Solid–liquid phase change in planetary cores

Ludovic Huguet; Quentin Kriaa; Thierry Alboussière; Michael  Le Bars

doi:10.5802/crphys.216

Article de synthèse

Solid–liquid phase change in planetary cores
[Changement de phase dans les noyaux planétaires]

Ludovic Huguet ¹ ; Quentin Kriaa ² ; Thierry Alboussière ³ ; Michael Le Bars ⁴

¹ ISTerre, Université Grenoble Alpes, Université Savoie Mont Blanc, CNRS, IRD, Université Gustave Eiffel, 38000 Grenoble, France
² Physics of Fluids Group, Max Planck Center for Complex Fluid Dynamics, and J. M. Burgers Centre for Fluid Dynamics, University of Twente, P.O. Box 217, 7500AE Enschede, The Netherlands
³ Université de Lyon, ENSL, UCBL, UJM, CNRS, Laboratoire LGL-TPE, France
⁴ CNRS, Aix Marseille Univ, Centrale Marseille, IRPHE, Marseille, France

Comptes Rendus. Physique, Online first (2024), pp. 1-39.

Résumé
Abstract

Les phénomènes de cristallisation et de fusion se produisent dans divers contextes géophysiques à diverses échelles spatiales et temporelles. Ils prennent notamment place dans le noyau en fer des planètes telluriques et des lunes, où ils jouent un rôle primordial dans leur dynamique et dans la génération de leur champ magnétique. La cristallisation et la fusion se caractérisent par des écoulements multiphasiques complexes, des effets de flottabilité et une thermodynamique hors équilibre, difficilement accessibles à la modélisation théorique et aux simulations numériques. De plus, les profondeurs planétaires demeurent inaccessibles aux observations directes, et notre compréhension repose sur des données indirectes provenant de la sismologie, de la physique minérale, de la géochimie et du magnétisme. Par conséquent, les écoulements induits par un changement de phase dans les noyaux planétaires constituent un domaine de recherche à la fois passionnant et stimulant. Cet article donne un aperçu du rôle qu’ont les expériences de laboratoire en dynamique des fluides pour élucider des phénomènes de changement de phase solide-liquide se produisant à des milliers de kilomètres sous nos pieds ou dans d’autres planètes, ainsi que de leurs conséquences dynamiques. En établissant des parallèles avec la métallurgie, cet article navigue à travers toutes les échelles de la dynamique du changement de phase, des processus microscopiques (nucléation et cristallisation) à leurs conséquences macroscopiques (ségrégation solide-liquide et écoulements de grande échelle). Nous décrivons en détail les deux principaux régimes de solidification planétaire, descendant et ascendant, ainsi que la formation de couches de solides interconnectées (“mush”) ou dispersées (“slurry”) dans les diverses configurations pertinentes. Enfin, cette revue décrit les défis restants, notamment dans le cadre de missions spatiales en cours qui dévoileront sans aucun doute la diversité des régimes planétaires.

The ubiquitous phenomena of crystallization and melting occur in various geophysical contexts across many spatial and temporal scales. In particular, they take place in the iron core of terrestrial planets and moons, profoundly influencing their dynamics and magnetic field generation. Crystallization and melting entail intricate multiphase flows, buoyancy effects, and out-of-equilibrium thermodynamics, posing challenges for theoretical modeling and numerical simulations. Besides, due to the inaccessible nature of the planetary deep interior, our understanding relies on indirect data from seismology, mineral physics, geochemistry, and magnetism. Consequently, phase-change-driven flows in planetary cores constitute a compelling yet challenging area of research. This paper provides an overview of the role of laboratory fluid dynamics experiments in elucidating the solid–liquid phase change phenomena occurring thousands of kilometers beneath our feet and within other planetary depths, along with their dynamic repercussions. Drawing parallel with metallurgy, it navigates through all scales of phase change dynamics, from microscopic processes (nucleation and crystal growth) to macroscopic consequences (solid–liquid segregation and large-scale flows). The review delves into the two primary planetary solidification regimes, top-down and bottom-up, and elucidates the formation of mushy and/or slurry layers in the various relevant configurations. Additionally, it outlines remaining challenges, including insights from ongoing space missions poised to unveil the diverse planetary regimes.

Reçu le : 2024-04-15
Révisé le : 2024-10-10
Accepté le : 2024-10-11
Première publication : 2024-12-10

DOI : 10.5802/crphys.216

Keywords: Crystallization, Phase change, Two-phase flows, Planetary cores, Magnetic field
Mots-clés : Cristallisation, Changement de phase, Écoulements diphasiques, Noyaux planétaires, Champ magnétique

Affiliations des auteurs :

Ludovic Huguet ¹ ; Quentin Kriaa ² ; Thierry Alboussière ³ ; Michael Le Bars ⁴

¹ ISTerre, Université Grenoble Alpes, Université Savoie Mont Blanc, CNRS, IRD, Université Gustave Eiffel, 38000 Grenoble, France
² Physics of Fluids Group, Max Planck Center for Complex Fluid Dynamics, and J. M. Burgers Centre for Fluid Dynamics, University of Twente, P.O. Box 217, 7500AE Enschede, The Netherlands
³ Université de Lyon, ENSL, UCBL, UJM, CNRS, Laboratoire LGL-TPE, France
⁴ CNRS, Aix Marseille Univ, Centrale Marseille, IRPHE, Marseille, France

Licence :

CC-BY 4.0

Droits d'auteur : Les auteurs conservent leurs droits

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     title = {Solid{\textendash}liquid phase change in planetary cores},
     journal = {Comptes Rendus. Physique},
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Ludovic Huguet; Quentin Kriaa; Thierry Alboussière; Michael  Le Bars. Solid–liquid phase change in planetary cores. Comptes Rendus. Physique, Online first (2024), pp. 1-39. doi : 10.5802/crphys.216.

Bibliographie
Cité par

[1] U. Christensen; P. Olson; G. Glatzmaier Numerical modelling of the geodynamo: a systematic parameter study, Geophys. J. Int., Volume 138 (1999), pp. 393-409 | DOI

[2] M. Landeau; A. Fournier; H.-C. Nataf; D. Cébron; N. Schaeffer Sustaining Earth’s magnetic dynamo, Nat. Rev. Earth Environ., Volume 3 (2022) no. 4, pp. 255-269 | DOI

[3] R. R. Kerswell; W. V. R. Malkus Tidal instability as the source for Io’s magnetic signature, Geophys. Res. Lett., Volume 25 (1998) no. 5, pp. 603-606 | DOI

[4] M. Le Bars; M. A. Wieczorek; Ö. Karatekin; D. Cébron; M. Laneuville An impact-driven dynamo for the early Moon, Nature, Volume 479 (2011) no. 7372, pp. 215-218 | DOI

[5] C. A. Dwyer; D. J. Stevenson; F. Nimmo A long-lived lunar dynamo driven by continuous mechanical stirring, Nature, Volume 479 (2011) no. 7372, pp. 212-214 | DOI

[6] M. Le Bars; D. Cébron; P. Le Gal Flows driven by libration, precession, and tides, Annu. Rev. Fluid Mech., Volume 47 (2015) no. 1, pp. 163-193 | DOI

[7] M. Le Bars; A. Barik; F. Burmann; D. P. Lathrop; J. Noir; N. Schaeffer; S. A. Triana Fluid dynamics experiments for planetary interiors, Surv. Geophys., Volume 43 (2022) no. 1, pp. 229-261 | DOI

[8] D. Breuer; T. Rueckriemen; T. Spohn Iron snow, crystal floats, and inner-core growth: modes of core solidification and implications for dynamos in terrestrial planets and moons, Prog. Earth Planet. Sci., Volume 2 (2015) no. 1, 39 | DOI

[9] D. Breuer; T. Spohn; T. Van Hoolst; W. van Westrenen; S. Stanley; N. Rambaux Interiors of Earth-like planets and satellites of the solar system, Surv. Geophys., Volume 43 (2022) no. 1, pp. 177-226 | DOI

[10] J. C. E. Irving; S. Cottaar; V. Lekić Seismically determined elastic parameters for Earth’s outer core, Sci. Adv., Volume 4 (2018) no. 6, eaar2538 | DOI

