquid before the viscosity is calculated by the

viscosity model. It is necessary to present iso-viscosity lines on the phase diagram. As

an example, the iso-viscosity lines are calculated using the present viscosity model for

blast furnace slags at 1500 °C and 15 wt% Al2O3. In Figure 5.9, all viscosities are

presented within the full-liquid region. From the Figure 5.9, the viscosity is mainly

dependent on SiO2 concentration. The iso-viscosity lines are almost parallel to the

130

CaO-MgO axis, which has bias down to the MgO direction. It indicated that the

replacement of CaO by MgO will slightly decrease the slag viscosity at fixed SiO2

concentration. This behaviour is consistent with the fact that the viscosity parameters

of EMg are higher than ECa as a network modifier, which also matches the conclusion

from a review of binary viscosity data of SiO2-CaO and SiO2-MgO systems.

Figure 5.9 The model prediction of the iso-viscosity diagram at 1500 °C and 15 wt.%

Al2O3 and experiment data of Gultyai [83], Li [150], and Machin [68, 74]

5.1.7.2 Ladle Slag in Steelmaking Process

In steelmaking process, the desired viscosity of ladle slag (0.2-0.4 Pa.s) is lower than

BF final slag (0.4-0.6 Pa.s). Figure 5.10 shows effects of temperature and slag basicity

on viscosity at 30 wt% Al2O3 and 5 wt% MgO. The present model can well predict

Song’s data with average deviation 15%. At fixed Al2O3 and MgO concentrations,

the viscosities decrease significantly with increasing WCaO/WSiO2 ratio and the

decrement is more significant at low temperatures. For example, the viscosity is

decreased by approximately 0.13 Pa.s at 1450 °C when the WCaO/WSiO2 is increased

131

from 3 to 5.5. At 1550 °C, the decrement of the viscosity is only approximately 0.05

Pa.s when the WCaO/WSiO2 is increased from 3 to 5.5.

Figure 5.10 Effects of WCaO/WSiO2 and temperature on slag viscosity at 5 wt.% MgO

and 30 wt.% Al2O3 by present model in comparisons with Song’s data [107]

5.1.8 Conclusions

In conclusion, an accurate viscosity model has been developed in the system CaO-

MgO-Al2O3-SiO2 using a large number of critically reviewed experimental data. A

new term ‘probability’ based on composition and electronegativity was introduced to

describe the distribution of cations within the acidic oxide. The new model can

accurately predict viscosities for blast furnace slags and steel refining slags in the

system CaO-MgO-Al2O3-SiO2. The model developed also has good performance for

the sub-systems SiO2-Al2O3-CaO, SiO2-Al2O3-MgO, SiO2-Al2O3, SiO2-CaO, and

SiO2-MgO.

132

5.2 CaO-MgO-Al2O3-SiO2-“FeO” system in full composition range

5.2.1 Introduction

As one of the important physical properties of molten slag, viscosity performs an

important role in metallurgical processes. Abundant studies have been constructed by

researchers to investigate the correlation among slag composition, temperature, and

viscosity. There is a considerable demand for accurate viscosity data in mathematical

modeling for metallurgical processes, and although viscosity of slag can be measured

using the rotating cylinder method, reliable data for industrial application are limited

due to the difficulty and uncertainty of viscosity measurement at high temperature.

In the ironmaking process, the Blast furnace (BF) is the principal technology to

produce iron. The chemistries of these slags can be described by the system SiO2-

CaO-MgO-Al2O3-“FeO”. These slags have significant impacts on the gas

permeability and accretion formation in a blast furnace. In addition, the five

components are the major components of another smelting process, including

steelmaking, mould fluxes and copper-making process. A clear understanding of

viscosity changes during slag formation will help to improve the technical and

economic efficiency. High-temperature viscosity measurement is practically difficult,

time- and money-consuming. Therefore, it is necessary to use reliable viscosity data

to develop an accurate model to predict slag viscosity for CaO-MgO-Al2O3-SiO2-

“FeO” system.

5.2.2. Model Description

5.2.2.1 Silicate structure of SiO2-CaO-Al2O3-MgO-“FeO” system

The slag composition and temperature determined its momentary structures and

viscosity. According to the experimental data and network theory, the components of

the CaO-MgO-Al2O3-SiO2-“FeO” can be categorized into three groups: acidic oxide

(SiO2), basic oxide (CaO, MgO and “FeO”) and amphoteric oxide (Al2O3).

It is widely accepted the SiO2 forms a network structure through (SiO4) tetrahedral

units, which positively impact on the slag viscosity. In contrast, the basic oxide, either

“FeO”, CaO or MgO, will break the [SiO4] network, which negatively impacts on slag

viscosity. The insertion of O2-

will break the covalent bond between Si-O within the

133

(SiO4) tetrahedral unit and then balance the negative charge. This intermediate [Ca

(Mg)-SiO4]+ structure unit has one free positive charge, which is able to break another

SiO4 or compensate the AlO4 charges. The basic oxide “FeO” reported two possible

cations, Fe2+

and Fe3+

, which reported different modify ability in Wright’s viscosity

measurements of iron silicate slags with vary Fe3+

/Fe2+

ratio [192]. It concluded that

the modify ability of Fe3+

is 10-15% stronger than Fe2+

; because the Fe3+

is able to

compensate with 3 SiO4 units. However, it is difficult to form Fe-3[SiO4] structural

units because of the space limitation.

The Al2O3 can behave as either acidic or basic oxide depending on the concentrations

of other basic oxides. If sufficient Ca2+

, Mg2+,

and Fe2+

cations are present to balance

the (AlO4)- charges, the Al2O3 acts as an acidic oxide which is incorporated into the

silicate network in tetrahedron coordination. In the case of insufficient basic oxides,

Al3+

will behave the same as Ca2+

or Mg2+

to break the (SiO4) network.

In summary, in molten slag, the major roles network modifies, including Ca2+

, Mg2+

and Fe2+

is to compensate the Si-[O]- charge and [AlO4]

5-. Due to electrical force

between charges, it is accepted that when cations (Ca2+

, Mg2+,

and Fe2+

) concentration

is low, they have higher priority to balance the AlO4 charges than breaking the Si-O

covalent bond.

5.2.2.2 Temperature dependence

The temperature dependence of viscosity can be described by the Arrhenius-type

equation as Equation 5-8 shown.

Equation 5-8 Arrhenius type equation

1000*η A*exp AE

T

Where η is the viscosity in Pa.s, T is the absolute temperature in K, A is the pre-

exponential factor, EA represents the integral activation energy in J/mol.

134

5.2.2.3 Pre-exponential Factor A

A linear relationship between pre-exponent factor A and activation energy EA was

proposed by Urbain. The activation energy EA and pre-exponential factor A can be

determined by plotting ln(η) against 1/T under the same composition. This linear

correlation has been widely applied in different viscosity models, such as the

Shankar’s and Hu et al.’s model.

Equation 5-9 linear correlation between EA and pre-exponential factor A

* AlnA m E n

Where A the pre-exponential factor and EA is the activation energy from Equation

5-11. m and n are the model parameters are 0.4144 and 4.1485 respectively.

5.2.2.4 Fe2+

and Fe3+

Determination

The modify ability of Fe3+

is stronger than Fe2+

. Also, with abundant “FeO” existence

in silicate melts, the Fe2+

may convert to Fe3+

through breaking SiO4 unit. In the

present study, it is necessary to calculate the concentration of Fe3+

/Fe2+

for the model

establishment.

One of the most widely used methods to estimate Fe3+

/Fe2+

involves the use of

empirical equation relating to oxygen partial pressure to the iron redox state in

quenched silicate liquid. Computer based software, FactSage, was often utilized to

calculate the concentration of Fe3+

/Fe2+

[194].

5.2.2.5 Network Modify probability

With the study of silicate based mineralogy, Ramberg suggests that the silicate

structure (polymerized level of the SiO4 network) is dependent on basic oxide

concentrations, atomic radius and electronegativity [191]. The electronegativity of

Ca2+

, Mg2+

, Fe2+

, Fe3+

, AlO4 and SiO4 units are determined using Mulliken equation

as Equation 5-4, which is derived from 1st ionization energy and electron affinity of

the atom. The values of electronegativity are shown in Table 5.4.

135

Table 5.4 Electronegativity χ of basic oxide cations and network former units

Ca2+

Fe2+

Fe3+

Mg2+

(AlO4)

(SiO4)

Χ 3.07 3.2 3.3 3.82 6.674 6.985

The term “probability (P)” is introduced to describe the probability of Ca2+

(or Mg2+

,

Fe2+,

and Fe3+

) cations to connect with SiO4 and AlO4 tetrahedral unit as introduced in

Section 5.1. The PFe, as shown in Equation 5-10, are proposed to be the probability of

Fe2+

or Fe3+

connecting to the Si-O network respectively. Fe2+

and Fe3+

cations were

also required for (AlO4)- charge compensation. Therefore, the (1-PFe) are the

probability of cations to connect with AlO4.

Equation 5-10 probability calculation for Fe3+

and Fe2+

𝑃𝐹𝑒3+ =χ𝐹𝑒3+𝑀𝐹𝑒3+


𝑃𝐹𝑒2+ =χ𝐹𝑒2+𝑀𝐹𝑒2+


Where M is a molar fraction of a metal oxide; X is electronegativity of structure units

in slag system.

5.2.2.6 Activation Energy

In Arrhenius equation, EA is defined as the integral activation energy of silicate slag,

which is composed of metal oxides and can be expressed as Equation 5-11 shown:

Equation 5-11 Activation energy calculation

𝐸𝐴 = 𝐸𝐶𝑎𝑂 + 𝐸𝑀𝑔𝑂 + 𝐸𝐹𝑒𝑂 + 𝐸𝐹𝑒2𝑂3+ 𝐸𝐴𝑙2𝑂3

+ 𝐸𝑆𝑖𝑂2

Where Ei is the partial activation energy of i component (i = SiO2, Al2O3, CaO, MgO,

and FeO) calculating from Equation 5-12.

