2020
DOI: 10.1140/epjst/e2020-000045-2
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Non-axisymmetric growth of dendrite with arbitrary symmetry in two and three dimensions: sharp interface model vs phase-field model

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Cited by 15 publications
(18 citation statements)
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“…Note that expression (3.14) does not work for a three-dimensional crystal in the form of an elliptical paraboloid. In this case, a more general formula should be used [47].…”
Section: Thermo-solutal Dendritic Growth In An Undercooled Melt/solutionmentioning
confidence: 99%
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“…Note that expression (3.14) does not work for a three-dimensional crystal in the form of an elliptical paraboloid. In this case, a more general formula should be used [47].…”
Section: Thermo-solutal Dendritic Growth In An Undercooled Melt/solutionmentioning
confidence: 99%
“…The slight discrepancy between theory and modelling for a larger radius is explained by the fact that instead of the Ivantsov solutions for axisymmetric crystals, in this case, it is necessary to use the Horvey–Cahn solutions for non-axisymmetric ice crystals in the form of elliptical paraboloids [35,38].
Figure 5The tip radii in the basal (ρ6, solid line) and perpendicular (ρ2, dashed line) planes ( a ) and growth velocity ( b ) of a dendritic crystal according to the theory (expressions (3.11) and (4.18), lines) and phase-field simulations (symbols) for three-dimensional ice dendrites growing in pure water [47]. (Online version in colour.
…”
Section: A Behaviour Of the Main Functionsmentioning
confidence: 99%
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