Abstract
The viscosity of solid phase containing heterogeneous silicate melts is discussed in this review. The crucial parameters characterizing silicate melt structure are first presented, i.e., volume fraction of solid particles, particle shape and size. The measurement and calculation methods of these parameters are summarized and the influence of the parameters on viscosity is discussed. Next, a theoretical description of rheological behavior in heterogeneous silicate melts is given, focusing on non-Newtonian characteristics, e.g., shear-dependence, time-dependence, and yield stress. The viscosity models which were proposed in the last half century are reviewed and critically assessed. This paper concludes with opportunities and suggestions for future work.
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K. Mills and S. Sridhar: Ironmak. Steelmak. 1999, vol. 26, pp. 262-68.
J. Groen, D. Brooker, P. Welch and M. Oh: Fuel Process. Technol. 1998, vol. 56, pp. 103-27.
C. Senior and S. Srinivasachar: Energ. Fuel. 1995, vol. 9, pp. 277-83.
Y. Bottinga and D. F. Weill: Am. J. Sci. 1972, vol. 272, pp. 438-75.
D. Giordano, J. K. Russell and D. B. Dingwell: Earth. Planet. Sc. Lett. 2008, vol. 271, pp. 123-34.
G. Urbain, Y. Bottinga and P. Richet: Geochim. Cosmochim. Ac. 1982, vol. 46, pp. 1061-72.
P. Riboud, Y. Roux, L. Lucas and H. Gaye: Fachberichte Huttenpraxis Metallweiterverarbeitung. 1981, vol. 19, pp. 859-69.
T. Iida, H. Sakai, Y. Kita and K. Murakami: High Temp. Mat. Pr-isr. 2000, vol. 19, pp. 153-64.
S.-H. Seok, S.-M. Jung, Y.-S. Lee and D.-J. Min: ISIJ int. 2007, vol. 47, pp. 1090-96.
W. Song, L. Tang, X. Zhu, Y. Wu, Z. Zhu and S. Koyama: Fuel. 2010, vol. 89, pp. 1709-15.
W. Pitcher: J. Geol. Soc. London. 1979, vol. 136, pp. 627-62.
D. B. Dingwell and S. L. Webb: Phys. Chem. Miner. 1989, vol. 16, pp. 508-16.
R. Fåhræus and T. Lindqvist: American Journal of Physiology–Legacy Content. 1931, vol. 96, pp. 562-68.
C. Tiu and D. Boger: J. Texture. Stud. 1974, vol. 5, pp. 329-38.
A. Einstein: Ann. Phys-new. York. 1906, vol. 19, pp. 289-306.
R. Roscoe: British Journal of Applied Physics. 1952, vol. 3, pp. 267-69.
I. M. Krieger and S. H. Maron: J. Colloid. Sci. 1951, vol. 6, pp. 528-38.
18. H. Ishibashi: J. Volcanol. Geoth. Res. 2009, vol. 181, pp. 78-88.
19. H. Sato: J. Miner. Petr. Sci. 2005, vol. 100, pp. 133-42.
20. A. Kondratiev and E. Jak: Metall. Mater. Trans. B. 2001, vol. 32, pp. 1027-32.
21. A.-M. Lejeune and P. Richet: J. Geophys. Res. 1995, vol. 100, pp. 4215-29.
22. H. M. Mader, E. W. Llewellin and S. P. Mueller: J. Volcanol. Geoth. Res. 2013, vol. 257, pp. 135-58.
23. S. Campagnola, A. Vona, C. Romano and G. Giordano: Chem. Geol. 2016, vol. 424, pp. 12-29.
H. Saxén and X. Zhang: in Proceedings of the International Conference on Engineering Application of Neural Networks, 1997, pp. 167–70.
T. Utigard and A. Warczok: in Proceedings of COPPER, 1995, pp. 423–37.
26. V. Gupta and A. Santra: Steel India. 1994, vol. 17, pp. 74-78.
27. W. Sage and J. McIlroy: Journal of Engineering for Power. 1960, vol. 82, pp. 145-53.
28. J. Watt and F. Fereday: J. Inst. Fuel. 1969, vol. 42, pp. 99-103.
R.C. Streeter, E.K. Diehl, and H.H. Schobert: in The Chemistry of Low-Rank Coals, 1984, p. 195.