[11] L. Waszek; J. Irving; T.-S. Pham; H. Tkalvcić Seismic insights into Earth’s core, Nat. Commun., Volume 14 (2023) no. 1, 6029 | DOI

[12] A. Deuss Heterogeneity and anisotropy of Earth’s inner core, Annu. Rev. Earth Planet. Sci., Volume 42 (2014) no. 1, pp. 103-126 | DOI

[13] R. C. Weber; P.-Y. Lin; E. J. Garnero; Q. Williams; P. Lognonne Seismic detection of the lunar core, Science, Volume 331 (2011) no. 6015, pp. 309-312 | DOI

[14] R. F. Garcia; J. Gagnepain-Beyneix; S. Chevrot; P. Lognonné Very preliminary reference Moon model, Phys. Earth Planet. Inter., Volume 188 (2011) no. 1, pp. 96-113 | DOI

[15] R. F. Garcia; A. Khan; M. Drilleau et al. Lunar seismology: An update on interior structure models, Space Sci. Rev., Volume 215 (2019), pp. 1-47 | DOI

[16] S. C. Stähler; A. Khan; W. B. Banerdt et al. Seismic detection of the martian core, Science, Volume 373 (2021) no. 6553, pp. 443-448 | DOI

[17] H. Samuel; M. Drilleau; A. Rivoldini et al. Geophysical evidence for an enriched molten silicate layer above Mars’s core, Nature, Volume 622 (2023) no. 7984, pp. 712-717 | DOI

[18] J. C. E. Irving; V. Lekić; C. Durán et al. First observations of core-transiting seismic phases on Mars, Proc. Natl. Acad. Sci. USA, Volume 120 (2023) no. 18, e2217090120 | DOI

[19] M. C. Flemings Solidification processing, Metall. Mater. Trans. B, Volume 5 (1974), pp. 2121-2134 | DOI

[20] W. Kurz; D. J. Fisher; M. Rappaz Fundamentals of Solidification, Trans Tech Publications, 2023 | DOI

[21] R. Deguen; T. Alboussière; D. Brito On the existence and structure of a mush at the inner core boundary of the Earth, Phys. Earth Planet Inter., Volume 164 (2007) no. 1, pp. 36-49 | DOI

[22] O. Lielausis; A. Mikelsons; E. Shcherbinin; Y. Gelfgat Electric currents in molten metals and their interaction with a magnetic field, Proceedings of the I.U.T.A.M. Symposium “Metallurgical Applications of MHD”, 1982, pp. 234-245

[23] T. Alboussière; R. Moreau; D. Camel Influence of a magnetic field on the solidification of metallic alloys, C. R. Acad. Sci. Paris, Volume 313 (1991), pp. 749-755 | DOI

[24] P. Lehmann; R. Moreau; D. Camel; R. Bolcato Modification of interdendritic convection in directional solidification by a uniform magnetic field, Acta Mater., Volume 46 (1998) no. 11, pp. 4067-4079 | DOI

[25] K. Hirose; S. Labrosse; J. Hernlund Composition and state of the core, Annu. Rev. Earth Planet. Sci., Volume 41 (2013), pp. 657-691 | DOI

[26] J. S. Knibbe; W. van Westrenen The thermal evolution of Mercury’s Fe–Si core, Earth Planet. Sci. Lett., Volume 482 (2018), pp. 147-159 | DOI

[27] G. Morard; C. Sanloup; G. Fiquet; M. Mezouar; N. Rey; R. Poloni; P. Beck Structure of eutectic Fe–FeS melts to pressures up to 17 GPa: implications for planetary cores, Earth Planet. Sci. Lett., Volume 263 (2007) no. 1–2, pp. 128-139 | DOI

[28] A. S. Buono; D. Walker The Fe-rich liquidus in the Fe–FeS system from 1 bar to 10 GPa, Geochim. Cosmochim. Acta, Volume 75 (2011) no. 8, pp. 2072-2087 | DOI

[29] A. L. Edgington; L. Vovcadlo; L. Stixrude; I. G. Wood; D. P. Dobson; E. Holmström The top-down crystallisation of Mercury’s core, Earth Planet. Sci. Lett., Volume 528 (2019), 115838 | DOI

[30] A. Pommier; V. Laurenz; C. J. Davies; D. J. Frost Melting phase relations in the Fe–S and Fe–SO systems at core conditions in small terrestrial bodies, Icarus, Volume 306 (2018), pp. 150-162 | DOI

[31] K. Hikosaka; S. Tagawa; K. Hirose; Y. Okuda; K. Oka; K. Umemoto; Y. Ohishi Melting phase relations in Fe–Si–H at high pressure and implications for Earth’s inner core crystallization, Sci. Rep., Volume 12 (2022) no. 1, 10000 | DOI

[32] J. Liu; J. Li Solidification of lunar core from melting experiments on the Fe–Ni–S system, Earth Planet. Sci. Lett., Volume 530 (2020), 115834 | DOI

[33] A. Pease; J. Li Liquidus determination of the Fe–S and (Fe, Ni)–S systems at 14 and 24 GPa: Implications for the Mercurian core, Earth Planet. Sci. Lett., Volume 599 (2022), 117865 | DOI

[34] D. Ikuta; E. Ohtani; N. Hirao Two-phase mixture of iron–nickel–silicon alloys in the Earth’s inner core, Commun. Earth Environ., Volume 2 (2021) no. 1, 225 | DOI

[35] T. Komabayashi; G. Pesce; R. Sinmyo et al. Phase relations in the system Fe–Ni–Si to 200 GPa and 3900 K and implications for Earth’s core, Earth Planet. Sci. Lett., Volume 512 (2019), pp. 83-88 | DOI

[36] Y. Shibazaki; H. Terasaki; E. Ohtani; R. Tateyama; K. Nishida; K. I. Funakoshi; Y. Higo High-pressure and high-temperature phase diagram for Fe0.9Ni0.1–H alloy, Phys. Earth Planet. Inter., Volume 228 (2014), pp. 192-201 (High-Pressure Research in Earth Science: Crust, Mantle, and Core) | DOI

[37] F. Nimmo 8.02—Energetics of the core, Treatise on Geophysics (G. Schubert, ed.), Elsevier, Oxford, 2015, pp. 27-55 | DOI

[38] S. J. Braginsky Structure of the F layer and reasons for convection in the Earth’s core, Doklady Akad. Nauk SSSR, Volume 149 (1963), pp. 8-10

[39] J. R. Lister; B. A. Buffett The strength and efficiency of thermal and compositional convection in the geodynamo, Phys. Earth Planet. Inter., Volume 91 (1995) no. 1–3, pp. 17-30 | DOI

[40] C. J. Davies; A. Pommier Iron snow in the Martian core?, Earth Planet. Sci. Lett., Volume 481 (2018), pp. 189-200 | DOI

[41] J. A. Jacobs The Earth’s inner core, Nature, Volume 172 (1953) no. 4372, pp. 297-298 | DOI

[42] S. A. Hauck; J. M. Aurnou; A. J. Dombard Sulfur’s impact on core evolution and magnetic field generation on Ganymede, J. Geophys. Res., Volume 111 (2006) no. E9, pp. 2156-2202 | DOI

[43] Y. Fei; C. M. Bertka; L. W. Finger High-pressure iron-sulfur compound, Fe3S2, and melting relations in the Fe–FeS system, Science, Volume 275 (1997) no. 5306, pp. 1621-1623 | DOI

[44] L. Chudinovskikh; R. Boehler Eutectic melting in the system Fe–S to 44 GPa, Earth Planet. Sci. Lett., Volume 257 (2007) no. 1, pp. 97-103 | DOI

[45] A. Rivoldini; T. Van Hoolst; O. Verhoeven; A. Mocquet; V. Dehant Geodesy constraints on the interior structure and composition of Mars, Icarus, Volume 213 (2011) no. 2, pp. 451-472 | DOI

[46] M. Dumberry; A. Rivoldini Mercury’s inner core size and core-crystallization regime, Icarus, Volume 248 (2015), pp. 254-268 | DOI

