Coupled convective and morphological instability of the inner core boundary of the Earth

Physics of the Earth and Planetary Interiors

Volumn 189, Issue 3-4, 2011, Pages 134-141

  Alexandrov, D V ^a   Malygin, A P ^a  

^a URAL FEDERAL UNIVERSITY   (Russian Federation)

Author keywords

Constitutional supercooling; Inner core boundary; Morphological instability; Mushy layer; Nucleation; Slurry layer

Indexed keywords

ANALYTICAL SOLUTIONS; CONSTITUTIONAL SUPERCOOLING; CONVECTIVE HEAT; CONVECTIVE MOTIONS; INNER CORE; INNER CORE BOUNDARY; LAYER THEORY; LINEAR THEORY; LIQUID PHASE; MORPHOLOGICAL INSTABILITY; MORPHOLOGICAL STABILITY; MOVING BOUNDARIES; MUSHY LAYER; NON-LINEAR MODEL; SOLID-LIQUID INTERFACES; SOLIDIFICATION CONDITION;

LIQUIDS; MASS TRANSFER; NUCLEATION; PHASE INTERFACES; SOLIDIFICATION; STABILITY CRITERIA; SUPERCOOLING;

EARTH (PLANET);

CRYSTALLIZATION; EARTH; HEAT TRANSFER; INNER CORE; MASS TRANSFER; NUCLEATION; NUMERICAL MODEL; PHASE TRANSITION; SOLIDIFICATION; SUPERCOOLING; THERMAL CONVECTION;

EID: 82355173274     PISSN: 00319201     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.pepi.2011.08.004     Document Type: Article

References (47)