30. A. Kondratiev and E. Jak: Metall. Mater. Trans. B. 2001, vol. 32, pp. 1015-25.
31. H. R. Shaw: J. Geophys. Res. 1963, vol. 68, pp. 6337-43.
32. H. Shaw: Am. J. Sci. 1972, vol. 272, pp. 870-93.
33. H. Vogel: Zeitschrift für Physik. 1921, vol. 22, pp. 645-46.
34. G. S. Fulcher: J. Am. Ceram. Soc. 1925, vol. 8, pp. 339-55.
35. G. Tammann and W. Hesse: Z. Anorg. Allg. Chem. 1926, vol. 156, pp. 245-57.
36. D. Giordano and D. B. Dingwell: Earth. Planet. Sc. Lett. 2003, vol. 208, pp. 337-49.
37. A. N. Grundy, I.-H. Jung, A. D. Pelton and S. A. Decterov: Int. J. Mater. Res. 2008, vol. 99, pp. 1195-209.
38. A. N. Grundy, H. Liu, I.-H. Jung, S. A. Decterov and A. D. Pelton: Int. J. Mater. Res. 2008, vol. 99, pp. 1185-94.
39. E. Brosh, A. D. Pelton and S. A. Decterov: Int. J. Mater. Res. 2012, vol. 103, pp. 537-50.
40. W.-Y. Kim, A. D. Pelton and S. A. Decterov: Int. J. Mater. Res. 2012, vol. 103, pp. 313-28.
41. G. Wu, E. Yazhenskikh, K. Hack and M. Müller: Fuel Process. Technol. 2015, vol. 138, pp. 520-33.
42. G. Wu, E. Yazhenskikh, K. Hack, E. Wosch and M. Müller: Fuel Process. Technol. 2015, vol. 137, pp. 93-103.
43. S. Vargas, F. Frandsen and K. Dam-Johansen: Prog. Energ. Combust. 2001, vol. 27, pp. 237-429.
M. O. Chevrel, C. Cimarelli, L. deBiasi, J. B. Hanson, Y. Lavallée, F. Arzilli and D. B. Dingwell: Geochem, Geophys. 2015, vol. 16, pp. 870-89.
45. A. Vona, C. Romano, D. B. Dingwell and D. Giordano: Geochim. Cosmochim. Ac. 2011, vol. 75, pp. 3214-36.
46. H. Ishibashi and H. Sato: J. Volcanol. Geoth. Res. 2007, vol. 160, pp. 223-38.
47. C. Bale, P. Chartrand, S. Degterov, G. Eriksson, K. Hack, R. B. Mahfoud, J. Melançon, A. Pelton and S. Petersen: Calphad. 2002, vol. 26, pp. 189-228.
48. Y. Bottinga, P. Richet and D. Weill: Bulletin de Minéralogie. 1983, vol. 106, pp. 129-38.
49. A. Vona, C. Romano, D. Dingwell and D. Giordano: Geochimica et Cosmochimica Acta. 2011, vol. 75, pp. 3214-36.
50. M. D. Higgins: Am. Mineral. 2000, vol. 85, pp. 1105-16.
51. R. T. De Hoff and F. N. Rhines: Quantitative microscopy, McGraw Hill, New York, 1968.
52. C. R. Brugger and J. E. Hammer: Earth. Planet. Sc. Lett. 2010, vol. 300, pp. 246-54.
A.E.O.J. Delesse: in Procédé mécanique pour déterminer la composition des roches, F. Savy, 1866.
54. J. Mewis and N. J. Wagner: Colloidal suspension rheology, Cambridge University Press, Cambridge, 2012.
55. W. Pabst, E. Gregorová and C. Berthold: J. Eur. Ceram. Soc. 2006, vol. 26, pp. 149-60.
56.H. Goldsmith, S. Mason and F. Eirich: Rheology: Theory and applications. Academic Press, New York, 1967.
57. R. C. Kerr and J. R. Lister: J. Geol. 1991, vol. 99, pp. 457-67.
58. V. Jinescu: International Chemical Engineering. 1974, vol. 14, pp. 397-420.
59.T. G. Van de Ven: Colloidal Hydrodynamics, Academic Press, New YorK, 1989.