[47] T. Rückriemen; D. Breuer; T. Spohn The Fe snow regime in Ganymede’s core: a deep-seated dynamo below a stable snow zone, J. Geophys. Res. Planets, Volume 120 (2015), pp. 1095-1118 | DOI

[48] T. Rückriemen; D. Breuer; T. Spohn Top-down freezing in a Fe–FeS Core and Ganymede’s present-day magnetic field, Icarus, Volume 307 (2018), pp. 172-196 | DOI

[49] L. Huguet; J. A. Van Orman; S. A. Hauck; M. A. Willard Earth’s inner core nucleation paradox, Earth Planet. Sci. Lett., Volume 487 (2018), pp. 9-20 | DOI

[50] U. Svensson; A. Omstedt Simulation of supercooling and size distribution in frazil ice dynamics, Cold Reg. Sci. Technol., Volume 22 (1994) no. 3, pp. 221-233 | DOI

[51] L. Huguet; M. Le Bars; R. Deguen A laboratory model for iron snow in planetary cores, Geophys. Res. Lett., Volume 50 (2023) no. 24, e2023GL105697 | DOI

[52] D. Loper A nonequilibrium theory of a slurry, Continuum Mech. Thermodyn., Volume 4 (1992) no. 3, pp. 213-245 | DOI | Zbl

[53] F. Wilczyński; C. J. Davies; C. A. Jones A two-phase pure slurry model for planetary cores: one-dimensional solutions and implications for Earth’s F-layer, J. Fluid Mech., Volume 976 (2023), A5 | DOI

[54] U. R. Christensen Iron snow dynamo models for Ganymede, Icarus, Volume 247 (2015), pp. 248-259 | DOI

[55] J. W. Rutter; B. Chalmers A prismatic substructure formed during solidification of metals, Can. J. Phys., Volume 31 (1953) no. 1, pp. 15-39 | DOI

[56] W. W. Mullins; R. F. Sekerka Stability of a planar interface during solidification of a dilute binary alloy, J. Appl. Phys., Volume 35 (1964), pp. 444-451 | DOI

[57] H. Shimizu; J. P. Poirier; J. L. Le Mouël On crystallization at the inner core boundary, Phys. Earth Planet. Inter., Volume 151 (2005) no. 1, pp. 37-51 | DOI

[58] J. W. Christian The Theory of Transformations in Metals and Alloys, Elsevier, Newnes, 2002

[59] B. Chen; J. Li; S. A. Hauck II Non-ideal liquidus curve in the Fe–S system and Mercury’s snowing core, Geophys. Res. Lett., Volume 35 (2008) no. 7, L07201 | DOI

[60] S. Labrosse; J.-L. Poirier; J.-L. LeMouël The age of the inner core, Earth Planet. Sci. Lett., Volume 190 (2001), pp. 111-123 | DOI

[61] L. Huguet; T. Alboussière; M. I. Bergman; R. Deguen; S. Labrosse; G. Lesœur Structure of a mushy layer under hypergravity with implications for Earth’s inner core, Geophys. J. Int., Volume 204 (2016) no. 3, pp. 1729-1755 | DOI

[62] D. R. Fearn; D. E. Loper; P. H. Roberts Structure of the Earth’s inner core, Nature, Volume 292 (1981), pp. 232-233 | DOI

[63] J. Wong; C. J. Davies; C. A. Jones A regime diagram for the slurry F-layer at the base of Earth’s outer core, Earth Planet. Sci. Lett., Volume 560 (2021), 116791 | DOI

[64] P. H. Roberts; D. E. Loper Towards a theory of the structure and evolution of a dendrite layer, Stellar and Planetary Magnetism, Gordon & Breach Science Publishers Ltd, 1983 (ISBN-10: 0677164300, ISBN-13: 978-0677164304)

[65] H. Haack; E. R. D. Scott Asteroid core crystallization by inward dendritic growth, J. Geophys. Res., Volume 97 (1992) no. E9, pp. 14727-14734 | DOI

[66] N. L. Chabot; H. Haack Evolution of Asteroidal Cores, University of Arizona Press, 2006, pp. 747-771

[67] L. Huguet Cristallisation et convection sous hyper-gravité, PhD thesis, Ecole Normale Supérieure de Lyon (2014)

[68] K. Jackson; J. Hunt; D. Uhlmann; T. Seward On origin of equiaxed zone in castings, Trans. Metall. Soc. AIME, Volume 236 (1966) no. 2, pp. 149-158

[69] D. Turnbull Formation of crystal nuclei in liquid metals, J. Appl. Phys., Volume 21 (1950) no. 10, pp. 1022-1028 | DOI

[70] D. W. Gomersall; S. Y. Shiraishi; R. G. Ward Undercooling phenomena in liquid metal droplets, J. Aust. Inst. Metals, Volume 10 (1965) no. 3, pp. 220-222

[71] J. Schade; A. McLean; W. Miller Surface tension measurements on oscillating droplets of undercooled liquid metals and alloys, Undercooled Alloy Phases (E. W. Collings; C. C. Koch, eds.), The Metall. Soc. AIME, 1987, pp. 233-248

[72] F. C. Frank Supercooling of liquids, Proc. R. Soc. Lond. A., Volume 215 (1952) no. 1120, pp. 43-46 | DOI

[73] K. F. Kelton; G. W. Lee; A. K. Gangopadhyay; R. W. Hyers; T. J. Rathz; J. R. Rogers; M. B. Robinson; D. S. Robinson First X-ray scattering studies on electrostatically levitated metallic liquids: demonstrated influence of local icosahedral order on the nucleation barrier, Phys. Rev. Lett., Volume 90 (2003) no. 19, 195504 | DOI

[74] T. Schenk; D. Holland-Moritz; V. Simonet; R. Bellissent; D. M. Herlach Icosahedral short-range order in deeply undercooled metallic melts, Phys. Rev. Lett., Volume 89 (2002) no. 7, 075507 | DOI

[75] P. Ganesh; M. Widom Ab initio simulations of geometrical frustration in supercooled liquid Fe and Fe-based metallic glass, Phys. Rev. B, Volume 77 (2008) no. 1, 014205 | DOI

[76] M. Inui; K. Maruyama; Y. Kajihara; M. Nakada Icosahedral ordering in liquid iron studied via x-ray scattering and Monte Carlo simulations, Phys. Rev. B, Volume 80 (2009) no. 18, 180201 | DOI

[77] D. Shechtman; I. Blech; D. Gratias; J. W. Cahn Metallic phase with long-range orientational order and no translational symmetry, Phys. Rev. Lett., Volume 53 (1984) no. 20, 1951 | DOI

[78] D. Holland-Moritz; T. Schenk; V. Simonet; R. Bellissent; P. Convert; T. Hansen; D. M. Herlach Short-range order in undercooled metallic liquids, Mater. Sci. Eng.: A, Volume 375 (2004), pp. 98-103 | DOI

[79] R. Boehler; M. Ross 2.22—Properties of rocks and minerals, high-pressure melting, Treatise on Geophysics (G. Schubert, ed.), Elsevier, Oxford, 2015, pp. 573-582 | DOI

[80] G. Kurtuldu; P. Jarry; M. Rappaz Influence of Cr on the nucleation of primary Al and formation of twinned dendrites in Al–Zn–Cr alloys: Can icosahedral solid clusters play a role?, Acta Mater., Volume 61 (2013) no. 19, pp. 7098-7108 | DOI

[81] K. F. Kelton; A. K. Gangopadhyay; G. .W. Lee et al. X-ray and electrostatic levitation undercooling studies in Ti–Zr–Ni quasicrystal forming alloys, J. Non-Cryst. Solids, Volume 312 (2002), pp. 305-308 | DOI

[82] A. K. Gangopadhyay; M. E. Sellers; G. P. Bracker et al. Demonstration of the effect of stirring on nucleation from experiments on the International Space Station using the ISS-EML facility, NPJ Microgravity, Volume 7 (2021) no. 1, 31 | DOI

[83] D. M. Matson; L. Battezzati; P. K. Galenko et al. Electromagnetic levitation containerless processing of metallic materials in microgravity: rapid solidification, NPJ Microgravity, Volume 9 (2023) no. 1, 65 | DOI