136

In CaO-MgO-Al2O3-SiO2-“FeO” system, as a network modifier, there is three

possible structure units combination with Fe2+

, including free oxygen O2-

, SiO4-Fe-

SiO4, and SiO4-Fe-AlO4. As PFe defined before, one Fe2+

cation has the probability of

PFe to connect with one SiO4 tetrahedron. Therefore, the probability of SiO4-Fe-SiO4

and SiO4-Fe-AlO4 can be assumed as PFe2 and PFe*(1-PFe) respectively. As Equation

5-11 shown, the integral activation energy of FeO is calculated by the sum of

activation energy of each structural unit multiplied by its probability. The EFe0 is the

constant representing O2-

from FeO. Because of similar properties, the calculation of

CaO and MgO integral energy is expressed in Equation 5-12. Unlike Fe2+

, the Fe3+

is

able to compensate three negative charges, which should consider 4 types of structure

units as Equation 5-12 shown.

The impact of cations Ca, Mg, Al and Si were detailed discussed and introduced in

Section 5.1.

Equation 5-12 the partial activation energy calculation

𝐸𝐶𝑎 = 𝐸𝐶𝑎0 + 𝐸𝑆𝑖𝑂4−𝐶𝑎−𝑆𝑖𝑂4

∗ 𝑃𝐶𝑎2 + 𝐸𝑆𝑖𝑂4−𝐶𝑎−𝐴𝑙𝑂4

∗ 𝑃𝐶𝑎 ∗ (1 − 𝑃𝐶𝑎)

𝐸𝑀𝑔 = 𝐸0𝑀𝑔 + 𝐸𝑆𝑖𝑂4−𝑀𝑔−𝑆𝑖𝑂4

∗ 𝑃𝑀𝑔2 + 𝐸𝑆𝑖𝑂4−𝑀𝑔−𝐴𝑙𝑂4

∗ 𝑃𝑀𝑔 ∗ (1 − 𝑃𝑀𝑔)

𝐸𝐴𝑙 = 𝐸0𝐴𝑙 + 𝐸𝐴𝑙−3𝑆𝑖𝑂4

∗ [1 − (1 − 𝑃𝐶𝑎) ∗ (1 − 𝑃𝑀𝑔)]3

+ 𝐸𝐴𝑙𝑂4−𝐶𝑎−𝐴𝑙𝑂4∗

(1 − 𝑃𝐶𝑎)2 + 𝐸𝐴𝑙𝑂4−𝑀𝑔−𝐴𝑙𝑂4∗ (1 − 𝑃𝑀𝑔)

2+ 𝐸2𝐴𝑙𝑂4−𝐹𝑒2+ ∗ (1 − 𝑃𝐹𝑒2+)2 +

𝐸3𝐴𝑙𝑂4−𝐹𝑒3+ ∗ (1 − 𝑃𝐹𝑒3+)2

𝐸𝐹𝑒2+ = 𝐸0𝐹𝑒2+ + 𝐸𝑆𝑖𝑂4−𝐹𝑒2+−𝑆𝑖𝑂4

∗ 𝑃𝐹𝑒2+2 + 𝐸𝑆𝑖𝑂4−𝐹𝑒2+−𝐴𝑙𝑂4

∗ 𝑃𝐹𝑒2+ ∗ (1 − 𝑃𝐹𝑒2+)

𝐸𝐹𝑒3+ = 𝐸0𝐹𝑒3+ + 𝐸3𝑆𝑖𝑂4−𝐹𝑒3+ ∗ 𝑃𝐹𝑒3+

3 + 𝐸2𝑆𝑖𝑂4−𝐹𝑒3+−𝐴𝑙𝑂4∗ 𝑃𝐹𝑒3+

2 ∗ (1 − 𝑃𝐹𝑒3+) +

𝐸𝑆𝑖𝑂4−𝐹𝑒3+−2𝐴𝑙𝑂4∗ 𝑃𝐹𝑒3+ ∗ (1 − 𝑃𝐹𝑒3+)

2

𝐸𝑆𝑖2= 𝐸𝑆iO4

where P represents the probability of cations, Ca2+

, Mg2+

, Fe2+

and Fe3+

breaking

silicate network and Ei is parameters of structure units from Table 5.5.

137

Table 5.5 Activation energy parameters of all involved structural units in CaO-MgO-Al2O3-SiO2 system

Basic Oxide Acidic

Oxide

Amphoteric Oxide

Ca2+

Mg2+

Fe2+

Fe3+

SiO4 Al3+

𝐸𝐶𝑎0 -0.314 𝐸0

𝑀𝑔 -0.24 𝐸0𝐹𝑒2+ -0.11 𝐸0

𝐹𝑒3+ -0.14 𝐸𝑆iO4 7.21 𝐸0

𝐴𝑙 -0.53

𝐸𝑆𝑖𝑂4−𝐶𝑎−𝑆𝑖𝑂4 -7.38 𝐸𝑆𝑖𝑂4−𝑀𝑔−𝑆𝑖𝑂4

-9.09 𝐸𝑆𝑖𝑂4−𝐹𝑒2+−𝑆𝑖𝑂4 -5.32 𝐸3𝑆𝑖𝑂4−𝐹𝑒3+ -6.33 𝐸𝐴𝑙𝑂4−𝐶𝑎−𝐴𝑙𝑂4

23.78

𝐸𝑆𝑖𝑂4−𝐶𝑎−𝐴𝑙𝑂4 -0.71 𝐸𝑆𝑖𝑂4−𝑀𝑔−𝐴𝑙𝑂4

-0.51 𝐸𝑆𝑖𝑂4−𝐹𝑒2+−𝐴𝑙𝑂4 -0.22 𝐸2𝑆𝑖𝑂4−𝐹𝑒3+−𝐴𝑙𝑂4

-0.31 𝐸𝐴𝑙𝑂4−𝑀𝑔−𝐴𝑙𝑂4 15.83

𝐸𝑆𝑖𝑂4−𝐹𝑒3+−2𝐴𝑙𝑂4 -0.15 𝐸2𝐴𝑙𝑂4−𝐹𝑒2+ 13.45

𝐸3𝐴𝑙𝑂4−𝐹𝑒3+ 11.2

138

5.2.3 Model Performance

As Table 5.6 shown, the new model developed reported an overall 17% deviation

with the viscosity data comparing with other existing models for CaO-MgO-Al2O3-

SiO2-‘FeO’ system. As Figure 5.11 shown, the viscosity prediction accuracy was

significantly improved using present model; considering the two closest Urbain and

Zhang model reported 25% prediction deviations [131, 188].

Table 5.6 The prediction deviation of viscosity models for CaO-MgO-Al2O3-SiO2-

“FeO” system

Model Deviation (%)

Present 17.1

Zhang 24.9

Urbain 25.6

Factsage 34.2

QCV 36.8

Li 42.6

Iida 50.6

Mills 64.1

A detailed comparison of the viscosity model performance is carried out using the

three most accurate models: present model, Zhang model and Urbain model in the

viscosity range 0-2 Pa.s. As Figure 5.11 shown, the present model has superior

performance than both Zhang and Urbain models. It can be seen from Figure 5.11, the

calculated viscosity from Urbain and Zhang model was an under-estimation at large

viscosity region (>1 Pa.s). The experiment measurements (>1 Pa.s) was reported from

“Fe2O3” containing slags. Because both Urbain and Zhang model assumed only FeO

139

existence in the molten slag and did not consider the modify ability of Fe3+

is stronger

than Fe2+

, which is included in the present model development.

Figure 5.11 The comparison between experimental viscosity and calculated viscosity

using Current, Urbain [131] and Zhang model [145].

Sub-ternary and quaternary system

In addition, the present model can predict the viscosity of sub-ternary system of “FeO”

containing slags. In ternary system, the network modify ability of different basic

oxide can be determined. Figure 5.12 compared the viscosity of two ternary system,

CaO-SiO2-‘FeO’ and MgO-SiO2-‘FeO’. With the increasing of ‘FeO’ content, at 1500

oC and CaO (MgO)/SiO2=1.2 conditions, the measured viscosity steadily increased

for both ternary system. In addition, the viscosity of MgO-SiO2-‘FeO’ system is

higher than the CaO-SiO2-‘FeO’ system at 50 oC higher temperature. The trend

indicated that the modify ability of 3 basic oxides can be ranked as

CaO>MgO> ’FeO’.

140

Figure 5.12 40 wt% SiO2, 1500 oC for SiO2-CaO-“FeO” system by Chen [193],

Bockris [194] and Ji [114], 40 wt% SiO2, 1550 oC for SiO2-MgO-“FeO” system by

Chen [115], Ji [195] and Urbain [60]

5.2.4 Industrial Application

5.2.4.1 Blast Furnace Slag

The primary slag formed in the cohesive zone of the blast furnace contains high “FeO”

content. The “FeO” concentration in the slag will decrease when the burden moves

down and the reduction proceeds continuously. If initially formed primary slag is

viscous and stays locally, reduction of “FeO” will continuously increase its viscosity

making it more viscous. In the BF operation, if the primary slag forms at a lower

temperature, i.e., if the top of the cohesive zone moves upward, the viscosity of the

slag will be high and it may not be able to flow rapidly through the coke bed. The

localized viscous slag will fill the void, which reduces the surface area for indirect

reduction and also the gas permeability. It is desirable to have the primary slag

formed at a higher temperature so that its viscosity is low enough to allow the slag

drop quickly. As shown in Figure 5.13, the current model predictions are in very good

agreement with the experimental results that cover the “FeO” concentration from 0 to

25 wt%. The viscosities shown in Figure 5.13 are all for fully liquid slags. The

temperature impact on viscosity are more sensitive at low temperature than higher

temperature condition.

