ReviewPhilosophical transactions. Series A, Mathematical, physical, and engineering sciences2018
The boundary integral theory for slow and rapid curved solid/liquid interfaces propagating into binary systems.
Review in Philosophical transactions. Series A, Mathematical, physical, and engineering sciences, 2018. The graph could read no effect estimate from its abstract, so it casts no vote on the map. Cited by 5 papers.
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5 citing papers in PubMed.
- The effect of density changes on crystallization with a mushy layer.Philosophical transactions. Series A, Mathematical, physical, and engineering sciences · 2020Article
- The shape of dendritic tips.Philosophical transactions. Series A, Mathematical, physical, and engineering sciences · 2020Article
- Patterns in soft and biological matters.Philosophical transactions. Series A, Mathematical, physical, and engineering sciences · 2020Article
- Thermo-solutal and kinetic modes of stable dendritic growth with different symmetries of crystalline anisotropy in the presence of convection.Philosophical transactions. Series A, Mathematical, physical, and engineering sciences · 2018Review
- From atomistic interfaces to dendritic patterns.Philosophical transactions. Series A, Mathematical, physical, and engineering sciences · 2018Article
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3 authors.
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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. The modelling makes it possible to obtain selected structures in the form of dendritic, fractal or planar crystals.This article is part of the theme issue 'From atomistic interfaces to dendritic patterns'.
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