TY - JOUR

T1 - Directional Crystallization in the Presence of a Mushy Layer with Applications to the Earth’s Inner Core Boundary

AU - Alexandrov, Dmitri V.

AU - Alexandrova, Irina V.

AU - Nikishina, Margarita A.

AU - Malygin, Alexey P.

AU - Toropova, Liubov V.

N1 - The present research work consists of theoretical and computational parts, which were supported by different financial sources. L.V.T. acknowledges the Russian Science Foundation (project no. 21-79-10012) for the derivation of analytical expressions, their interpretation, and analysis. M.A.N. acknowledges the financial support from the Russian Foundation for Basic Research (project number 20-07-00887) for the determination and calculations of material thermodynamic properties under investigation. D.V.A. and I.V.A. are grateful to the Ministry of Science and Higher Education of the Russian Federation (project no. FEUZ-2023-0022) for numerical simulations carried out on the basis of the theory developed.

PY - 2023

Y1 - 2023

N2 - We formulate the mathematical model of directional crystallization of a binary melt with a mushy layer (region) between purely solid and liquid phases. This model is complicated by melt convection and pressure-dependent phase transition temperature. Approximate analytical solutions to this nonlinear moving-boundary problem are constructed. Namely, the concentration of impurity, fraction of solid phase, mushy region thickness, average fluid velocity, primary interdendritic spacing, mean radius of a chimney, and a characteristic distance between chimneys in a mushy region are found. Using this analytical solution, we describe the mushy region structure near the inner core boundary of the Earth, which is consistent with computer simulations and estimates existing in recent literature. A scheme illustrating the mushy region arrangement with chimneys at the inner core boundary of the Earth is presented. This arrangement based on the developed theory represents the novelty and importance of our study.

AB - We formulate the mathematical model of directional crystallization of a binary melt with a mushy layer (region) between purely solid and liquid phases. This model is complicated by melt convection and pressure-dependent phase transition temperature. Approximate analytical solutions to this nonlinear moving-boundary problem are constructed. Namely, the concentration of impurity, fraction of solid phase, mushy region thickness, average fluid velocity, primary interdendritic spacing, mean radius of a chimney, and a characteristic distance between chimneys in a mushy region are found. Using this analytical solution, we describe the mushy region structure near the inner core boundary of the Earth, which is consistent with computer simulations and estimates existing in recent literature. A scheme illustrating the mushy region arrangement with chimneys at the inner core boundary of the Earth is presented. This arrangement based on the developed theory represents the novelty and importance of our study.

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U2 - 10.3390/cryst13091361

DO - 10.3390/cryst13091361

M3 - Article

VL - 13

JO - Crystals

JF - Crystals

SN - 2073-4352

IS - 9

M1 - 1361

ER -