141

Figure 5.13 Comparisons of the viscosities between model predictions and

experimental data for different “FeO”-containing slags (in wt%) by Higgins [190];

Vyaktin [84] and Machin [80]

5.2.4.2 Coppermaking Slag

Figure 5.14 shows viscosity as a function of “FeO” at 1250 oC for a base slag 52 wt%

SiO2, 13.3 wt% Al2O3, 29.3 wt% CaO and 5.3 wt% MgO, which is a typical copper-

making slag. The viscosity of the fully liquid slag continuously increases with

decreasing “FeO” concentration in the slag. For example, it can be seen from Figure

5.14 that the viscosity of the slag with 30 wt% “FeO” is below 1 Pa.s. If “FeO” is

reduced to 15 wt% the viscosity of the slag will be 3.5 Pa.s at the same temperature

(1250 oC). The sensitivity of the viscosity to the “FeO” increases with decreasing the

“FeO” concentration in the slag. It can be seen from Figure 5.14 that FactSage

predicted viscosities are much lower than the predictions of the present model, in

particular at low “FeO” concentrations.

142

Figure 5.14 Viscosity as a function of “FeO” at 1250 oC, base slag 52% SiO2, 13.3%

Al2O3, 29.3% CaO, 5.3% MgO by Higgins [190]

5.2.5 Conclusion

In conclusion, an existing model by the present author has been optimized and

extended to describe the viscous behavior of fully liquid slag in the CaO-MgO-Al2O3-

SiO2-“FeO” system using a large number of reviewed experimental data. A new term

‘probability’ based on composition and electronegativity was introduced to describe

the distribution of cations within the acidic oxide. The new model can accurately

predict viscosities for both blast furnace primary slags, steelmaking slags and copper

making slags in the CaO-MgO-Al2O3-SiO2-“FeO” system.

143

Chapter 6 : Structure studies of silicate slag by Raman spectroscopy

In the present study, Raman spectroscopy was utilized on quenched glass samples of

SiO2-CaO, SiO2-CaO-Al2O3, and SiO2-CaO-MgO system to investigate the network

impact of CaO, MgO and Al2O3 referring to the network theory. The Raman

spectrum information, including peak location and intensity, were quantitatively

analyzed correspond to the network structure of silicate glass. Various

physiochemical properties such as viscosity, density, and liquidus temperature can be

derived from a proposed mathematical definition called “degree of polymerization”

(DP). The present methodology can be extended to predict the other physicochemical

properties of silicate melts for metallurgical processes.

144

6.1 Introduction

The structure and properties of amorphous slags are of widespread interest because of

their importance in the process optimization of pyro-metallurgy field. Many

spectroscopic methods have been developed to determine the structure of slags and

distinctively identify the microstructural units within the amorphous silicate glasses

[196-198]. Raman spectroscopy, as an analytical technique for the study of molten

slag, has been widely utilized and accepted by other researchers [41]. The

microstructural information was obtained through the analysis of peak shift and

intensity of Raman spectrum, which indicates the types of vibration units and its

relative concentration.

For CaO-MgO-Al2O3-SiO2 slag system, the Raman spectrum study was performed by

other researchers, as the summary in the Table 6.1. The alumina silicate system has

been well studied; however, the focus composition range is different from the blast

furnace slag composition. In addition, Different Raman spectrum will report varied

results of amorphous glass phase due to instrument factors, such as intensity of laser

light, which did not allow the cross-reference comparison of Raman results of

amorphous glass.

For silicate glass, most of the researchers focus on the high-frequency band ranging

from 800-1200 cm-1

[199]. However, limited information was provided for the low-

frequency band (300-700 cm-1

), which is the critical region in the study of fused silica

(amorphous phase). In the alumina silicate glass, it is accepted that the Al2O3 behavior

as a network former, connecting with SiO4, was not clearly revealed in the Raman

spectra of other researchers [4].

In the present study, Raman spectroscopy was utilized on quenched glass samples of

SiO2-CaO, SiO2-CaO-Al2O3, and SiO2-CaO-MgO system to identify the potential

vibration units in the low-frequency region to further investigate the impact of CaO,

MgO, and Al2O3 on fused silica. A quantitative analysis was performed on the Raman

spectroscopy to identify and estimate the abundance of silicate continuous ring and

discrete anions (Dn and Q

n) of silicate melts.

145

6.2 Methodology

6.2.1 Sample Preparation

The quenched slag samples were prepared for the SiO2-CaO, SiO2-CaO-MgO and

SiO2-CaO-Al2O3 system. The designed composition was shown in Table 6.1.

Approximately 0.25g mixture was prepared for each experiment runs. The CaCO3

(99%), SiO2 (98%), MgO (99%) and Al2O3 (99.9%) powders were weighed, mixed

and grinded for 30 minutes to obtain homogeneous mixtures. The mixture melted in a

graphite crucible at designed temperature for 2 hours to achieve complete fusion,

homogenization and equilibrium status under Ar atmosphere condition. The schematic

diagram is shown in Figure 6.1. The quenched glasses will be mounted and polished

for Raman spectroscopy analysis. In addition, the electro-probe microanalysis (EPMA)

were constructed for each sample to confirm the sample reliability, and the outcomes

were shown in Table 6.1.

Figure 6.1 Schematic diagram of equilibrium experiment settings

146

Table 6.1 The experiment designed condition and EPMA results

Design Composition Experiment

Temperature

EPMA Results

CaO/SiO2

Mol/Mol%

Additive

Mol%

oC SiO2

Mol%

CaO

Mol%

SiO2-CaO system

No.1-4

0.55 0 1773 63.2 36.8

0.7 0 1773 58.7 41.3

0.9 0 1553 52.6 47.4

1.1 0 1466 47.6 52.4

MgO Mol%

SiO2-CaO-MgO system

No.1-14

0.8 5 1500 52 43.1 4.9

1 5 1500 46.7 48.3 5

1.2 5 1500 43.4 51.5 5.1

147

0.8 10 1500 50.3 39.6 10.1

1 10 1500 44.1 45.9 10

1.2 10 1500 39.8 50.4 9.8

2 10 1500 58.3 32 9.7

2 10 1600 59.4 30.3 10.3

0.8 15 1500 47.1 37.8 15.1

1 15 1500 42.5 42.5 15

1.2 15 1500 37.1 48.1 14.8

0.8 20 1500 43.5 36.3 20.2

1 20 1500 41.1 39.5 19.4

1.2 20 1500 35.6 44.6 19.8

Al2O3

148

Mol%

SiO2-CaO-Al2O3 system

No.1-15

0.8 5 1500 52.7 42.8 4.5

1 5 1500 47.3 47.5 5.2

1.2 5 1500 43.1 51.8 5.1

0.8 10 1600 48.9 41.3 9.8

1 10 1500 45.5 44.6 9.9

1.2 10 1300 45.3 44.6 10.1

1.2 10 1500 45.2 44.5 10.3

1.2 10 1600 44.7 45.3 10

0.8 15 1500 47.2 38.1 14.7

1 15 1500 42 42.9 15.1

1.2 15 1500 37.6 46.9 15.5

149

0.8 20 1500 44.5 35.4 20.1

1 20 1500 38.9 40.7 20.4

1.2 20 1500 35.3 45.4 19.3

150

6.2.2 Raman Analysis

The quenched material was mounted in epoxy resin and polished for Raman

spectroscopy measurements (Company: Ranishaw; Model: inVia). The Raman

spectrum was recorded at room temperature in the frequency range of 100-1500

cm-1

using excitation wavelength of 514 nm semiconductor laser with a power of

1 mw. The instrument was calibrated in the air by utilization of electronic grade

silica. The measurements were performed under ambient pressure and room

temperature. There was no detectable temperature increase by laser touch to the

samples.

For one sample, measurements were taken on three different locations on

separate pieces of quenched glasses to evaluate the consistency and stability of

the instrument. The average deviations of three measurements at one sample

were within 1%. The peak deconvolution is necessary for the quantitative

analysis of the spectra by researchers. As Figure 6.2 shown, the baseline was

firstly removed for spectra of 52.6SiO2-47.4CaO system, and then the two bands

were fitted by Gaussian function using software “PeakFit” program.

Figure 6.2 Typical deconvolution of Raman spectrum of a 52.6 mol% SiO2-47.4 mol%

CaO sample

151

6.3 Raman Results

6.3.1 Structure of alumina silicate system

The random network theory was accepted for the description of amorphous silicate

structure. In silicate based slag of SiO2-CaO-Al2O3-MgO system, the SiO2 forms a

network structure by the connection of SiO4 tetrahedral unit. The addition of basic

oxide; the CaO and MgO tends to break the Si-O-Si bond. The AlO4 from Al2O3 binds

with a SiO4 unit with the existence of cations to compensate the charge, which

improves the polymerization degree of silicate slag. From Raman spectrum, the

interpreted microstructure units supported the development of network theory [200].

The fused glasses silica has been studied using Raman spectroscopy [201]. In the low-

frequency region, the two major peaks of glasses silica located at 495 cm-1

and 606

cm-1

in Raman spectrum. Galeener’s study pointed out that the two peaks can be

assigned to 4 and 3-folded rings respectively through the calculation of bond angle

using the energy minimization method [38]. The structure of fused silica can be

estimated as the combination of 4-3 folded rings due to the fact that the angel between

O-Si-O is approximately 133o. The required energy of 2-fold ring is >5eV comparing

to 3-fold=0.51 eV and 4-fold ring=0.16 eV; while 2-fold planar rings are not possibly

excepted since they require an unreasonably large amount strain energy for the bond

angle=60o [38].

In SiO2-CaO glasses, with the addition of basic oxide, a board band appears in the

spectra ranging 800-1200 cm-1

shift. The addition of Ca2+

and O- polarize the discrete

anions, which was expected as the breaking silicate planar ring and form 4 different

discrete anions with O2-

, according to the SiO4 structural unit. After the peak

deconvolution, 4 peaks were reported and assigned in the high-frequency region. The

description of microstructure units and assigned peak location were summarized in

Table 6.2. The peak Q4 indicated the initiation of network breakage, which

polymerize of non-bridging oxygen [O]-. As the continues addition O

2- from basic

oxide, the abundance of [O]- will increased upon to 4 and become individual unit,

which did not support the formation of network.