60. W. B. Russel, D. A. Saville and W. R. Schowalter: Colloidal dispersions, Cambridge University Press, Cambridge, 1989.
61. H. De Bruijn: Recueil des travaux chimiques des Pays-Bas. 1942, vol. 61, pp. 863-74.
62. S. Wright, L. Zhang, S. Sun and S. Jahanshahi: J. Non-cryst. Solids. 2001, vol. 282, pp. 15-23.
63. S. Wright, L. Zhang, S. Sun and S. Jahanshahi: Metall. Mater. Trans. B. 2000, vol. 31, pp. 97-104.
64. T. Kattamis and T. Piccone: Mat. Sci. Eng. A-struct. 1991, vol. 131, pp. 265-72.
65. C. W. Macosko and R. G. Larson: Rheology: principles, measurements, and applications, VCH, New York, 1994.
66. R. Farris: Tran. Soc. Rheol. 1968, vol. 12, pp. 281-301.
67. M. O. Saar, M. Manga, K. V. Cashman and S. Fremouw: Earth. Planet. Sc. Lett. 2001, vol. 187, pp. 367-79.
68. F. Ryerson, H. Weed and A. Piwinskii: J. Geophys. Res. 1988, vol. 93, pp. 3421-36.
69. W. Song, L. Tang, Z. Zhu and Y. Ninomiya: Aiche J. 2013, vol. 59, pp. 2726-42.
70. E. Garboczi, K. Snyder, J. Douglas and M. Thorpe: Phys. Rev. E. 1995, vol. 52, pp. 819-28.
71. S. Hoover, K. Cashman and M. Manga: J. Volcanol. Geoth. Res. 2001, vol. 107, pp. 1-18.
72. A. R. Philpotts, J. Shi and C. Brustman: Nature. 1998, vol. 395, pp. 343-46.
73. H. V. Atkinson: Prog. Mater. Sci. 2005, vol. 50, pp. 341-412.
74. I. R. Rutgers: Rheol. Acta. 1962, vol. 2, pp. 202-10.
75. I. R. Rutgers: Rheol. Acta. 1962, vol. 2, pp. 305-48.
76. M. M. Cross: J. Colloid. Sci. 1965, vol. 20, pp. 417-37.
77.J. R. Van Wazer: Viscosity and Flow Measurement: A Laboratory Handbook of Rheology. Interscience Publishers, New York, 1963.
78. H. Pinkerton and G. Norton: J. Volcanol. Geoth. Res. 1995, vol. 68, pp. 307-23.
79. R. Buscall: J. Rheol. 2010, vol. 54, pp. 1177-83.
80. H. Walls, S. B. Caines, A. M. Sanchez and S. A. Khan: J. Rheol. 2003, vol. 47, pp. 847-68.
81. M. Manga: J. Volcanol. Geoth. Res. 1998, vol. 86, pp. 107-15.
82. A. Kouchi, A. Tsuchiyama and I. Sunagawa: Contrib. Mineral. Petr. 1986, vol. 93, pp. 429-38.
83. Y. Harada, K. Kusada, S. Sukenaga, H. Yamamura, Y. Ueshima, T. Mizoguchi, N. Saito and K. Nakashima: ISIJ int. 2014, vol. 54, pp. 2071-76.
84. N. Saito, K. Kusada, S. Sukenaga, Y. Ohta and K. Nakashima: ISIJ int. 2012, vol. 52, pp. 2123-29.
85. G. Bossis and J. F. Brady: J. Chem. Phys. 1989, vol. 91, pp. 1866-74.
86. H. Laun, R. Bung, S. Hess, W. Loose, O. Hess, K. Hahn, E. Hädicke, R. Hingmann, F. Schmidt and P. Lindner: J. Rheol. 1992, vol. 36, pp. 743-87.
