Abstract
In order to get a deeper physical insight into the problem of directional solidification, which is a common feature both for the materials processing and crystal growth, the analytical description of the non-linear model was provided for the case of the binary solutions with a mushy layer. Both convective and conductive conditions of the liquid phase were considered, the Stefan-type model was adjusted for the nonstationary case, the validation of the models prediction was given through the comparison of analytical data and field experiment for the behavior of phase transition interfaces between the pure ice and mushy layer and the liquid phase and mushy layer.
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References
A.M. Meirmanov, in The Stefan problem (W. De Gruyter Expositions in Mathematics, Berlin, 1992), p. 244
N.A. Avdonin, in Mathematical description of crystallization processes (Zinatne Publishing House, Riga, 1980), p. 176
M.V. Koyalo, in Problems of the theory of crystallization, Latvian Univ. Publishing House, Riga, 1974), pp. 56–75
G.P. Ivantsov, Dokl. Akad. Nauk SSSR 81, 179 (1951)
V.T. Borisov, in Theory of the two-phase zone of a metal ingot (Metallurgia Publishing House, Moscow, 1987), p. 222
D.V. Alexandrov, I.G. Nizovtseva, I.V. Alexandrova, Int. J. Heat Mass Transfer 128, 46 (2019)
R.N. Hills, D.E. Loper, P.H. Roberts, Q. J. Appl. Math. 36, 505 (1983)
M.G. Worster, J. Fluid Mech. 167, 481 (1986)
YuA Buyevich, D.V. Alexandrov, V.V. Mansurov, in Macrokinetics of crystallization (New York and Wallingford, Begell House, 2001), p. 183.
A.C. Fowler, IMA J. Appl. Math. 35, 159 (1985)
D.V. Alexandrov, J. Crystal Growth 222, 816 (2001)
D.V. Alexandrov, Acta Mater. 49, 759 (2001)
D.V. Alexandrov, D.L. Aseev, J. Fluid Mech. 527, 57 (2005)
D.L. Aseev, D.V. Alexandrov, Acta Mater. 54, 2401 (2006)
D.V. Alexandrov, A.P. Malygin, I.V. Alexandrova, Ann. Glaciol. 44, 118 (2006)
D.V. Alexandrov, A.P. Malygin, Int. J. Heat Mass Transfer 49, 763 (2006)
D.V. Alexandrov, A.P. Malygin, Dokl. Earth Sci. 411A, 1407 (2006)
D.V. Alexandrov, D.L. Aseev, I.G. Nizovtseva, H.-N. Huang, D. Lee, Int. J. Heat Mass Transfer 50, 3616 (2007)
J. Morison, M. McPhee, R. Muench, EOS. Trans. AGU 74, 393 (1993)
J.S. Wettlaufer, M.G. Worster, H.E. Huppert, J. Geophys. Res. 105, 1123 (2000)
S. Martin, P. Kauffman, J. Fluid Mech. 64, 507 (1974)
D.V. Alexandrov, I.G. Nizovtseva, Int. J. Heat Mass Transfer 51, 5204 (2008)
D.V. Alexandrov, YuA Buyevich, V.V. Mansurov, P.N. Vabishchevich, A.G. Churbanov, Proceedings of Saint-Venant Symposium (1997) 529–534.
G.K. Batchelor, Ann. Rev. Fluid Mech. 6, 227 (1974)
YuA Buyevich, D.V. Alexandrov, Heat transfer in dispersions (Begell House, Connecticut, 2005)
D.K. Perovich, A.J. Gow, J. Geophys. Res. 101, 18327 (1996)
H.E. Huppert, M.G. Worster, Nature 314, 703 (1985)
M.G. McPhee, in The geophysics of sea ice (Plenum, New York, 1986), pp. 133–141
M.G. McPhee, J. Geophys. Res. 92, 6987 (1987)
M.G. McPhee, G.A. Maykut, J.H. Morison, J. Geophys. Res. 92, 7017 (1987)
D. Notz, M.G. McPhee, M.G. Worster, G.A. Maykut, K.H. Schlünzen, H. Eicken, J. Geophys. Res. 108, 322316 (2003)
I.G. Nizovtseva, P.K. Galenko, Philos. Trans. R. Soc. A 376, 20170202 (2018)
P.R. Owen, W.R. Thomson, J. Fluid Mech. 15, 321 (1963)
A.M. Yaglom, B.A. Kader, J. Fluid Mech. 62, 601 (1974)
D.V. Alexandrov, P.K. Galenko, L.V. Toropova, Philos. Trans. R. Soc. A 376, 20170215 (2018)
P.K. Galenko, D.V. Alexandrov, E.A. Titova, Philos. Trans. R. Soc. A 376, 20170218 (2018)
E.V. Makoveeva, D.V. Alexandrov, Philos. Trans. R. Soc. A 37620170327 (2018)
D.V. Alexandrov, A.A. Ivanov, I.V. Alexandrova, Philos. Trans. R. Soc. A 376, 20170217 (2018)
D.V. Alexandrov, I.A. Bashkirtseva, L.B. Ryashko, Philos. Trans. R. Soc. A 376, 20170216 (2018)
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Nizovtseva, I.G. On the theory of non-stationary directional solidification with a phase transition layer. Eur. Phys. J. Spec. Top. 229, 405–416 (2020). https://doi.org/10.1140/epjst/e2019-900145-8
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DOI: https://doi.org/10.1140/epjst/e2019-900145-8