152

Table 6.2 The description of assigned peak information in Raman spectrum silicate structural units, black ball is Si and white ball is O. white

ball with – sign is O-

Peak Raman

Shift Structural Drawing

Ref

D2

4-fold ring 480-500 4[SiO4]

D3

3-fold ring 590-610 3[SiO4]

Q1

Individual SiO4 tetrahedral unit 850-880 [SiO4]

4-

153

Q2

Si2O7 dimer 900-930 (O)O

--Si-2O-Si-2O

-

Q3

Si2O6 chain 950-980

(O)O--Si-2O-Si-2O

-

Q4

Si2O6 sheet 1040-1060

SiO4-Si-O-(O)

154

6.3.2.1 Raman Peak Shift

In SiO2-CaO system, the increasing CaO content indicated the degradation of silicate network,

which means the polymerization degree of silicate network decreased. The Raman spectrum

of glasses with the composition different CaO/SiO2 is shown in Figure 6.3. In Figure 6.3, as

the green and red dot line indication, the low-frequency band shift from left to right, and the

high-frequency band shifts from right to left.

In the low-frequency region, as the discussion before, the low-frequency band (Dn)

represented the silicate planar ring. The addition of CaO tends to break the silicate network,

which degraded the 4 folded to 3 folded ring. The high-frequency band (Qn) represented the

broken silicate units with cations ions Ca2+

. The 2-fold rings possibly exist in SiO2-CaO

system and show a dominantly strong polarized Raman line at (ring-stretch) frequencies

around 1100 cm-1

under low CaO content condition. At high CaO/SiO2 ratio, the breakage of

silicate network potentially forms the individual SiO4 unit, which reported the Raman peak

shift from right to left.

From the view of vibration units, the insertion of CaO not only changed the silicate structure

but also vary the vibration modes from bending vibration to stretching vibration. The

attachment of CaO onto silicate will form [SiO4-x CaO] structural units, which initial the

stretching vibration and form the bands at 1000 cm-1

region. In high-frequency region, as

Figure 6.3 shown, the peak shifted to left due to the decreasing of electrons density from

Park’s study, which might be referred to degradation of silicate polymerization network.

From the study of McMillan, the doubly charged cations M2+

of the large ionic radius and

small ionization potential (small Z/r2) should preferentially occupy the Q3 (sheet) sites [4].

The Z/r2 of Ca2+

(=2) is much smaller than Mg2+

(=3.9). Therefore, due to the cations size

difference, the Ca2+

ion would charge compensate two open O- ions because of the large size

of the [CaO6], whereas the Mg2+

is balanced with two adjacent corner-shared O- ions because

of the small size the [MgO6]. The substitution of Ca2+

by Mg2+

will slightly increase the

polymerization degree of silicate network, which is also shown in the viscosity study of SiO2-

CaO-MgO system [56, 57, 202].

155

Figure 6.3 the Raman spectrum of SiO2-CaO system, which covers the CaO/SiO2 ratio from

0.55 to 1.1

From the network theory and experiment viscosity data, it is known that MgO has a similar

impact as CaO, which modify and reduce the polymerization degree of silicate network. The

Raman spectrum of SiO2-CaO based with different MgO content is shown in Figure 6.4. As

the green and red dot line indication, the low-frequency band shift from left to right, and the

high-frequency band shifts from right to left. The peak shifting become steady comparing to

Figure 6.3, which indicate that the internal micro-structure of molten slag approaches

equilibrium status. Also, it can be noted that the intensity of peak at approximate 800 cm-1

significantly increased from 5mol % MgO to 20 mol% MgO, which will be discussed in the

later section.

Figure 6.4 the Raman spectrum of SiO2—MgO—CaO system under CaO/SiO2=1 and 1500 oC condition, which covers the different MgO concentrations.

From the network theory, it is known that Al2O3 would be converted to [AlO4]-, which binds

with SiO4 units and form the silicate network. As amphoteric oxide Al2O3, its role was

156

dependent on the amount of basic oxide. Large amounts of basic oxide are capable of

compensating [AlO4]- charges and push the Al towards the network former and vice versa.

The Raman spectrum of SiO2-CaO- Al2O3 of different Al2O3 content was shown in Figure 6.5.

As Figure 6.5 (a) shown, it is obvious that the addition of Al2O3 increase the width of the

band in the low-frequency region comparing to the Raman spectrum of SiO2-CaO and SiO2-

CaO-MgO system, which evidently indicated the formation of combinations between [AlO4]-

and SiO4 units. The polymerization length could not be directly identified using Raman

techniques. After peak deconvolution, a novel peak was identified and recorded as D1 at

approximately 500 cm-1

regions. The bands were further deconvluted to compare the trend.

As Figure 6.5 (b) shown, The addition of Al2O3 shift the peaks Q1-Q4 to the right, which

indicates the enhancement of polymerization degree of silicate network.

Figure 6.5 (a) left, the Raman spectrum of SiO2—Al2O3—CaO system under CaO/SiO2=1

and 1500 oC condition, which covers the different Al2O3 concentrations. (b) Right, the peak

deconvolution outcomes of left spectra

6.3.2.2 Peak Intensity

It is known that the peaks area is proportional to the abundance of the structural unit. The

relative occupancy of deconvolution peak can be utilized as a supporting information to

determine the viscosity impact of CaO, MgO, and Al2O3 on the silicate network.

Theoretically, the addition of CaO and MgO would decrease the polymerization degree of

silicate network; and Al2O3 is considered to be the contrary. The role of peaks can be

determined within silicate through the comparison of peak area at different basicity and slag

system.

157

The relative area occupancy of different peaks of (a) SiO2-CaO-MgO and (b) SiO2-CaO-

Al2O3 system were shown in Figure 6.6 under CaO/SiO2 =1 condition. As Figure 6.6 (a), for

SiO2-CaO-MgO system, the addition of MgO decreased the relative abundance of peak Q4,

D2, and D3; however, the concentration of Q1, Q2 and Q3 increased. It is known that the role

of basic oxide is to break the silicate network; therefore, the structure units of peak Q4, D2

and D3 contributed to the formation of silicate network.

For the SiO2-CaO-Al2O3 system, when Al2O3 content increased, Figure 6.6 (b) showed the

increasing of the relative abundance of peak D1, D2, and Q4; however, the concentration of Q1,

Q2, Q3 and D3 decreased. From the analysis of peak shift and concentration of SiO2-CaO-

Al2O3 system, it should be noted that peak D1 and D2 is relevant to SiO4-AlO4 network units;

and D3 should belong to pure SiO4 network unit. However, both the increasing slope and

decreasing slope is gently comparing to the Raman spectrum of SiO2-CaO and SiO2-CaO-

MgO system; because the cations Ca2+

or Mg2+

was utilized for charge compensation of

[AlO4]- unit.

Figure 6.6 The relative area occupancy of different peaks of (a) SiO2-CaO-MgO system

ranging of CaO/SiO2 =1, (b) right, relative area occupancy of different peaks of SiO2-CaO-

Al2O3 system ranging of CaO/SiO2 =1

6.3.2.3 Temperature Impact

It is accepted that the temperature will influence the silicate melts structure, which could be

identified by Raman spectrum. A 45 SiO2- 10 Al2O3- 45 CaO mol% sample was molten at

100 oC interval from 1300-1600

oC, which knew that the liquidus temperature is approximate

1268 oC from FactSage prediction. The target composition belongs to the wollastonite

primary phase field. When the quenching temperature decreased, as Figure 6.7 shown, the

high frequency region of spectra of become closer comparing to the Raman spectra of

158

wollastonite mineral [202]. This phenomenon can only be observed in the high frequency

region of spectra; because the low frequency region is relevant to the network former unit

AlO4 and SiO4.

Figure 6.7 Raman spectrum of 45 SiO2- 10 Al2O3- 45 CaO mol% sample at 1300, 1500 and

1600 oC and wollastonite [202]

6.3.3 Bond energy and the lattice energy

The shift of a vibration frequency is originated from the shift of energy [203]. Assuming CaO,

MgO, and Al2O3 as ionic compounds in the molten slag, the bond force (energy) should be

considered to explain the peak shift. Coulomb interaction [203, 204], the interacting force

between static electrically charged particles, is given by the formula:

Equation 6-1 Coulomb interaction calculation

E = k𝑄1𝑄2

𝑟1−2

Where k is the Coulomb’s constant 8.99 *109 Nm

2/C

2, Q1=Z1Qe is the quantity of charge on

the charge 1, Q2=Z2Qe is the quantity of charge on the charge 2, Z1 and Z2 is the number of

electrons in the outermost energy level, Qe=1.602*10-19

C is the charge of the electron and r1-

2 is the distance between the two charges.

In the case of CaO, MgO and Al2O3, the nature of electrostatic forces of cations and O- are

attractive. The ionic radius of Al3+

, Ca2+

, Mg2+

and O2-

ions were 0.535Å, 0.329Å, 1.068Å,

159

and 1.4 Å respectively [207, 208]. The electrostatic energy was calculated for one Al-O, Ca-

O and Mg-O bond according to the Coulomb interaction. The bond energy of one mole bond

is given by multiplication of Avogadro’s number, NA=6.022 * 1023

.

For one mol Al-O bond

Equation 6-2 Examples of Coulomb interaction calculation

EAl−O = 8.99 ∗ 1093 ∗ 2 ∗ (1.602 ∗ 10−19)2

(0.535 + 1.4) ∗ 10−10= 7.1541 ∗ 10−18 ∗ 6.022 ∗ 1023

= 4308 KJ/mol

For one mole Ca-O bond

ECa−O = 8.99 ∗ 1092 ∗ 2 ∗ (1.602 ∗ 10−19)2

(1.068 + 1.4) ∗ 10−10= 3.739 ∗ 10−18J ∗ 6.022 ∗ 1023

= 2251 KJ/mol

For one mole Mg-O bond

EMg−O = 8.99 ∗ 1092 ∗ 2 ∗ (1.602 ∗ 10−19)2

(0.329 + 1.4) ∗ 10−10= 5.337 ∗ 10−18J ∗ 6.022 ∗ 1023

= 3214 KJ/mol

For one mole SiO4 tetrahedral unit by Bongiorno [209]

ESi−O = 1.441 ∗ 10−17 ∗ 6.022 ∗ 1023 = 8677 𝐾𝐽/𝑚𝑜𝑙

As a result, in the SiO2-CaO-Al2O3 system, when SiO4 units are substituted by AlO4, the

lattice energy is weaker by an amount of 4369 (KJ/mol). The lattice energy decreases; hence

the respective Raman bands shift to smaller wavenumber (shift to left). In the SiO2-CaO-

MgO system, when Ca2+

ions were substituted by Mg2+

ions, the lattice energy is enlarged by

an amount of 963 (KJ/mol), which cause the Raman bands shift to larger wavenumbers (shift

to right)

6.3.4. Summary

From the quantitative analysis of Raman spectra of quenched slag sample of SiO2-CaO, SiO2-

CaO-MgO and SiO2-CaO-Al2O3 system, it can be concluded that:

When system basicity increased, the low-frequency band (400-700 cm-1

) shift to right

and high-frequency band (800-1200 cm-1

) shift to left

160

A new peak appears at the 350 cm-1

position in the Raman spectra of SiO2-Al2O3-

CaO comparing to SiO2-CaO system, which can be assumed as AlO4-SiO4 ring

structure unit.