87. J. F. Brady and J. F. Morris: J. Fluid. Mech. 1997, vol. 348, pp. 103-39.
88. R. G. Egres and N. J. Wagner: J. Rheol. 2005, vol. 49, pp. 719-46.
89. Y. Yue, C. Moisescu, G. Carl and C. Rüssel: Phys. Chem. Glasses. 1999, vol. 40, pp. 243-47.
90. G. A. Macdonald: Am. J. Sci. 1953, vol. 251, pp. 169-91.
91. G. Robson: Nature. 1967, vol. 216, pp. 251-52.
92. H. Shaw, T. Wright, D. Peck and R. Okamura: Am. J. Sci. 1968, vol. 266, pp. 225-64.
93. G. Hulme: Geophys. J. Int. 1974, vol. 39, pp. 361-83.
94. T. Murase and A. R. McBirney: Geol. Soc. Am. Bull. 1973, vol. 84, pp. 3563-92.
95. H. Pinkerton and R. Sparks: Nature. 1978, vol. 276, pp. 383-85.
96. A. R. McBirney and T. Murase: Annu. Rev. Earth. Pl. Sc. 1984, vol. 12, pp. 337-57.
97. L. Caricchi, L. Burlini, P. Ulmer, T. Gerya, M. Vassalli and P. Papale: Earth. Planet. Sc. Lett. 2007, vol. 264, pp. 402-19.
N. Tonmukayakul and Q. Nguyen: World, 2001.
99. S. Mueller, E. Llewellin and H. Mader: Geophys. Res. Lett. 2011, vol. 38, p. L13316.
100. S. Mueller, E. Llewellin and H. Mader: Proc. Royal. Soc. A. 2010, vol. 466, pp. 1201-28.
101. E. Gay, P. Nelson and W. Armstrong: Aiche J. 1969, vol. 15, pp. 815-22.
W. Zhaohui: Denmark Institute of Hydrodynamics and Hydraulic Engineering, 1982.
103. C. Wildemuth and M. Williams: Rheol. Acta. 1984, vol. 23, pp. 627-35.
104. M. Dragoni and A. Tallarico: J. Volcanol. Geoth. Res. 1994, vol. 59, pp. 241-52.
105. G. K. Sigworth: Can. Metall. Quart. 1996, vol. 35, pp. 101-22.
106. L. Heymann, S. Peukert and N. Aksel: Rheol. Acta. 2002, vol. 41, pp. 307-15.
107. A. Castruccio, A. Rust and R. Sparks: Earth. Planet. Sc. Lett. 2010, vol. 297, pp. 471-80.
108. P. Moitra and H. M. Gonnermann: Geochem, Geophys. 2015, vol. 16, pp. 1-26.
109. H. A. Barnes: J. Non-newton. Fluid. 1999, vol. 81, pp. 133-78.
110. Q. Nguyen and D. Boger: Annu. Rev. Fluid. Mech. 1992, vol. 24, pp. 47-88.
111. J. J. Stickel and R. L. Powell: Annu. Rev. Fluid. Mech. 2005, vol. 37, pp. 129-49.
112. R. Brückner and Y. Yue: J. Non-cryst. Solids. 1994, vol. 175, pp. 118-28.
113. D. G. Thomas: J. Colloid. Sci. 1965, vol. 20, pp. 267-77.
114. V. Vand: The Journal of Physical Chemistry. 1948, vol. 52, pp. 277-99.
115. D. J. Jeffrey and A. Acrivos: Aiche J. 1976, vol. 22, pp. 417-32.
116. T. Dabak and O. Yucel: Rheol. Acta. 1986, vol. 25, pp. 527-33.
117. D.-M. Liu: J. Mater. Sci. 2000, vol. 35, pp. 5503-07.
118. V. Vand: The Journal of Physical Chemistry. 1948, vol. 52, pp. 300-14.
119. M. Mooney: J. Colloid. Sci. 1951, vol. 6, pp. 162-70.
120. M. A. Duchesne, A. M. Bronsch, R. W. Hughes and P. J. Masset: Fuel. 2013, vol. 114, pp. 38-43.
I. M. Krieger and T. J. Dougherty: Transactions of The Society of Rheology (1957-1977). 1959, vol. 3, pp. 137-52.
122. T. Kitano, T. Kataoka and T. Shirota: Rheol. Acta. 1981, vol. 20, pp. 207-09.
123. K. Evans and A. Gibson: Compos. Sci. Technol. 1986, vol. 25, pp. 149-62.
J. Parkhouse and A. Kelly: Proc. R. Soc. Lond. A, 1995, pp. 737–46
O. Rahli, L. Tadrist, and R. Blanc: Comptes Rendus de l’Académie des Sciences-Series IIB-Mechanics-Physics-Astronomy., 1999, vol. 327, pp. 725–29.
