The boundary integral theory for slow and rapid curved solid/liquid interfaces propagating into binary systems

Philosophical Transactions. Series A, Mathematical, Physical, and Engineering Sciences
Peter K GalenkoEkaterina A Titova

Abstract

The boundary integral method for propagating solid/liquid interfaces is detailed with allowance for the thermo-solutal Stefan-type models. Two types of mass transfer mechanisms corresponding to the local equilibrium (parabolic-type equation) and local non-equilibrium (hyperbolic-type equation) solidification conditions are considered. A unified integro-differential equation for the curved interface is derived. This equation contains the steady-state conditions of solidification as a special case. The boundary integral analysis demonstrates how to derive the quasi-stationary Ivantsov and Horvay-Cahn solutions that, respectively, define the paraboloidal and elliptical crystal shapes. In the limit of highest Péclet numbers, these quasi-stationary solutions describe the shape of the area around the dendritic tip in the form of a smooth sphere in the isotropic case and a deformed sphere along the directions of anisotropy strength in the anisotropic case. A thermo-solutal selection criterion of the quasi-stationary growth mode of dendrites which includes arbitrary Péclet numbers is obtained. To demonstrate the selection of patterns, computational modelling of the quasi-stationary growth of crystals in a binary mixture is carried out....Continue Reading

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Jan 10, 2018·Philosophical Transactions. Series A, Mathematical, Physical, and Engineering Sciences·Dmitri V AlexandrovIrina V Alexandrova
Jan 10, 2018·Philosophical Transactions. Series A, Mathematical, Physical, and Engineering Sciences·Eugenya V Makoveeva, Dmitri V Alexandrov

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Citations

Jan 10, 2018·Philosophical Transactions. Series A, Mathematical, Physical, and Engineering Sciences·P K Galenko, D V Alexandrov
Jan 10, 2018·Philosophical Transactions. Series A, Mathematical, Physical, and Engineering Sciences·Dmitri V AlexandrovLyubov V Toropova
Apr 14, 2020·Philosophical Transactions. Series A, Mathematical, Physical, and Engineering Sciences·Irina G Nizovtseva, Dmitri V Alexandrov
Apr 14, 2020·Philosophical Transactions. Series A, Mathematical, Physical, and Engineering Sciences·Dmitri V Alexandrov, Andrey Yu Zubarev
Apr 14, 2020·Philosophical Transactions. Series A, Mathematical, Physical, and Engineering Sciences·Dmitri V Alexandrov, Peter K Galenko
Jun 24, 2021·Journal of Physics. Condensed Matter : an Institute of Physics Journal·L V ToropovaG Demange
Jul 20, 2021·Philosophical Transactions. Series A, Mathematical, Physical, and Engineering Sciences·Dmitri V AlexandrovMarkus Rettenmayr
Jul 20, 2021·Philosophical Transactions. Series A, Mathematical, Physical, and Engineering Sciences·Dmitri V Alexandrov, Peter K Galenko
Jul 20, 2021·Philosophical Transactions. Series A, Mathematical, Physical, and Engineering Sciences·Dmitri V Alexandrov, Andrey Yu Zubarev
Jul 20, 2021·Philosophical Transactions. Series A, Mathematical, Physical, and Engineering Sciences·Eugenya V Makoveeva, Dmitri V Alexandrov
Aug 4, 2021·Journal of Physics. Condensed Matter : an Institute of Physics Journal·D V AlexandrovL V Toropova
Sep 26, 2018··E. A. Titova, E. A. Titova
Apr 2, 2020··Irina V. RakhmatullinaDmitri V. Alexandrov
Dec 7, 2019··L. V. Toropova, L. V. Toropova
Dec 9, 2020··Ilya O. StarodumovIrina G. Nizovtseva

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