Peak D1, D2, D3 and Q4 can be classified as network former group contributing to the

polymerization of silicate network. In contrast, the peak Q1, Q2, and Q3 can be

classified as network modify the group, which degraded the silicate network.

It can be noted that when sample quenched temperature close to its liquidus

temperature, the Raman spectrum is closer to its primary phase field.

6.4 Thermodynamic Analysis

6.4.1 Degree of Polymerization

The degree of polymerization (DP) is defined as the abundance of monomeric units in a

polymer. In the silicate based system, DP referred to the silica tetrahedral, which can be

determined from the frequency shifts and intensity changes of Raman spectra [198]. From the

Raman study of SiO2-CaO, SiO2-CaO-MgO and SiO2-CaO-Al2O3 system, the peaks can be

classified into two groups. The peak D1, D2, D3, and Q4 should be classified as network

formed group; because the increasing basicity will also increase these peaks intensity. And

the peak Q1, Q2, and Q3 should be classified as network modify group. In the present study,

the ratio (high polymerized unit)/ (low polymerized unit) was used to represent the DP index

for one quenched slag sample, as shown below.

In silicate network, CaO, MgO, and Al2O3 as ionic compounds in the molten slag, the bond

force (energy) should be involved to determine the DP. The correspond bond energy was

calculated using Coulomb interaction equation as Equation 6-2. The details is shown in Table

6.3. It should be noted that the distribution of Ca2+

and Mg2+

charge compensation is not

determined, which has to assume 50% equal share.

Equation 6-3 the degree of polymerization calculation

DP =D1 + D2 + D3 + 𝑄4

Q1 + Q2 + Q3=

∑ 𝑄𝑛 ∗ 𝐸𝑛 ∗ 𝐶𝑛𝐻𝑖𝑔ℎ 𝑝𝑜𝑙𝑦𝑚𝑒𝑟𝑖𝑧𝑒𝑑 𝑢𝑛𝑖𝑡

∑ 𝑄𝑛 ∗ 𝐸𝑛 ∗ 𝐶𝑛𝐿𝑜𝑤 𝑝𝑜𝑙𝑦𝑚𝑒𝑟𝑖𝑧𝑒𝑑 𝑢𝑛𝑖𝑡

161

Where Q is the number of the structural unit within the peak n, for example, in peak D2 (4

folded ring), there are 4 connected SiO4 units. En is the bond energy of structural units within

the peak from D1 to Q4, which is calculated using Coulomb equation, Cn is the relative

concentration of the peak n in Raman spectrum

Table 6.3 Summary of the bond energy of each deconvoluted peaks

Peak Structural Unit Bond Energy (KJ/mol)

D1 AlO4-SiO4 7553

D2 4 [SiO4] 23368

D3 3 [SiO4] 17526

Q1 [SiO4]4-

individual unit 8677

Q2 Si2O7 dimer 10721

Q3 Si2O6 chain 13421

Q4 Si2O5 sheet 15772

As Figure 6.8 shown, the proposed DP was a plot against the slag sample in the present study.

It can be seen that the DP index decreased as basicity increased within SiO2-CaO, SiO2-CaO-

MgO, and SiO2-CaO-Al2O3 system. In the basicity = 0.8-1.1 ranges, the DP index slightly

increases as Mg2+

ion substitutes for Ca2+

.

162

Figure 6.8 DP index again basicity of SiO2-CaO, SiO2-CaO-MgO, and SiO2-CaO-Al2O3

system

6.4.2 Density

Density is a physical variable of molten oxides in operation optimization, which is relevant to

the slag/metal separation. It is also an important thermodynamic variable for calculating

critical dimensionless numbers, such as Reynolds, Prand, and Nusselts, which are used in

fluid transmission and can be extended to the estimation of blast furnace operation [210]. The

densities of molten slags can be simulated using the partial molar volume. The effect of the

SiO2 and Al2O3 on density can be represented by empirical equation from Mill’s study [211].

It should be noted that the reference temperature for calculation is 1773 K and require

adjustment to other temperatures by applying a temperature coefficient of -0.01%/K [211].

The relationship between density and DP is shown in Figure 6.9. A linear equation can be

proposed to estimate the slag density with Raman spectrum information.

Figure 6.9 DP index against the estimated densities of slag samples

163

6.4.3 Viscosity & Activation Energy

Viscosity is a measure of the impediment of flow. The size of the constituents present in the

melt constitutes the barrier or impediment to movement. Since silicates contain different

structural units with varying sizes; it is necessary to relate the viscosity to the structure of

silicates. The abundance of several structural units is consistent with the activation energy of

slags. Consequently, it is possible that activation energy of a composition is a mathematical

function of the DP index.

As Equation 6-4 shown, the Arrhenius type equation was used to determine the activation

energy. The activation energy of slag samples in the current study can be determined from

existing viscosity data. As Figure 6.10 shown, the calculated activation energy from

experimental results has a positive relationship with DP for SiO2-CaO, SiO2-CaO-MgO, and

SiO2-CaO-Al2O3 system. A polynomial equation, as Equation 6-4 shown, can use to describe

the trend. The DP index, which can be experimentally measured, can potentially be used to

quantify and predict the viscosity of the melts [210].

Equation 6-4 Arrhenius-type equation

η = A ∗ exp (𝐸𝐴

T)

E𝐴 = 0.214 ∗ 𝐷𝑃2 + 4.453 ∗ 𝐷𝑃 + 11.73

Figure 6.10 DP index of each Raman spectrum against the activation energy

164

6.5 Conclusion

The structure and properties of amorphous slags are of widespread interest because of their

importance in the process optimization of pyro-metallurgy field. Raman spectroscopy is an

analytical technique for the study of the microstructure of molten slag of the silicate-based

system. The impact of Al2O3 and MgO on SiO2-CaO based system was investigated by

utilization of Raman spectrum on quenched glasses samples. A significant correlation was

determined between the quantitative information of Raman spectrum and a polymerization

degree of slag sample in the present study, which supported the silicate network theory. In the

present study, a quantitative analysis was performed on the Raman spectrum to estimate the

degree of polymerization of silicate slag, which can extend to the relevant physiochemistry

properties, such as density and chain dimensions (DP). The present methodology can be

extended to predict the other physicochemical properties of silicate melts for metallurgical

processes.

165

Chapter 7 : Experimental and modeling study of suspension system

7.1 Introduction

The dynamic viscosity of suspensions is of interest in many disciplines of engineering, such

as mechanical, chemical and civil engineering. The suspension viscosity ηsus primarily

depends on (1) the solid fraction, (2) shape and size of particles, (3) the suspending

Newtonian liquid, (4) Temperature, and (5) shear rate (for non-Newtonian suspension). There

is a research gap that the suspension viscosity was rarely studied in high-temperature region

and its correlation with room temperature data. It is known that the precipitation of solid

particles in molten slag was commonly observed in iron, steel, copper and other

pyrometallurgy process. Most of viscosity measurement assumed the full liquid slag system.

As literature review in the Section 2.5, limited viscosity study of molten slag was constructed.

With the assumption of suspension at 25 oC, the suspension viscosity model did not include

the temperature information, why may not suitable for the prediction at smelting temperature

(>1000 oC). It is necessary to explore and compare the suspension viscosity by the systematic

variation of the parameters at both room and smelting temperature conditions.

For the viscosity measurements at high temperature, the potential fault was caused from

obtaining the steady viscosity values and determination of the solid proportion. In Kondratiev

and Wu’s study, the solid proportion of molten slag was determined using software FactSage

prediction and Slag Atlas respectively [9, 213]. From the researches on phase equilibrium, the

experimental results demonstrated that both tools can’t provide an accurate prediction of

phase mixture at a high temperature, which may cause large deviation on the determination of

solid fraction. A reliable technique is required to obtain reliable viscosity values and the solid

proportion of solid/liquid mixtures.

The mathematical models of viscosity simulation were significant for both the fundamental

development and industrial application. Early on 1909, as Equation 7-1 shown, Einstein

proposed a mathematical expression to predict the suspension viscosity using liquid viscosity

and solid fraction f [173]. Thomas, Roscoe and other researchers continue on the

development of viscosity model through varying the mathematical expression of solid

fraction f, which extend the prediction range of different suspension system [173]165-175].


166

Equation 7-1 relative viscosity calculation

η𝑠𝑢𝑠

η𝑙𝑖𝑞= η𝑟𝑒𝑙𝑎 = f(𝑓)

Where η𝑠𝑢𝑠 is suspension viscosity in Pa.s, η𝑙𝑖𝑞 is the liquid viscosity in Pa.s, f is the solid

volume fraction in vol%

The present study aims to: 1) Experimentally measure the suspension viscosity at room and

smelting temperature using reliable techniques and 2) examine the applicability of the

existing models and optimize them if necessary.

7.2 Methodology

The viscosities of two-phase mixtures at both room and smelting temperatures were measured

by rotation spindle techniques. Two model series, LV III and HB III from Brookfield, were

utilized to cover the viscosity range 0-1 Pa.s and 0.6-20 Pa.s respectively. The Rheocalc

software on PC was utilized to control the rotation speed and record the torque readings.