[84] J. Li; Q. Wu; J. Li et al. Shock melting curve of iron: A consensus on the temperature at the Earth’s inner core boundary, Geophys. Res. Lett., Volume 47 (2020) no. 15, e2020GL087758 | DOI

[85] R. G. Kraus; R. J. Hemley; S. J. Ali et al. Measuring the melting curve of iron at super-Earth core conditions, Science, Volume 375 (2022) no. 6577, pp. 202-205 | DOI

[86] L. Huguet; S. A. Hauck; J. A. Van Orman; Z. Jing Implications of the homogeneous nucleation barrier for top-down crystallization in Mercury’s Core, Mercury: Current and Future Science of the Innermost Planet, Volume 2047, Lunar and Planetary Institute, 2018, p. 6101

[87] A. J. Wilson; D. Alfè; A. M. Walker; C. J. Davies Can homogeneous nucleation resolve the inner core nucleation paradox?, Earth Planet. Sci. Lett., Volume 614 (2023), 118176 | DOI

[88] A. J. Wilson; A. M. Walker; D. Alfè; C. J. Davies Probing the nucleation of iron in Earth’s core using molecular dynamics simulations of supercooled liquids, Phys. Rev. B, Volume 103 (2021) no. 21, 214113 | DOI

[89] Y. Sun; F. Zhang; M. I. Mendelev; R. M. Wentzcovitch; K.-M. Ho Two-step nucleation of the Earth’s inner core, Proc. Natl. Acad. Sci. USA, Volume 119 (2022) no. 2, e2113059119 | DOI

[90] C. J. Davies; M. Pozzo; D. Alfè Assessing the inner core nucleation paradox with atomic-scale simulations, Earth Planet. Sci. Lett., Volume 507 (2019), pp. 1-9 | DOI

[91] M. Lasbleis; M. Kervazo; G. Choblet The fate of liquids trapped during the earth’s inner core growth, Geophys. Res. Lett., Volume 47 (2020) no. 2, e2019GL085654 | DOI

[92] C. Beckermann; C. Y. Wang Multiphase/-scale modeling of alloy solidification, Annu. Rev. Heat Transfer, Volume 6 (1995), pp. 115-198 | DOI

[93] M. G. Worster Convection in mushy layers, Annu. Rev. Fluid Mech., Volume 29 (1997) no. 1, pp. 91-122 | DOI

[94] D. L. Feltham; N. Untersteiner; J. S. Wettlaufer; M. G. Worster Sea ice is a mushy layer, Geophys. Res. Lett., Volume 33 (2006) no. 14, L14501 | DOI

[95] S. M. Copley; A. F. Giamei; S. M. Johnson; M. F. Hornbecker The origin of freckles in unidirectionally solidified castings, Metall. Trans., Volume 1 (1970) no. 8, pp. 2193-2204 | DOI

[96] J. R. Sarazin; A. Hellawell Channel formation in Pb–Sb, Pb–Sn, and Pb–Sn–Sb alloy ingots and comparison with the system NH $_{4}$ Cl–H $_{2}$ O, Metall. Trans. A, Volume 19 (1988) no. 7, pp. 1861-1871 | DOI

[97] C. F. Chen; F. Chen Experimental study of directional solidification of aqueous ammonium chloride solution, J. Fluid Mech., Volume 227 (1991), pp. 567-586 | DOI

[98] S. Tait; C. Jaupart Compositional convection in a reactive crystalline mush and melt differentiation, J. Geophys. Res., Volume 97 (1992) no. B5, pp. 6735-6756 | DOI

[99] M. G. Worster; R. C. Kerr The transient behaviour of alloys solidified from below prior to the formation of chimneys, J. Fluid Mech., Volume 269 (1994), pp. 23-44 | DOI

[100] M. G. Worster; J. S. Wettlaufer Natural convection, solute trapping, and channel formation during solidification of saltwater, J. Phys. Chem. B, Volume 101 (1997) no. 32, pp. 6132-6136 | DOI

[101] M. I. Bergman; M. Macleod-Silberstein; M. Haskel; B. Chandler; N. Akpan A laboratory model for solidification of Earth’s core, Phys. Earth Planet. Inter., Volume 153 (2005) no. 1–3, pp. 150-164 (Studies of the Earth’s Deep Interior SEDI 2004) | DOI

[102] M. I. Bergman; D. R. Fearn; J. Bloxham; M. C. Shannon Convection and channel formation in solidifying Pb–Sn alloys, Metall. Mater. Trans. A, Volume 28 (1997) no. 3, pp. 859-866 | DOI

[103] D. E. Loper; P. H. Roberts A study of conditions at the inner core boundary of the Earth, Phys. Earth Planet. Inter., Volume 24 (1981) no. 4, pp. 302-307 | DOI

[104] M. G. Worster Instabilities of the liquid and mushy regions during solidification of alloys, J. Fluid Mech., Volume 237 (1992), pp. 649-669 | DOI | Zbl

[105] A. J. Wells; J. S. Wettlaufer; S. A. Orszag Maximal potential energy transport: A variational principle for solidification problems, Phys. Rev. Lett., Volume 105 (2010) no. 25, 254502 | DOI

[106] A. J. Wells; J. S. Wettlaufer; S. A. Orszag Brine fluxes from growing sea ice, Geophys. Res. Lett., Volume 38 (2011) no. 4, L04501 | DOI

[107] A. J. Wells; J. S. Wettlaufer; S. A. Orszag Nonlinear mushy-layer convection with chimneys: stability and optimal solute fluxes, J. Fluid Mech., Volume 716 (2013), pp. 203-227 | DOI | Zbl

[108] D. W. Jones; M. G. Worster Fluxes through steady chimneys in a mushy layer during binary alloy solidification, J. Fluid Mech., Volume 714 (2013), pp. 127-151 | DOI

[109] P. C. Carman Flow of Gases Through Porous Media, Academic Press, 1956

[110] T. Takaki; S. Sakane; M. Ohno; Y. Shibuta; T. Aoki Permeability prediction for flow normal to columnar solidification structures by large–scale simulations of phase–field and lattice Boltzmann methods, Acta Mater., Volume 164 (2019), pp. 237-249 | DOI

[111] M. G. Worster Natural convection in a mushy layer, J. Fluid Mech., Volume 224 (1991), pp. 335-359 | DOI | Zbl

[112] R. J. McDonald; J. D. Hunt Convective fluid motion within the interdendritic liquid of a casting, Metall. Mater. Trans. B, Volume 1 (1970) no. 6, pp. 1787-1788 | DOI

[113] K. H. Esbensen; V. F. Buchwald Planet(oid) core crystallisation and fractionation-evidence from the Agpalilik mass of the Cape York iron meteorite shower, Phys. Earth Planet. Inter., Volume 29 (1982) no. 3, pp. 218-232 | DOI

[114] M. I. Bergman; D. R. Fearn Chimneys on the Earth’s inner-outer core boundary?, Geophys. Res. Lett., Volume 21 (1994) no. 6, pp. 477-480 | DOI

[115] M. I. Bergman; D. R. Fearn; J. Bloxham Suppression of channel convection in solidifying Pb–Sn alloys via an applied magnetic field, Metall. Mater. Trans. A, Volume 30 (1999) no. 7, pp. 1809-1815 | DOI

[116] A. Hellawell; P. M. Herbert The development of preferred orientations during the freezing of metals and alloys, Proc. R. Soc. Lond.. Series A. Math. Phys. Sci., Volume 269 (1962) no. 1339, pp. 560-573 | DOI

[117] S. Corrsin Further generalization of Onsager’s cascade model for turbulent spectra, Phys. Fluids, Volume 7 (1964), pp. 1156-1159 | DOI

[118] S. Tateno; K. Hirose; Y. Ohishi; Y. Tatsumi The structure of iron in Earth’s inner core, Science, Volume 330 (2010) no. 6002, pp. 359-361 | DOI

[119] L. Vovcadlo; I. G. Wood; M. J. Gillan; J. Brodholt; D. P. Dobson; G. D. Price; D. Alfè The stability of bcc-Fe at high pressures and temperatures with respect to tetragonal strain, Phys. Earth Planet. Inter., Volume 170 (2008) no. 1–2, pp. 52-59 | DOI