1. Alexandrov D.V. Solidification with a quasiequilibrium mushy region: exact analytical solution of nonlinear model. J. Cryst. Growth. 2001, 222:816-821.
2. Alexandrov D.V. Solidification with a quasiequilibrium two-phase zone. Acta Mater. 2001, 49:759-764.
3. Alexandrov D.V., Malygin A.P. Convective instability of directional crystallization in a forced flow: the role of brine channels in a mushy layer on nonlinear dynamics of binary systems. Int. J. Heat Mass Trans. 2011, 54:1144-1149.
4. Alexandrov D.V., Malygin A.P., Alexandrova I.V. Solidification of leads: approximate solutions of non-linear problem. Ann. Glaciol. 2006, 44:118-122.
5. Alexandrov D.V., Nizovtseva I.G. To the theory of underwater ice evolution, or nonlinear dynamics of false bottoms. Int. J. Heat Mass Trans. 2008, 51:5204-5208.
6. Alexandrov D.V., Nizovtseva I.G., Lee D., Huang H.-N. Solidification from a cooled boundary with a mushy layer under conditions of nonturbulent and turbulent heat and mass transfer in the ocean. Int. J. Fluid Mech. Res. 2010, 37:1-14.
7. Alfe D., Gillan M.J., Price G.D. Composition and temperature of the Earth's core constrained by ab initio calculations and seismic data. Earth Planet. Sci. Lett. 2002, 195:91-98.
8. Anderson W., Ahrens T. An equation of state for liquid iron and implications for the Earth's core. J. Geophys. Res. 1994, 99:4273-4284.
9. Aseev D.L., Alexandrov D.V. Directional solidification of binary melts with a non-equilibrium mushy layer. Int. J. Heat Mass Trans. 2006, 49:4903-4909.
10. Aseev D.L., Alexandrov D.V. Nonlinear dynamics for the solidification of binary melt with a nonequilibrium two-phase zone. Physics-Doklady 2006, 51:291-295.
11. Aseev D.L., Alexandrov D.V. Unidirectional solidification with a mushy layer. The influence of weak convection. Acta Mater. 2006, 54:2401-2406.
12. Batchelor G.K. Transport properties of two-phase materials with random structure. Annu. Rev. Fluid Mech. 1974, 6:227-255.
13. Bloxham J., Jackson A. Fluid flow near the surface of Earth's outer core. Rev. Geophys. 1991, 29:97-120.
14. Boehler R. Temperatures in the Earth's core from melting-point measurements of iron at high static pressures. Nature 1993, 363:534-536.
15. Borisov V.T. Theory of Two-phase (Mushy) Zone of a Metal Ingot 1987, Metallurgiya Publishing House, Moscow.
16. Braginsky S. Structure of the F layer and reasons for convection in the Earth's core. Dokl. Akad. Nauk SSSR Engl. Trans. 1963, 149:1311-1314.
17. Buffett B.A. Earth's core and the geodynamo. Science 2000, 288:2007-2012.
18. Buyevich Yu.A., Alexandrov D.V., Mansurov V.V. Macrokinetics of Crystallization 2001, Begell House Inc., New York.
19. Chernov A.A., Givargizov Ye.I., Bagdasarov Kh.S. Modern Crystallography. Crystallization Processes, vol. 3 1990, Nauka Publishing House, Moscow.
20. Deguen R., Alboussière T., Brito D. On the existence and structure of a mush at the inner core boundary of the Earth. Phys. Earth Planet. Int. 2007, 164:36-49.
21. Editorial Studies of the Earth's deep interior - eighth symposium. Phys. Earth Planet. Inter. 2005, 153:1-2.
22. Fearn D.R., Loper D.E., Roberts P.H. Structure of the Earth's inner core. Nature 1981, 292:232-233.
23. Fedoryuk M.V. Asymptotics, Integrals and Series 1987, Nauka Publishing House, Moscow.
24. Flemings M.C. Solidification Processing 1974, McGrow Hill Book Company, New York.
25. Frenkel J. Kinetic theory of liquids 1955, Dover, New York.
26. Hills R.N., Loper D.E., Roberts P.H. A thermodynamically consistent model of a mushy zone. Quart. J. Mech. Appl. Math. 1983, 36:505-539.
27. Huppert H.E., Worster M.G. Vigorous motions in magma chambers and lava lakes. Chaotic Processes in the Geological Sciences 1992, vol. 41:141-173. Springer-Verlag, New York.
28. Ivantsov G.P. Diffusion supercooling in crystallization of a binary mixture. Dokl. Akad. Nauk SSSR. 1947, 81:179-182.
29. Kerr R.C., Woods A.W., Worster M.G., Huppert H.E. Solidification of an alloy cooled from above. Part 1. Equilibrium growth. J. Fluid Mech. 1990, 216:323-342.
30. Loper D.E., Roberts P.H. On the motion of an iron-alloy core containing a slurry. Geophys. Astrophys. Fluid Dyn. 1978, 9:289-321.
31. Loper D.E., Roberts P.H. A study of conditions at the inner core boundary of the Earth's. Phys. Earth Planet. Int. 1981, 24:302-307.
32. Loper D.E. Structure of the inner core boundary. Geophys. Astrophys. Fluid Dyn. 1983, 25:139-155.
33. Loper D.E. Dynamo energetics and the structure of the outer core. Geophys. Astrophys. Fluid Dyn. 1989, 49:213-219.
34. Loper D.E. A model of the dynamical structure of Earth's outer core. Phys. Earth Planet. Int. 2000, 117:179-196.
35. Makkonen L. Solid fraction in dendritic solidification of a liquid. Appl. Phys. Lett. 2010, 96:091910-1-091910-3.
36. Morse S.A. Adcumulus growth of the inner core. Geophys. Res. Lett. 1986, 13:1466-1469.
37. Morse S.A. No mushy zones in the Earth's core. Geochim. Cosmochim. Acta 2002, 66:2155-2165.
38. Mullins W.W., Sekerka R.F. Stability of a planar interface during solidification of a dilute binary alloy. J. Appl. Phys. 1964, 35:444-451.
39. Nayfen A.H. Introduction to perturbation techniques 1981, Wiley-Interscience Publication, New York, Chichester, Brisbane, Toronto.
40. Raghavan, V., 1988. Phase Diagrams of Ternary Iron Alloys. The Indian Institute of Metals, Calcutta, 379 pp.
41. Scheil E. Bemerkungen zur schichtkiistallbildung. Z. Metalld. 1942, 34:70-72.
42. Shimizu H., Poirier J.P., Le Mouël J.L. On crystallization at the inner core boundary. Phys. Earth Planet. Int. 2005, 151:37-51.
43. Stacey F.D., Anderson O.L. Electrical and thermal conductivities of Fe-Ni-Si alloy under core conditions. Phys. Earth Planet. Int. 2001, 124:153-162.
44. Stefan J. Über die theorie der eisbildung, insbesondere über die eisbildung im polarmeere. Ann. Phys. Chem. 1891, 42:269-286.
45. Worster M.G. Solidification of an alloy from a cooled boundary. J. Fluid Mech. 1986, 167:481-501.
46. Worster M.G. Natural convection in a mushy layer. J. Fluid Mech. 1991, 224:335-359.
47. Zeldovich Ya.B. On the theory of formation of a new phase. Cavitation. Zh. Eksperiment. Tekhnich. Fiz. 1942, 12:525-536.