The suspension viscosity was calculated using Equation 7-2 below. The equipment constant

K, a function of the spindle/crucible geometries and the rheometer, was determined using the

standard silicon oil (Brookfield product) with known viscosity.

Equation 7-2 Viscosity calculation

𝜂 = 𝐾τ

𝛺

Where η [Pa.s] is the viscosity of the suspension, τ [N.m-1

] is the torque at a certain rotation

speed Ω [m.s-1

], and K is the equipment constant. The K value was calculated through

calibration of standard silicon oil.

7.2.1 Calibration

The equipment constant K, a constant parameter of the spindle/crucible, was determined

through calibration of standard silicon oil from Brookfield Engineering. The standard silicon

oil is a liquid polymerized siloxane with a certain length of polydimethylsiloxane chain,

which determine the standard viscosity at 25 oC. From Brookfield Engineering, the physical






167

properties of silicon oil are shown in Table 7.1. In the present study, five standard silicon oil

were utilized for calibration, which covering the viscosity ranges from 0.05 to 1 Pa.s.

Table 7.1 Physical properties of silicon oil in present study

Silicon Oil Viscosity

(Pa.s)

Density

(kg/m3)

A 0.0498 965±4

B 0.098 965±4

C 0.21 968±4

D 0.498 968±4

E 1 968±4

In a general run, the crucible, spindle bob, and silicon oil were kept inside the water bath (25

oC) for 30 minutes to achieve homogeneous temperature condition. The rheometer will report

70 torque at the 3-second interval at 3 different rotational speed. The overall equipment

constant K was calculated using Equation 7-2 and accepted if the relative difference is within

1% from 5 standard silicon oil. The calibrated crucible, spindle, and rheometer were later

used in the room-temperature, and the devices for high-temperature viscosity study were re-

calibrated through the same procedure.

7.2.2 Viscosity Study of Suspension at Room Temperature

In the viscosity study at room temperature, the silicon oil and paraffin were employed to

simulate the molten slag liquid and precipitated minerals respectively. The standard silicon

oil with known viscosity at 25 oC was purchased from Brookfield Engineering. The piece of

paraffin was grinded to fine particles and sieved to three group sizes: <100, 100-200 μm and

200-300 μm. The impact of various parameters have been systematically investigated, which

include, 1) liquid viscosity, 2) solid fraction, 3) particle size and 4) temperature. The

experimental conditions were shown in Table 7.2 below.

Table 7.2: Experimental condition of viscosity measurement at room temperature

Run Silicon

Oil

Temperature

(oC)

Paraffin Solid Proportion

(vol %)

Paraffin

Size

168

(Pa.s) (μm)

1-3 0.05 10, 25, 40 0-32 (at 25 oC)

0-21 (at 10 and 40 oC)

100-200

4-8 0.1 10, 25, 40 0-32 (at 25 oC)

0-21 (at 10 and 40 oC)

<100

100-200

200-300

9-11 0.2 10, 25, 40 0-32 (at 25 oC)

0-21 (at 10 and 40 oC)

100-200

12-14 0.5 10, 25, 40 0-32 (at 25 oC)

0-21 (at 10 and 40 oC)

100-200

15-19 1 10, 25, 40 0-32 (at 25 oC)

0-21 (at 10 and 40 oC)

<100

100-200

200-300

The experimental setup is schematically shown in Figure 7.1. A crucible having an inner

diameter of 28 mm was used to hold the solution mixture. In a general run, the container with

silicon oil, paraffin particle, and spindle bob was kept inside the water bath for 30 minutes,

which allow the mixture achieve the designed temperature. The oil-paraffin mixtures were

stirred extensively by the spindle to ensure homogenization environment. During the

measurement, the Rheocale software from computer controlled and recorded the measured

torque readings at three different pre-set rotation speed. 70 values were taken at 3-second

interval at each rotation speed. The first part fluctuation values were ignored because the

solid dispersion did not achieve equilibrium. With the known equipment constant from the

calibration process, the viscosity value was calculated using Equation 7-2. The results were

averaged and calculated over the measurements of 3 different rotation speeds.

169

Figure 7.1 Schematic diagram of room temperature measurements

7.2.3 Viscosity Study of Suspension at Smelting Temperature

The experimental of high-temperature viscosity measurement include two parts: the first part

is to measure the suspension viscosity at designed temperature. Synchronously, the

equilibrium experiments were constructed to determine the phase information at the

temperature of solid appearing within the viscosity measurement. Electron probe X-ray

microanalysis (EPMA) was used for microstructural and elemental analyses of the quenched

samples, which can determine the accurate solid proportion and phase.

The equipment for high-temperature viscosity measurements and equilibrium experiments

were schematically shown in Figure 7.2 below. The features and description of the devices

have been introduced, by the present author in a previous publication. Two industrial slag

samples from blast furnace of Baosteel (BS slag) and JingTang (JT slag) were tested in the

present study.

170

Figure 7.2 Schematic diagram of (a) left, high-temperature viscosity measurement (b) right,

equilibrium experiments

7.3 Results

In the viscosity study of suspension, the effect of various parameters on the suspension

viscosity has been investigated. These parameters are:

Liquid viscosity & solid fraction

Particle diameter

Temperature

Shear rate

7.3.1 Room Temperature

All results were obtained by varying the shear rate (rotational speed) and measuring the

corresponding shear stress. These measurements have been constructed at the five species

standard silicon oil and three sizes of paraffin, which is displayed in Table 7.3. It has been

found that at low solid proportion, the suspension behavior as a Newtonian fluid, which

report the constant ratio of shear stress to rate. However, when the solid proportion increased

above 25%, the suspension deviated to shear thinning fluid, which was separately shown in

Table 7.4 at a different shear rate (rotational speed). The shear thinning fluid behavior would

be discussed in the later section.

171

Table 7.3. Viscosity measurements of suspension of solid proportion from 0-22 vol%

Viscosity (Pa.s) at different Solid Proportion (vol %)

ηLiq

(Pa.s)

D

(um)

T (oC) 0 2 5 7 10 12 15 17 20 22

0.05 100-200 10 0.0678 0.082 0.102 0.142 0.17

0.05 25 0.04975 0.053 0.06 0.067 0.076 0.089 0.101 0.121 0.141 0.16

0.05 40 0.03948 0.046 0.054 0.076 0.096

0.1 100-200 10 0.183 0.21 0.235 0.269 0.318

0.1 <100 25 0.0961 0.115 0.145 0.18 0.245

0.1 100-200 25 0.0961 0.102 0.117 0.13 0.145 0.167 0.199 0.223 0.266 0.298

0.1 200-300 25 0.0961 0.121 0.147 0.193 0.288

0.1 100-200 40 0.0727 0.085 0.107 0.146 0.215

0.2 100-200 10 0.259 0.312 0.357 0.537 0.63

0.2 25 0.192 0.207 0.235 0.255 0.276 0.325 0.381 0.451 0.53 0.59


172

0.2 40 0.148 0.177 0.23 0.302 0.432

0.5 100-200 10 0.653 0.776 1.043 1.38 1.91

0.5 25 0.484 0.525 0.601 0.683 0.796 0.877 0.994 1.15 1.39 1.57

0.5 40 0.386 0.461 0.598 0.812 1.226

1 100-200 10 1.72 2.03 2.77 4.8

1 <100 25 1.26 1.66 2.05 2.9

1 100-200 25 1.185 1.25 1.41 1.65 1.75 2.03 2.35 2.89 3.33

1 200-300 25 1.3 1.7 2.06 2.91

1 40 1.31 1.655 2.33 4.04

Table 7.4. Viscosity measurements of suspension of solid proportion from 25-32 vol %

Shear Stress (torque) at different rotational speed (rpm)

ηLiq

(Pa.s)

T

(oC)

26.5 vol% paraffin

Torque / rpm

29 vol% paraffin

Torque / rpm

32 % paraffin

Torque / rpm


173

0.05 25 44.6 / 75

59.4 / 100

71.1 / 125

85.2 / 150

98.1 / 175

Average viscosity = 0.179 Pa.s

34.4 / 50

51.7 / 75

65.8 / 100

83.9 / 125

97.6 / 150


41.5 / 50

62.2 / 75

80.9 / 100

98.8 / 125


0.1 25 48.8 / 30

53.32 / 35

62.2 / 40

70.1 / 45

78.9 / 50


62.3 / 150

72.7 / 175

82.1 / 200

89.4 / 225

95.8 / 250


58.4 / 125

70.1 / 150

77.6 / 175

86.4 / 200

95.1 / 225


0.2 25 53.32 / 150

62.2 / 175

70.1 / 200

78.9 / 225

53.32 / 150

62.2 / 175

70.1 / 200

78.9 / 225

53.32 / 150

62.2 / 175

70.1 / 200

78.9 / 225

174

86.9 / 250


86.9 / 250


86.9 / 250


0.5 25 38.7 / 20

48.4 / 25

57.1 / 30

65.7 / 35

74.5 / 40

83.1 / 45

90.32 / 50


50.9 / 20

63.67 / 25

73.4 / 30

85.1 / 35

95.4 / 40


16.1 / 5

32 / 10

48 / 15

64.1 / 20

79 / 25

89 / 30


1 25 53.32 / 150

62.2 / 175

70.1 / 200

78.9 / 225

86.9 / 250


53.32 / 150

62.2 / 175

70.1 / 200

78.9 / 225

86.9 / 250


53.32 / 150

62.2 / 175

70.1 / 200

78.9 / 225

86.9 / 250


175

7.3.2 Smelting Temperature

Figure 7.3 presents the viscosity of Baosteel slag and JingTang slag with a variation

of temperature ranging from 1575 to 1375 oC. The viscosity information and

elemental analysis from EPMA were summarized in Table 7.5. The solid fraction was

calculated using matrices method with a known composition. Both of the elemental

analysis results and viscosity increasing confirmed the solid precipitation when the

temperature reduced to 1400 oC. The solid proportions were calculated from the

composition of liquid (glass phase) and solid (melilite phase) by EPMA analysis. In

addition, the FactSage (version 6.2) and phase equilibrium chart (from Slag Atlas)

were utilized to compare the liquid and solid proportion and composition for these

two samples, which is quite different from the EPMA results.