[120] A. B. Belonoshko; T. Lukinov; J. Fu; J. Zhao; S. Davis; S. I. Simak Stabilization of body-centred cubic iron under inner-core conditions, Nat. Geosci., Volume 10 (2017) no. 4, pp. 312-316 | DOI

[121] M. I. Bergman; D. M. Cole; J. R. Jones Preferred crystal orientations due to melt convection during directional solidification, J. Geophys. Res.: Solid Earth, Volume 107 (2002) no. B9, ECV-6 | DOI

[122] M. I. Bergman Measurements of electric anisotropy due to solidification texturing and the implications for the Earth’s inner core, Nature, Volume 389 (1997) no. 6646, pp. 60-63 | DOI

[123] M. I. Bergman Estimates of the Earth’s inner core grain size, Geophys. Res. Lett., Volume 25 (1998) no. 10, pp. 1593-1596 | DOI

[124] I. Sumita; S. Yoshida; M. Kumazawa; Y. Hamano A model for sedimentary compaction of a viscous medium and its application to inner-core growth, Geophys. J. Int., Volume 124 (1996) no. 2, pp. 502-524 | DOI

[125] A. Scheinberg; L. T. Elkins-Tanton; G. Schubert; D. Bercovici Core solidification and dynamo evolution in a mantle-stripped planetesimal, J. Geophys. Res., Volume 121 (2016) no. 1, pp. 2-20 | DOI

[126] J. A. Neufeld; J. F. J. Bryson; F. Nimmo The top-down solidification of iron asteroids driving dynamo evolution, J. Geophys. Res., Volume 124 (2019) no. 5, pp. 1331-1356 | DOI

[127] F. Chen Stability analysis on convection in directional solidification of binary solutions (invited review paper), Proc.-Nat. Sci. Council Republic of Chin. Part a Phys. Sci. Eng., Volume 25 (2001) no. 2, pp. 71-83

[128] R. Deguen Dynamique de la cristallisation de la graine: expériences et modèles, PhD thesis, Université Joseph-Fourier-Grenoble I (2009)

[129] S. Anders; D. Noto; Y. Tasaka; S. Eckert Simultaneous optical measurement of temperature and velocity fields in solidifying liquids, Exp. Fluids, Volume 61 (2020), pp. 1-19 | DOI

[130] T. Campanella; C. Charbon; M. Rappaz Grain refinement induced by electromagnetic stirring: A dendrite fragmentation criterion, Metall. Mater. Trans. A, Volume 35 (2004), pp. 3201-3210 | DOI

[131] M. Stefan-Kharicha; A. Kharicha; M. Wu; A. Ludwig On the coupling mechanism of equiaxed crystal generation with the liquid flow driven by natural convection during solidification, Metall. Mater. Trans. A, Volume 49 (2018), pp. 1708-1724 | DOI

[132] S. Ritterbex; T. Tsuchiya Viscosity of hcp iron at Earth’s inner core conditions from density functional theory, Sci. Rep., Volume 10 (2020) no. 1, 6311 | DOI

[133] V. Regard; C. Faccenna; O. Bellier; J. Martinod Laboratory experiments of slab break-off and slab dip reversal: insight into the Alpine Oligocene reorganization, Terra Nova, Volume 20 (2008) no. 4, pp. 267-273 | DOI

[134] T. Duretz; S. M. Schmalholz; T. V. Gerya Dynamics of slab detachment, Geochem. Geophys. Geosyst., Volume 13 (2012) no. 3, Q03020 | DOI

[135] D. Bercovici; G. Schubert; Y. Ricard Abrupt tectonics and rapid slab detachment with grain damage, Proc. Natl. Acad. Sci. USA, Volume 112 (2015) no. 5, pp. 1287-1291 | DOI

[136] S. F. Daly; Cold Regions Research and Engineering Laboratory (U.S.) Frazil Ice Dynamics, 84, US Army Corps of Engineers, Cold Regions Research & Engineering Laboratory, 1984

[137] A. Souriau; G. Poupinet The velocity profile at the base of the liquid core from PKP(BC+Cdiff) data: An argument in favour of radial inhomogeneity, Geophys. Res. Lett., Volume 18 (1991) no. 11, pp. 2023-2026 | DOI

[138] T. Ohtaki; S. Kaneshima Independent estimate of velocity structure of Earth’s lowermost outer core beneath the northeast Pacific from PKiKP- PKPbc differential traveltime and dispersion in PKPbc, J. Geophys. Res.: Solid Earth, Volume 120 (2015) no. 11, pp. 7572-7586 | DOI

[139] A. M. Dziewonski; D. L. Anderson Preliminary reference Earth model, Phys. Earth Planet. Inter., Volume 25 (1981) no. 4, pp. 297-356 | DOI

[140] T. Alboussière; R. Deguen; M. Melzani Melting-induced stratification above the Earth’s inner core due to convective translation, Nature, Volume 466 (2010) no. 7307, pp. 744-747 | DOI

[141] M. Monnereau; M. Calvet; L. Margerin; A. Souriau Lopsided growth of Earth’s inner core, Science, Volume 328 (2010) no. 5981, pp. 1014-1017 | DOI

[142] D. Gubbins; B. Sreenivasan; J. Mound; S. Rost Melting of the Earth’s inner core, Nature, Volume 473 (2011) no. 7347, pp. 361-363 | DOI

[143] M. A. Hallworth; H. E. Huppert; A. W. Woods Crystallization and layering induced by heating a reactive porous medium, Geophys. Res. Lett., Volume 31 (2004) no. 13, L13605 | DOI

[144] M. A. Hallworth; H. E. Huppert; A. W. Woods Dissolution-driven convection in a reactive porous medium, J. Fluid Mech., Volume 535 (2005), pp. 255-285 | DOI | Zbl

[145] J. Yu; M. I. Bergman; L. Huguet; T. Alboussière Partial melting of a Pb–Sn mushy layer due to heating from above, and implications for regional melting of Earth’s directionally solidified inner core, Geophys. Res. Lett., Volume 42 (2015), pp. 7046-7053 | DOI

[146] F. Chen Formation of double-diffusive layers in the directional solidification of binary solution, J. Cryst. Growth, Volume 179 (1997) no. 1–2, pp. 277-286 | DOI

[147] H. M. Fritz; F. Mohammed; J. Yoo Lituya Bay landslide impact generated mega-tsunami 50 th Anniversary, Tsunami Science Four Years after the 2004 Indian Ocean Tsunami: Part II: Observation and Data Analysis, Birkhäuser, Basel, 2009, pp. 153-175 | DOI

[148] F. Necker; C. Härtel; L. Kleiser; E. Meiburg High-resolution simulations of particle-driven gravity currents, Int. J. Multiphase Flow, Volume 28 (2002) no. 2, pp. 279-300 | DOI | Zbl

[149] R. Ouillon; E. Meiburg; B. R. Sutherland Turbidity currents propagating down a slope into a stratified saline ambient fluid, Environ. Fluid Mech., Volume 19 (2019) no. 5, pp. 1143-1166 | DOI

[150] A. Köhler; J. N. McElwaine; B. Sovilla GEODAR data and the flow regimes of snow avalanches, J. Geophys. Res.: Earth Surf., Volume 123 (2018) no. 6, pp. 1272-1294 | DOI

[151] C. T. Crowe; J. D. Schwarzkopf; M. Sommerfeld; Y. Tsuji Multiphase Flows with Droplets and Particles, 2, CRC Press, Boca Raton, 2011 | DOI

[152] Q. Kriaa; B. Favier; M. Le Bars Two-way coupling Eulerian numerical simulations of particle clouds settling in a quiescent fluid, Phys. Rev. Fluids, Volume 8 (2023) no. 7, 074302 | DOI

[153] C. D. McConnochie; C. Cenedese; J. N. McElwaine Entrainment into particle-laden turbulent plumes, Phys. Rev. Fluids, Volume 6 (2021) no. 12, 123502 | DOI

[154] T. Zürner; C. Toupoint; D. De Souza; D. Mezouane; R. Monchaux Settling of localized particle plumes in a quiescent water tank, Phys. Rev. Fluids, Volume 8 (2023) no. 2, 024301 | DOI