126. A. Donev, I. Cisse, D. Sachs, E. A. Variano, F. H. Stillinger, R. Connelly, S. Torquato and P. M. Chaikin: Science. 2004, vol. 303, pp. 990-3.
127. L. Onsager: Physical Review. 1932, vol. 40, p. 1028.
128. W. Kuhn and H. Kuhn: Helv. Chim. Acta. 1945, vol. 28, pp. 97-127.
N. Guven and R. Pollastro: Clay-water interface and its rheological implications, Clay Minerals Society, 1992.
v.H. Eilers: Kolloid-Zeitschrift., 1941, vol. 97, pp. 313–21.
131. F. Ferrini, D. Ercolani, B. De Cindio, L. Nicodemo, L. Nicolais and S. Ranaudo: Rheol. Acta. 1979, vol. 18, pp. 289-96.
132. B. A. Horri, P. Ranganathan, C. Selomulya and H. Wang: Chem. Eng. Sci. 2011, vol. 66, pp. 2798-806.
133. J. Chong, E. Christiansen and A. Baer: J. Appl. Polym. Sci. 1971, vol. 15, pp. 2007-21.
134. A. Nzihou, L. Attias, P. Sharrock and A. Ricard: Powder Technol. 1998, vol. 99, pp. 60-69.
135. B. Bournonville and A. Nzihou: Powder Technol. 2002, vol. 128, pp. 148-58.
136. P. Senapati, B. Mishra and A. Parida: Powder Technol. 2010, vol. 197, pp. 1-8.
137. R. Champallier, M. Bystricky and L. Arbaret: Earth. Planet. Sc. Lett. 2008, vol. 267, pp. 571-83.
138. R. Blissett and N. Rowson: Fuel. 2013, vol. 111, pp. 555-63.
139. D. Quemada: Rheol. Acta. 1978, vol. 17, pp. 632-42.
140. M. Hirai, K. Takebayashi, Y. Yoshikawa and R. Yamaguchi: ISIJ int. 1993, vol. 33, pp. 405-12.
141. O. Melnik and R. Sparks: Nature. 1999, vol. 402, pp. 37-41.
142. A. Costa: Geophys. Res. Lett. 2005, vol. 32, p. L22308.
143. A. Costa, O. Melnik and R. Sparks: Earth. Planet. Sc. Lett. 2007, vol. 260, pp. 137-51.
144. A. Costa, O. Melnik, R. Sparks and B. Voight: Geophys. Res. Lett. 2007, vol. 34, p. L02303.
145. C. I. Mendoza and I. Santamaria-Holek: J. Chem. Phys. 2009, vol. 130, pp. 1-22.
146. B. Cordonnier, K. U. Hess, Y. Lavallee and D. B. Dingwell: Earth. Planet. Sc. Lett. 2009, vol. 279, pp. 263-72.
147. N. Frankel and A. Acrivos: Chem. Eng. Sci. 1967, vol. 22, pp. 847-53.
148. M. Doi and S. Edwards: The Theory of Polymer Dynamics, Clarendon Press, Oxford University 1986.
149. M. Sengun and R. Probstein: Rheol. Acta. 1989, vol. 28, pp. 394-401.
150. A. P. Shapiro and R. F. Probstein: Phys. Rev. Lett. 1992, vol. 68, pp. 1422-25.
151. M. Z. Sengun and R. F. Probstein: PhysicoChem. Hydrodyn. 1989, vol. 11, pp. 229-41.
152. H. Brouwers: Phys. Rev. E. 2010, vol. 81, p. 051402.
153. F. Boyer, É. Guazzelli and O. Pouliquen: Phys. Rev. Lett. 2011, vol. 107, p. 188301.
154. G. Scott and D. Kilgour: Journal of Physics D: Applied Physics. 1969, vol. 2, p. 863.
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Liu, Z., Pandelaers, L., Blanpain, B. et al. Viscosity of Heterogeneous Silicate Melts: A Review. Metall Mater Trans B 49, 2469–2486 (2018). https://doi.org/10.1007/s11663-018-1374-9
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DOI: https://doi.org/10.1007/s11663-018-1374-9