The quantity of SiO2 content performs a critical role in the slag fluidity. At high

temperature, SiO2 from gangue mineral integrated with CaO, formed molten slag,

resulted in a good fluency of slag within blast furnace operation. As Figure 7.3 shown,

the viscosity of BS slag is slightly higher than JT slag (approximate 0.05 Pa.s) in the

full liquid region. The viscosity difference was enlarged as temperature decreasing,

because of SiO2. According to the elemental analysis from EPMA, in fully liquid slag,

BS slag has 2 wt% SiO2 higher than JT slag, which contributed to the higher viscosity.

When temperature decreased, the melilite precipitation of BS slag occurred at a higher

temperature than JT slag, which reports high solid fraction at the same temperature;

hence enlarge the viscosity difference. At the same temperature, according to the

results at Table 7.5, the solid proportion of BS slag is higher than JT slag, 20% > 10%

at 1400 and 40 %> 27 % at 1375 oC respectively. In the present study, it has found

that only small quantity of SiO2 will impact on the viscosity of both fully liquid slag

(1500oC) and solid containing slag (1400

oC), which can become a critical issue in the

low-temperature region of the smelting process.

Table 7.5. The elemental analysis of Baosteel and JingTang slag from EPMA analysis,

where the minor element include Na2O, K2O, FeO and etc

Slag Temperature

(oC)

Phase SiO2 CaO Al2O3 MgO Viscosity

(Pa.s)

176

JT 1400 Liquid 33.1 39.4 14.5 7.7 Bulk

Viscosity=

0.553

JT Solid

10 vol%

21.9 43 31.7 3.5

JT 1375 Liquid 33.1 38.8 13.3 8.4 Bulk

Viscosity=

0.746

JT Solid

27 vol%

28.9 42.5 24.4 4.3

BS 1400 Liquid 35.3 39.9 14.6 8 Bulk

Viscosity=

0.888

BS Solid

20 vol%

29.9 42.1 20.7 7.3

BS 1375 Liquid 37.3 39 9.7 10 Bulk

Viscosity=

1.226

BS Solid

40 vol%

28.9 41.8 24.7 4.5

Figure 7.3 The viscosity measurements of Baosteel and Jintang blast furnace slag

sample

177

7.3.3 Effect of liquid viscosity and solid fraction

It is accepted that the liquid viscosity and solid fraction are the two significant

parameters for the viscosity of suspensions. From the view of model simulation

(Einstein Model [9] Equation 7-3), it is expected that the relative viscosity has a

proportional positive correlation with solid fraction only and not dependent on the

liquid viscosity.

Figure 7.4 shows that the effect of liquid viscosity and solid fraction [f] on the relative

viscosity for particle diameters d=100-200 µm at 25 oC. From low (2 vol%) to high

(32 vol%) solid fraction, the relative viscosity of the suspension rapidly increased

upon to 5 times of the liquid viscosity. And, it can be noted that the deviations of

relative viscosity among different liquid viscosity is negligible at low solid fraction

range (0-15 vol%) and slightly increased to 5% at high solid fraction (15-32 vol%). It

indicated that the effect of liquid viscosity is not constant and raised as a solid

addition. At a high solid fraction, the liquid with large viscosity will momentarily

retain and accelerate the particles. This dissipation of energy will appear as “extra

viscosity”, which was observed in the torque measurements.

Equation 7-3 Einstein equation of relative viscosity

η𝑠𝑢𝑠

η𝑙𝑖𝑞= η𝑟𝑒𝑙𝑎 = (1 +

5

2𝑓)

178

Figure 7.4 The relative viscosity of oil-paraffin system at different solid fraction and

liquid viscosity at 25 oC

7.3.4 Effect of particle diameter

In the present study, the impact of particle diameter on solution viscosity was

investigated using three different sizes’ paraffin, which was <100 µm, 100-200 µm

and 200-300 µm. Figure 7.5 (a) and (b) demonstrate the viscosities of different

particle size group at low (0.1 Pa.s) and high (1 Pa.s) liquid viscosity condition

respectively. For suspensions based on a liquid with high viscosity (1 Pa.s), the effect

of particle size on the suspension viscosity is negligible, which reported only 0.5%

deviations. But for suspensions based on a liquid with low viscosity (0.1 Pa.s), a trend

can be observed that larger particle will generate a higher suspension viscosity. At 32

vol% solid fraction, the 200-300 and <100 µm reported 0.523 Pa.s and 0.48 Pa.s

respectively, which is approximately 8% deviations. In the low liquid viscosity

condition (0.1 Pa.s), the particles of greater size possess more inertia such that on

interaction with rotational bob, which will momently stop and accelerate during

rotation. This energy dissipation appears as “extra viscosity”. However, in the high

liquid viscosity condition (1 Pa.s), this inertia phenomenon occurred on all three sizes

paraffin because of the increment of liquid viscosity.

179

Figure 7.5 The suspension viscosity at different solid fraction and particle size at (a)

top, 0.1 Pa.s liquid viscosity and (b) bottom, 1 Pa.s liquid viscosity

7.3.5 Effect of Temperature

Temperature is another significant factor impacting on the viscosity, which was

encounter within the calculation of liquid viscosity. It is known that temperature has a

negatively proportional correlation with solution viscosity. When the temperature

increase, the liquid viscosity will decrease but did not impact on the expression of a

solid fraction under the assumption of thermal expansion of solid particle is negligible.

Therefore, the suspension viscosity will reduce as [ηsus]= [ηLiq]*[f], which is

confirmed by the viscosity measurements at room and steelmaking temperatures.



180

The Arrhenius type equation can express the temperature dependence of the slag

viscosity as Equation 7-4 shown, which was widely utilized in the model development

of liquid slag. In the present study, it has found that the applicable range of Arrhenius

type equation can be extended to the dilute suspension with a solid fraction from 0-15

vol% at different liquid viscosity. The suspension viscosity follows the correlation in

the form lnη = A +B

𝑇, where constants B are close for present paraffin/oil study. As

Figure 7.6 (b) shown, the temperature dependence of 15 vol% suspension was

confirmed at different liquid viscosity and Namburu’s viscosity study {Namburu,

2007 #1976}.

Equation 7-4 Arrhenius-type Equation

η = A ∗ e𝐵𝑇

Where η is the apparent viscosity Pa.s and T is the temperature K.

181

Figure 7.6 The temperature dependence on the oil-paraffin system suspension

viscosity (a) 0.05 liquid viscosity suspension at 5, 10, 15 and 20 vol% and (b) 15 vol%

suspension at liquid viscosity 0.05, 0.2 and 0.5 Pa.s by Wright [163]

7.3.6 Effect of Shear Rate

It is known that the viscosity of a fluid is correlated with the shear stress and shear

rate. Figure 7.7 (a) and (b) shows the shear rate has been investigated for a various

solid fraction and liquid viscosity. Figure 7.7 (a) compared that the shear rate

(rotational speed) of 5% solid fraction at different liquid viscosity suspension. As the

liquid viscosity increased, the suspension kept as Newtonian behavior. The R2 value

of 5% solid fraction at low viscosity suspension (0.05 Pa.s) and high viscosity liquid

suspension (1 Pa.s) is 0.998 and 0.999 respectively, which was the Newtonian fluid

behavior. The impact of liquid viscosity on fluid behavior is negligible.

When the solid fraction increased, it is found that fluid slightly shifts to shear thinning

behavior. Figure 7.7(b) compared that the shear rate of 0.1 Pas liquid viscosity

suspension at a different solid fraction (10%, 20%, and 30%). The results indicated

that at high solid proportion, the suspension slightly shifted to shear thinning solution,

which can be observed from R2=0.997 at 10% solid fraction to R

2=0.989 at 30% solid

fraction. This behavior was also observed in Wu’s viscosity study at above 15% solid

suspension system. The critical point transforming the Newtonian to non-Newtonian

fluid could not be accurately determined, because the boundary condition between

them is not quantitatively defined.

In Coussot’s study, he proposed that at high shear rates an increase of the suspension

viscosity could occur due to secondary flow, grain-inertia effects (i.e. momentum

transfer due to collisions between particles with fluctuating velocities or transition to

turbulence) [215]. This phenomenon was observed in section 3.3 and 3.4 as discussed

before. At high shear rates, the shear rate brought in additional rotational force and

may cancel the impact of “extra viscosity”, which cause decreasing of shear stress and

shift the fluid from Newtonian to shear-thinning type.

182

Figure 7.7 The measured torque at different rotational speed for (a) 5% solid fraction

at 0.05 and 1 Pa.s silicon oil. (b) 10, 20 and 30 % solid fraction at 0.5 Pa.s silicon oil

7.4 Model Simulation

7.4.1 Model Review and Evaluation

11 existing models were reviewed and evaluated in the present study using the

viscosity database at room temperature condition. Equation 7-5 is used to calculate

the difference between the measured and the calculated viscosity values.

183

Equation 7-5 error deviation calculation

1*

exp Calc

expn

Where Δ is the average deviation, exp is the experimental viscosity, Calc is the

calculated viscosity and n is the number of data.

Figure 7.8 (a) and (b) present the comparison of viscosity deviations of existing

models. Ranging from 0.05 to 5.5 Pa.s, the Kunitz model reported an outstanding

agreement with experimental data with 2.95% deviations [174]. Figure 7.8 (b) also

demonstrated that the Kunitz model fitted well with the experiment measurements

comparing to other models. The model prediction of 0-20% solid fraction fitted with

Happel model, which matches the conclusion of Wu. However, with the continues

addition of solid, the suspension viscosity will shift towards to the Kunitz prediction.