[155] M. Dadonau; J. L. Partridge; P. F. Linden The effect of double diffusion on entrainment in turbulent plumes, J. Fluid Mech., Volume 884 (2020), A6 | DOI

[156] H. Rahimipour; D. Wilkinson Dynamic behaviour of particle clouds, 11th Australasian Fluid Mechanics Conference University of Tasmania, Hobart, Australia, 1992

[157] G. J. Ruggaber Dynamics of sediment clouds related to open-water sediment disposal, PhD thesis, MIT (2000)

[158] J. W. M. Bush; B. A. Thurber; F. Blanchette Particle clouds in homogeneous and stratified environments, J. Fluid Mech., Volume 489 (2003), pp. 29-54 | DOI | Zbl

[159] B. Zhao; A. W. K. Law; E. Eric Adams; D. Shao; Z. Huang Effect of air release height on the formation of sediment thermals in water, J. Hydraul. Res., Volume 50 (2012) no. 5, pp. 532-540 | DOI

[160] A. C. H. Lai; B. Zhao; A. W.-K. Law; E. E. Adams Two-phase modeling of sediment clouds, Environ. Fluid Mech., Volume 13 (2013) no. 5, pp. 435-463 | DOI

[161] M. Landeau; R. Deguen; P. Olson Experiments on the fragmentation of a buoyant liquid volume in another liquid, J. Fluid Mech., Volume 749 (2014), pp. 478-518 | DOI

[162] P. Peñas; O. R. Enríquez; J. Rodríguez-Rodríguez Bubble-laden thermals in supersaturated water, J. Fluid Mech., Volume 924 (2021), A31 | DOI

[163] Q. Kriaa; E. Subra; B. Favier; M. Le Bars Effects of particle size and background rotation on the settling of particle clouds, Phys. Rev. Fluids, Volume 7 (2022) no. 12, 124302 | DOI

[164] R. Deguen; P. Olson; P. Cardin Experiments on turbulent metal-silicate mixing in a magma ocean, Earth Planet. Sci. Lett., Volume 310 (2011) no. 3, pp. 303-313 | DOI

[165] G. Boffetta; A. Mazzino Incompressible Rayleigh–Taylor turbulence, Annu. Rev. Fluid Mech., Volume 49 (2017) no. 1, pp. 119-143 | DOI

[166] S. Carey Influence of convective sedimentation on the formation of widespread tephra fall layers in the deep sea, Geology, Volume 25 (1997) no. 9, pp. 839-842 | DOI

[167] A. Fries; J. Lemus; P. A. Jarvis; A. B. Clarke; J. C. Phillips; I. Manzella; C. Bonadonna The influence of particle concentration on the formation of settling-driven gravitational instabilities at the base of volcanic clouds, Front. Earth Sci., Volume 9 (2021), 640090 | DOI

[168] M. Mizukami; R. N. Parthasarathy; G. M. Faeth Particle-generated turbulence in homogeneous dilute dispersed flows, Int. J. Multiph. Flow, Volume 18 (1992) no. 3, pp. 397-412 | DOI | Zbl

[169] V. Manville; C. J. N. Wilson Vertical density currents: a review of their potential role in the deposition and interpretation of deep-sea ash layers, J. Geol. Soc., Volume 161 (2004) no. 6, pp. 947-958 | DOI

[170] S. Harada; T. Mitsui; K. Sato Particle-like and fluid-like settling of a stratified suspension, Eur. Phys. J. E, Volume 35 (2012) no. 1, 1 | DOI

[171] Y. Yamamoto; F. Hisataka; S. Harada Numerical simulation of concentration interface in stratified suspension: continuum–particle transition, Int. J. Multiph. Flow, Volume 73 (2015), pp. 71-79 | DOI

[172] R. Kimura Cell formation in the convective mixed layer, Fluid Dyn. Res., Volume 3 (1988) no. 1, pp. 395-399 | DOI

[173] E. Climent; J. Magnaudet Large-scale simulations of bubble-induced convection in a liquid layer, Phys. Rev. Lett., Volume 82 (1999) no. 24, pp. 4827-4830 | DOI

[174] Y. Mezui; M. Obligado; A. Cartellier Buoyancy-driven bubbly flows: scaling of velocities in bubble columns operated in the heterogeneous regime, J. Fluid Mech., Volume 952 (2022), A10 | DOI

[175] R. F. Mudde Gravity-driven bubbly flows, Annu. Rev. Fluid Mech., Volume 37 (2005) no. 1, pp. 393-423 | DOI

[176] K. Iga; R. Kimura Convection driven by collective buoyancy of microbubbles, Fluid Dyn. Res., Volume 39 (2007) no. 1, pp. 68-97 | DOI | Zbl

[177] C. Beckermann; C. Y. Wang Equiaxed dendritic solidification with convection: Part III. Comparisons with NH $_{4}$ Cl–H $_{2}$ O experiments, Metall. Mater. Trans. A, Volume 27 (1996) no. 9, pp. 2784-2795 | DOI

[178] A. Kharicha; M. Stefan-Kharicha; A. Ludwig; M. Wu Simultaneous observation of melt flow and motion of equiaxed crystals during solidification using a dual phase particle image velocimetry technique. Part I: Stage characterization of melt flow and equiaxed crystal motion, Metall. Mater. Trans. A, Volume 44 (2013), pp. 650-660 | DOI

[179] R. S. Rerko; H. C. de Groh; C. Beckermann Effect of melt convection and solid transport on macrosegregation and grain structure in equiaxed Al–Cu alloys, Mater. Sci. Eng.: A, Volume 347 (2003) no. 1–2, pp. 186-197 | DOI

[180] M. Wu; A. Ludwig Modeling equiaxed solidification with melt convection and grain sedimentation-I: Model description, Acta Mater., Volume 57 (2009) no. 19, pp. 5621-5631 | DOI

[181] C. Beckermann Modelling of macrosegregation: applications and future needs, Int. Mater. Rev., Volume 47 (2002) no. 5, pp. 243-261 | DOI

[182] S. Sakane; T. Takaki; M. Ohno; Y. Shibuta; T. Aoki Two-dimensional large-scale phase-field lattice Boltzmann simulation of polycrystalline equiaxed solidification with motion of a massive number of dendrites, Comput. Mater. Sci., Volume 178 (2020), 109639 | DOI

[183] N. Yamanaka; S. Sakane; T. Takaki Multi-phase-field lattice Boltzmann model for polycrystalline equiaxed solidification with motion, Comput. Mater. Sci., Volume 197 (2021), 110658 | DOI

[184] T. Takaki Large-scale phase-field simulations for dendrite growth: A review on current status and future perspective, IOP Conference Series: Materials Science and Engineering, Volume 1274, IOP Publishing, 2023 | DOI

[185] B. Appolaire; V. Albert; H. Combeau; G. Lesoult Experimental study of free growth of equiaxed NH4Cl crystals settling in undercooled NH $_{4}$ Cl–H $_{2}$ O melts, ISIJ Int., Volume 39 (1999) no. 3, pp. 263-270 | DOI

[186] A. Badillo; D. Ceynar; C. Beckermann Growth of equiaxed dendritic crystals settling in an undercooled melt, Part 1: Tip kinetics, J. Cryst. Growth, Volume 309 (2007) no. 2, pp. 197-215 | DOI

[187] A. Hellawell; S. Liu; S. Lu Dendrite fragmentation and the effects of fluid flow in castings, Jom, Volume 49 (1997) no. 3, pp. 18-20 | DOI

[188] A. Ludwig; M. Stefan-Kharicha; A. Kharicha; M. Wu Massive formation of equiaxed crystals by avalanches of mushy zone segments, Metall. Mater. Trans. A, Volume 48 (2017), pp. 2927-2931 | DOI

[189] S. Anders; D. Noto; M. Seilmayer; S. Eckert Spectral random masking: a novel dynamic masking technique for PIV in multiphase flows, Exp. Fluids, Volume 60 (2019), pp. 1-6 | DOI

[190] J. Wong; C. J. Davies; C. A. Jones A Boussinesq slurry model of the F-layer at the base of Earth’s outer core, Geophys. J. Int., Volume 214 (2018) no. 3, pp. 2236-2249 | DOI

[191] D. E. Loper; P. H. Roberts On the motion of an iron-alloy core containing a slurry: I. General theory, Geophys. Astrophys. Fluid Dyn., Volume 9 (1977) no. 1, pp. 289-321 | DOI

[192] P. Olson; M. Landeau; B. H. Hirsh Laboratory experiments on rain-driven convection: implications for planetary dynamos, Earth Planet. Sci. Lett., Volume 457 (2017), pp. 403-411 | DOI

[193] A. J. Wells; M. G. Worster Melting and dissolving of a vertical solid surface with laminar compositional convection, J. Fluid Mech., Volume 687 (2011), pp. 118-140 | DOI | Zbl

[194] L. Gagliardi; O. Pierre-Louis Thin film modeling of crystal dissolution and growth in confinement, Phys. Rev. E, Volume 97 (2018) no. 1, 012802 | arXiv | DOI

[195] B. Favier; J. Purseed; L. Duchemin Rayleigh–Bénard convection with a melting boundary, J. Fluid Mech., Volume 858 (2019), pp. 437-473 | DOI

[196] R. G. Rice; P. J. Jones Complete dissolution of spherical particles in free-fall, Chem. Eng. Sci., Volume 34 (1979) no. 6, pp. 847-852 | DOI

[197] R. G. Rice Transpiration effects in solids dissolution, Chem. Eng. Sci., Volume 37 (1982) no. 10, pp. 1465-1469 | DOI

[198] T. Elperin; A. Fominykh Mass and heat transfer during solid sphere dissolution in a non-uniform fluid flow, Heat Mass Transf., Volume 41 (2005) no. 5, pp. 442-448 | DOI

[199] R. G. Rice; D. D. Do Dissolution of a solid sphere in an unbounded, stagnant liquid, Chem. Eng. Sci., Volume 61 (2006) no. 2, pp. 775-778 | DOI

[200] L. Huguet; V. Barge-Zwick; M. Le Bars Dynamics of a reactive spherical particle falling in a linearly stratified fluid, Phys. Rev. Fluids, Volume 5 (2020) no. 11, 114803 | DOI

[201] J. Zhang; M. J. Mercier; J. Magnaudet Core mechanisms of drag enhancement on bodies settling in a stratified fluid, J. Fluid Mech., Volume 875 (2019), pp. 622-656 | DOI | Zbl

[202] N. He; Y. Cui; D. W. Q. Chin; T. Darnige; P. Claudin; B. Semin Sedimentation of a single soluble particle at low Reynolds and high Péclet numbers, Phys. Rev. Fluids, Volume 9 (2024) no. 4, 44502 | DOI

[203] Q. Kriaa Flows induced by the settling and phase change of particles: iron rain and iron snow in planetary interiors, PhD thesis, Aix-Marseille Universite (2023)

[204] R. C. Kerr Convective crystal dissolution, Contrib. Mineral. Petrol., Volume 121 (1995) no. 3, pp. 237-246 | DOI

[205] N. Magnan; T. Heinemann; H. N. Latter A physical picture for the acoustic resonant drag instability, Mont. Not. R. Astron. Soc., Volume 529 (2024) no. 1, pp. 688-701 | DOI

[206] V. F. Cormier Texture of the uppermost inner core from forward-and back-scattered seismic waves, Earth Planet. Sci. Lett., Volume 258 (2007) no. 3, pp. 442-453 | DOI

[207] V. F. Cormier; J. Attanayake Earth’s solid inner core: Seismic implications of freezing and melting, J. Earth Sci., Volume 24 (2013) no. 5, pp. 683-698 | DOI

[208] A. Lincot; P. Cardin; R. Deguen; S. Merkel Multiscale model of global inner-core anisotropy induced by hcp alloy plasticity, Geophys. Res. Lett., Volume 43 (2016) no. 3, pp. 1084-1091 | DOI

[209] M. I. Bergman; L. Giersch; M. Hinczewski; V. Izzo Elastic and attenuation anisotropy in directionally solidified (hcp) zinc, and the seismic anisotropy in the Earth’s inner core, Phys. Earth Planet. Inter., Volume 117 (2000) no. 1, pp. 139-151 | DOI

[210] D. Brito; D. Elbert; P. Olson Experimental crystallization of gallium: ultrasonic measurements of elastic anisotropy and implications for the inner core, Phys. Earth Planet. Inter., Volume 129 (2002) no. 3–4, pp. 325-346 | DOI

[211] R. Deguen Structure and dynamics of Earth’s inner core, Earth Planet. Sci. Lett., Volume 333 (2012), pp. 211-225 | DOI

[212] F. Guillard; P. Golshan; L. Shen; J. R. Valdes; I. Einav Dynamic patterns of compaction in brittle porous media, Nat. Phys., Volume 11 (2015) no. 10, pp. 835-838 | DOI

[213] C. David; T.-f. Wong; W. Zhu; J. Zhang Laboratory measurement of compaction-induced permeability change in porous rocks: Implications for the generation and maintenance of pore pressure excess in the crust, Pure Appl. Geophys., Volume 143 (1994), pp. 425-456 | DOI

[214] T. W. Barraclough; J. R. Blackford; S. Liebenstein; S. Sandfeld; T. J. Stratford; G. Weinländer; M. Zaiser Propagating compaction bands in confined compression of snow, Nat. Phys., Volume 13 (2017) no. 3, pp. 272-275 | DOI

[215] H. J. S. Fernando; R.-r. Chen; B. A. Ayotte Development of a point plume in the presence of background rotation, Phys. Fluids, Volume 10 (1998) no. 9, pp. 2369-2383 | DOI

[216] J. C. Goodman; G. C. Collins; J. Marshall; R. T. Pierrehumbert Hydrothermal plume dynamics on Europa: Implications for chaos formation, J. Geophys. Res., Volume 109 (2004) no. E3, E03008 | DOI

[217] D. Frank; J. R. Landel; S. B. Dalziel; P. F. Linden Anticyclonic precession of a plume in a rotating environment, Geophys. Res. Lett., Volume 44 (2017) no. 18, pp. 9400-9407 | DOI

[218] B. R. Sutherland; Y. Ma; M. R. Flynn et al. Plumes in rotating fluid and their transformation into tornados, J. Fluid Mech., Volume 924 (2021), A15 | Zbl

[219] D. Frank; J. R. Landel; S. B. Dalziel; P. F. Linden Effects of background rotation on the dynamics of multiphase plumes, J. Fluid Mech., Volume 915 (2021), A2 | DOI | Zbl

[220] B. A. Ayotte; H. J. S. Fernando The motion of a turbulent thermal in the presence of background rotation, J. Atmos. Sci., Volume 51 (1994) no. 13, pp. 1989-1994 | DOI

[221] K. R. Helfrich Thermals with background rotation and stratification, J. Fluid Mech., Volume 259 (1994), pp. 265-280 | DOI

[222] Q. Kriaa; M. Landeau; M. Le Bars Influence of planetary rotation on metal-silicate mixing and equilibration in a magma ocean, Phys. Earth Planet. Inter., Volume 352 (2024), 107168 | DOI

[223] D. Bercovici; E. Mulyukova Two-phase magnetohydrodynamics: Theory and applications to planetesimal cores, Phys. Earth Planet. Inter., Volume 300 (2020), 106432 | DOI

[224] K. Aujogue; A. Pothérat; I. Bates; F. Debray; B. Sreenivasan Little earth experiment: an instrument to model planetary cores, Rev. Sci. Instrum., Volume 87 (2016) no. 8, 084502 | DOI

[225] K. Aujogue; A. Pothérat; B. Sreenivasan; F. Debray Experimental study of the convection in a rotating tangent cylinder, J. Fluid Mech., Volume 843 (2018), pp. 355-381 | DOI

[226] J. S. Turner; I. H. Campbell Convection and mixing in magma chambers, Earth-Sci. Rev., Volume 23 (1986) no. 4, pp. 255-352 | DOI