184

Figure 7.8 The model prediction vs experimental results at (a) top, different models

and (b) bottom, 1 Pa.s liquid viscosity

Figure 7.9 (a) and (b) present the predicted viscosities as functions of particle fraction

for JT and BS slag samples respectively. The prediction of high-temperature viscosity

involving two steps, which is the prediction of liquid viscosity and then suspension

viscosity. The liquid viscosity can be accurately determined using the existing Han

model, which report an outstanding agreement with slag viscosity ranging from 1450-

1600 oC as Figure 7.9 shown. The liquid viscosity of slag was re-calculated at

different liquid compositions of JT and BS slag as temperature decreasing. Then, the

information of solid fraction and liquid viscosity were utilized to calculate final

suspension viscosity by different models as Figure 7.9 shown. A comparison of the

experimental data with the model predictions evidently shows that Einstein model

reported an outstanding prediction performance in the present study.

As the model reviewed, Einstein model is applicable only to dilute sphere particles,

which is contracted to the known solid %. From EPMA analysis, the solid fraction at

1375 oC is 40 and 27 wt% for BS and JT slag respectively. The contradiction

indicated that there is a factor impacting on suspension viscosity, which wasn’t

considered. It is necessary to address the limitations of direct methods by further

model modifications.

185

Figure 7.9 The model prediction vs experimental results of (a) top JingTang slag and

(b) bottom, Baosteel slag

7.4.2 Model Optimization

The Kunitz model was investigated as a basement; due to its outstanding performance

for the viscosity measurements at room temperature. As Table 7.6 shown, Kunitz

model includes two parts: 1) the numerator (1+0.5f) and 2) the denominator (1-f)4,

where f is the solid fraction.

The numerator (1+0.5f) is derived from the velocity gradient equation by considering

the perturbation in the flow field due to the presence of a continuously decreasing

number of particles per unit volume. Thomas pointed out that the (1+0.5f) expression,

186

which is derived from Einstein study, only applicable to the dilute suspension system.

With concentrated suspensions, it is necessary to account for the hydrodynamic

interaction of particles, particle rotation, collision and higher order agglomerate

formation. The parameter 0.5 can only utilize when the solid spheres with diameter

large compared to liquid molecule dimensions, which is suitable for the present study.

Many of the existing theoretical and experimental equations can be expressed as a

power series as Equation 7-6 shown. Present study continues to use 0.5 for the

coefficient k1, because of outstanding prediction performance from Kunitz model.

After accounting for the hydrodynamic interaction of spheres, the coefficient ranges

from -2.3 to 50 to the value of k2 from different authors. The coefficients of various

combinations of terms in Equation 7-5 were determined using a nonlinear least

squares procedure by minimizing the deviations, which report k2=1.

Equation 7-6 relative viscosity calculation

η𝑟𝑒𝑙𝑎 = (1 + 𝑘1𝑓 + 𝑘2𝑓2 + 𝑘3𝑓3 + ⋯ 𝑘𝑛𝑓ｎ)

The denominator is (1-f)4 is an argued mathematical expression, which was derived

from the integral under the condition of consistently irregular distribution of

dispersing particles. Einstein, Toda, and Kunitz proposed the index parameter as 2, 3

and 4 respectively. The index 2, 3 and 4 was derived from the dispersion energy

calculation. With the solid fraction increased, the index parameters step wisely

increased from 2 to 4, which reflects suspension changing from smooth to rigid

structure because of the high solid fraction. This phenomenon was also approved in

the present study in previous sections. The suspension with large liquid viscosity

reported a higher relative viscosity than a suspension with low liquid viscosity as the

mixing behaviors changed when solid fraction and liquid viscosity increased. At room

temperature condition, the index parameter is 4, which demonstrate an outstanding

prediction performance.

At high-temperature condition, it is widely accepted that the liquid molecular is more

violent, which can be observed from the viscosity decreasing. Wilson reported that the

relation between temperature and excess energy of mixing was smoothed to the

187

temperatures for the mixtures by plotting against the temperature in the liquid/gas

interface. Although, the mixing behavior could not be directly observed at the high-

temperature condition. It can be estimated that the mixing behaviors are smooth

structure due to the excess energy of mixing. Therefore, the index parameter should

decrease stepwise decreased as temperature increasing. In the present study, for

different temperature range, from 10-50 oC and 1300-1500

oC, the index parameter

was and 1.8 respectively. Overall, the mathematical expression of Kunitz model was

optimized for different temperature range and a solid fraction as Table 7.6 shown.

Table 7.6. Summary of optimized model

Old Kunitz Equation Room Temperature Steelmaking Temperature

η𝑟𝑒𝑙𝑎 =1 + 0.5𝑓

(1 − f)4

η𝑟𝑒𝑙𝑎 =1 + 0.5𝑓 + 𝑓2

(1 − f)4

η𝑟𝑒𝑙𝑎 =1 + 0.5𝑓 + 𝑓2

(1 − f)𝑥

Where x is 1.8 for 1400 oC

suspension viscosity, will

decrease if temperature

increase and vice versa

As Figure 7.10 shown, the optimized model demonstrated an outstanding agreement

with experimental data of the present study, Wu, and Wright at both temperature

ranges [9, 163]. It indicated that the viscosity estimation should be divided into two

temperature ranges because of different mixing behaviors.

188

Figure 7.10 The comparison between experimental data and model predictions by

Wright [163] and Wu [9]

7.4.3 Model Application

The modified model has shown superior prediction performance on the silicon

oil/paraffin and two industrial slags systems for a range of viscosity between 0.05 Pa.s

to 5 Pa.s. A further application would be considered on the suspension viscosity on a

wider viscosity temperature range of other disciplines of engineering. At room

temperature condition, as Figure 7.11 shown, the present model is capable of

predicting the suspension viscosity ranging from 0.005 Pa.s to 200 Pa.s. At high

temperature, it can be noted that, under the condition of minimizing deviations, the

index parameter is 3.8 and 1.7 for Louise and Wright respectively [162, 163]. It again

approved the conclusion that the index parameter is decreased from 4 when

189

temperature increased upon 25 oC. Further study is required for the correlation

between temperature and energy of dispersion terms.

Figure 7.11 The comparison of model prediction and other researchers results at (a)

room temperature by Chong [153] and Namburu [160], (b) high temperature by

Louise [159] and Wright [163]

190

7.5 Conclusion

In summary, the experiments at both room temperature and steelmaking temperature

were carried out to study the effect of the presence of solid particles in liquid on

viscosity. Five silicon oil with different viscosities and paraffin particles were

employed to simulate the molten slag condition and confirm the impact of (a) liquid

viscosity, (b) solid fraction, (c) particle diameter, (d) temperature and (e) shear rate on

the suspension viscosity. The viscosities of two industrial slags were determined to

range from 1375 to 1575 oC. It has been found, at either high liquid viscosity

condition or large particle size condition, the particles are momentarily retarded and

then accelerated. Their inertia affects the amount of energy required. This dissipation

of energy appears as “extra viscosity”. The two-phase mixtures slightly deviated from

Newtonian fluid to shear thinning fluid when the particle fraction above 25 wt%.

In the present study, 11 existing viscosity models were reviewed, which use the

different mathematical equation to determine the nrela. While the experimentally

determined viscosities were agreed well by Kunitz model in the room temperature

results, which was optimized to covering concentrated suspension at the high-

temperature condition. The coefficient of the numerator (1+0.5f) was re-optimized to

(1+0.5f+f2) by accounting the hydrodynamic interaction of particles. The index of the

denominator (1-f)4 is 4 at room temperature, and stepwise decreased as temperature

increasing due to the excess energy of mixing. The optimized model demonstrated an

outstanding prediction performance covering the viscosity range from 0.005 Pa.s to

200 Pa.s at different temperatures (room-1500 oC). Further study is required for the

correlation between temperature and energy of dispersion terms.

191

Chapter 8 : Conclusions

There is an increasing focus on process optimization and energy usage efficiency of

blast furnace ironmaking. During the operation, slag viscosity plays a significant role

in controlling the process, which has a direct impact on the metal/slag efficiency. In

the present study, the viscosity of blast furnace slag relevant to ironmaking process

was systematically investigated. A comprehensive literature review has been

constructed covering the fundamentals of the viscosity theory, experimental data and

mathematical models on the CaO-MgO-Al2O3-SiO2, its binary and ternary system.

Due to uncertainty, the viscosity measurements of the CaO-MgO-Al2O3-SiO2 system

were critically evaluated following the three steps: 1 Experimental techniques, 2 Data

consistency, and 3 Cross-reference comparison. In addition, the viscosity

measurements of minor elements’ impact on molten slag were reviewed. The structure

of silicate melts (glass phase) were reviewed using different characterization

techniques. The viscosity behavior of solid impact on molten slag was investigated to

fully understand and control the slag fluidity in blast furnace operation.

The following list represents the work that has been completed by the present Ph.D.

candidate:

1. Review and evaluated the experimental methodologies, viscosity data, and models

relevant to the blast furnace slag in CaO-MgO-Al2O3-SiO2 system (Chapter 2)

2. Based on the collected data and models, an accurate viscosity model has been

developed to predict the viscosity of blast furnace slag in CaO-MgO-Al2O3-SiO2

system (Chapter 4-5)

3. Research on the viscosity impact of minor elements on the blast furnace final slag

in CaO-MgO-Al2O3-SiO2 based system. (Chapter 4-5)

4. Quantitative investigation of the microstructural units of silicate slag utilizing

Raman spectroscopy. (Chapter 6)

5. Investigation of the solid phase impact on the viscosity of liquid slag. (Chapter 7)

192

Chapter 9 : Reference

[1] AK.Biswas, "Principles of Blast Furnace Ironmaking", Coothea Publishing House,

Brisbane, Australia, 1981

[2] R. Benesch, R. Kopec, A. Ledzki, JB. Guillot and W. Zymla: "The physico-

chemical properties of the blast furnace slags with TiO2 addition", Archives of

metallurgy, 1996, vol. 41, pp. 15-24.

[3] V.D. Eisenhüttenleute: "Slag Atlas", Verlag Stahleisen, 1995

[4] T.S. Kim and J.H. Park: "Structure-viscosity relationship of low-silica calcium

aluminosilicate melts", ISIJ International, 2014, vol. 54, pp. 2031-2038.

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