[227] R. S. J. Sparks; H. E. Huppert; J. S. Turner The fluid dynamics of evolving magma chambers, Philos. Trans. R. Soc. Lond.. Ser. A, Math. Phys. Sci., Volume 310 (1997) no. 1514, pp. 511-534 | DOI

[228] M. B. Holness; R. Farr; J. A. Neufeld Crystal settling and convection in the Shiant Isles main sill, Contrib. Mineral. Petrol., Volume 172 (2017), 7 | DOI

[229] M. B. Holness; M. J. Stock; D. Geist Magma chambers versus mush zones: constraining the architecture of sub-volcanic plumbing systems from microstructural analysis of crystalline enclaves, Philos. Trans. R. Soc. A: Math. Phys. Eng. Sci., Volume 377 (2019) no. 2139, 20180006 | DOI

[230] O. Namur; M. C. S. Humphreys; M. B. Holness Crystallization of interstitial liquid and latent heat buffering in solidifying gabbros: skaergaard intrusion, greenland, J. Petrol., Volume 55 (2014) no. 7, pp. 1389-1427 | DOI

[231] J. Klein; S. P. Mueller; J. M. Castro The influence of crystal size distributions on the rheology of magmas: new insights from analog experiments, Geochem. Geophys. Geosyst., Volume 18 (2017) no. 11, pp. 4055-4073 | DOI

[232] M. A. Morales Maqueda; A. J. Willmott; N. R. T. Biggs Polynya dynamics: a review of observations and modeling, Rev. Geophys., Volume 42 (2004) no. 1, RG1004 | DOI

[233] S. Martin Frazil ice in rivers and oceans, Annu. Rev. Fluid Mech., Volume 13 (1981) no. 13, pp. 379-397 | DOI

[234] Y. Matsumura; K. I. Ohshima Lagrangian modelling of frazil ice in the ocean, Ann. Glaciol., Volume 56 (2015) no. 69, pp. 373-382 | DOI

[235] D. W. Rees Jones; A. J. Wells Frazil-ice growth rate and dynamics in mixed layers and sub-ice-shelf plumes, The Cryosphere, Volume 12 (2018) no. 1, pp. 25-38 | DOI

[236] A. Herman; M. Dojczman; K. Świszcz High-resolution simulations of interactions between surface ocean dynamics and frazil ice, The Cryosphere, Volume 14 (2020) no. 11, pp. 3707-3729 | DOI

[237] S. Ushio; M. Wakatsuchi A laboratory study on supercooling and frazil ice production processes in winter coastal polynyas, J. Geophys. Res.: Oceans, Volume 98 (1993) no. C11, pp. 20321-20328 | DOI

[238] M. Dubé; B. Turcotte; B. Morse Inner structure of anchor ice and ice dams in steep channels, Cold Reg. Sci. Technol., Volume 106–107 (2014), pp. 194-206 | DOI

[239] P. D. Barrette Understanding frazil ice: the contribution of laboratory studies, Cold Reg. Sci. Technol., Volume 189 (2021), 103334 | DOI

[240] S. S. Shy; R. E. Breidenthal Turbulent stratified interfaces, Phys. Fluids A: Fluid Dyn., Volume 3 (1991) no. 5, pp. 1278-1285 | DOI

[241] E. Kruger Dynamics of downdraughts and cold pools: an experimental and numerical study, PhD thesis, University of Cambridge (2020)

[242] G. Boffetta; A. Celani; F. D. Lillo; S. Musacchio The Eulerian description of dilute collisionless suspension, Europhys. Lett., Volume 78 (2007) no. 1, 14001 | DOI

[243] J. F. Reali; P. Garaud; A. Alsinan; E. Meiburg Layer formation in sedimentary fingering convection, J. Fluid Mech., Volume 816 (2017), pp. 268-305 | DOI | Zbl

[244] J. Lemus; A. Fries; P. A. Jarvis; C. Bonadonna; B. Chopard; J. Lätt Modelling settling-driven gravitational instabilities at the base of volcanic clouds using the lattice boltzmann method, Front. Earth Sci., Volume 9 (2021), 713175 | DOI

[245] Y.-J. Chou; Y.-C. Shao Numerical study of particle-induced Rayleigh–Taylor instability: effects of particle settling and entrainment, Phys. Fluids, Volume 28 (2016) no. 4, 043302 | DOI

[246] J. P. Mellado; B. Stevens; H. Schmidt; N. Peters Two-fluid formulation of the cloud-top mixing layer for direct numerical simulation, Theoret. Comput. Fluid Dyn., Volume 24 (2010) no. 6, pp. 511-536 | DOI | Zbl

[247] Y. Yamamoto Numerical simulation of concentration interface in stratified suspension: continuum–particle transition, Int. J. Multiphase Flow, Volume 73 (2015), pp. 71-79 | DOI

[248] J. P. Mellado Cloud-top entrainment in stratocumulus clouds, Annu. Rev. Fluid Mech., Volume 49 (2017) no. 49, pp. 145-169 | DOI | Zbl

[249] V. G. Levich Physicochemical Hydrodynamics, Prentice-Hall International Series in the Physical and Chemical Engineering Sciences, Prentice-Hall, Englewood Cliffs, NJ, 1962

[250] W. Q. Fu Radiative transfer, Atmospheric Science (J. M. Wallace; P. V. Hobbs, eds.), Academic Press, San Diego, 2006, pp. 113-152 | DOI

[251] H. R. Pruppacher; J. D. Klett Microphysics of Clouds and Precipitation, Atmospheric and Oceanographic Sciences Library, 18, Springer, Netherlands, Dordrecht, 2010 | DOI

[252] R. Wood Stratocumulus Clouds, Mon. Weather Rev., Volume 140 (2012) no. 8, pp. 2373-2423 | DOI

[253] M. Beniston Grand challenges in climate research, Front. Environ. Sci., Volume 1 (2013), 1 | DOI

[254] S. Malardel Atmospheric buoyancy-driven flows, Buoyancy-Driven Flows (C. Cenedese; E. P. Chassignet; J. Verron, eds.), Cambridge University Press, Cambridge, 2012, pp. 312-337 | DOI

[255] C. Muller; D. Yang; G. Craig et al. Spontaneous aggregation of convective storms, Annu. Rev. Fluid Mech., Volume 54 (2022) no. 1, pp. 133-157 | DOI

[256] D. J. Stevenson; E. E. Salpeter The phase diagram and transport properties for hydrogen-helium fluid planets, Astrophys. J. Suppl. Ser., Volume 35 (1977), pp. 221-237 | DOI

[257] N. Nettelmann; J. J. Fortney; K. Moore; C. Mankovich An Exploration of double diffusive convection in Jupiter as a result of Hydrogen–Helium phase separation, Mont. Not. R. Astron. Soc., Volume 447 (2015) no. 4, pp. 3422-3441 | DOI

[258] S. Markham; T. Guillot; C. Li Rainy downdrafts in abyssal atmospheres, Astron. Astrophys., Volume 674 (2023), A177 | DOI

[259] R. Hueso; T. Guillot; A. Sánchez-Lavega Convective storms and atmospheric vertical structure in Uranus and Neptune, Philos. Trans. R. Soc. A: Math. Phys. Eng. Sci., Volume 378 (2020) no. 2187, 20190476 | DOI

[260] T. Guillot; D. J. Stevenson; S. K. Atreya; S. J. Bolton; H. N. Becker Storms and the depletion of ammonia in Jupiter: I. Microphysics of “Mushballs”, J. Geophys. Res.: Planets, Volume 125 (2020) no. 8, e2020JE006403 | DOI

[261] V. Parmentier; A. P. Showman; Y. Lian 3D mixing in hot Jupiters atmospheres—I. Application to the day/night cold trap in HD 209458b, Astron. Astrophys., Volume 558 (2013), A91 | DOI

[262] C. Helling Exoplanet clouds, Annu. Rev. Earth Planet. Sci., Volume 47 (2019), pp. 583-606 | DOI

[263] M. S. Marley; A. S. Ackerman; J. N. Cuzzi; D. Kitzmann Clouds and hazes in exoplanet atmospheres, Comp. Climatol. Terr. planets, Volume 1 (2013), pp. 367-391 | DOI

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