The boundary integral equation describing a curvilinear solid/liquid interface with nonlinear phase transition temperature

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The boundary integral equation describing a curvilinear solid/liquid interface with nonlinear phase transition temperature. / Titova, E.; Ivanov, A.; Toropova, L.
в: Mathematical Methods in the Applied Sciences, Том 47, № 8, 30.05.2024, стр. 6842-6852.

Результаты исследований: Вклад в журнал › Материалы конференции › Рецензирование

BibTeX

@article{bc2f719bec454e349ff4aca6d603a124,

title = "The boundary integral equation describing a curvilinear solid/liquid interface with nonlinear phase transition temperature",

abstract = "The boundary integral equation (BIE) describes the dynamics of a curved crystallization front separating liquid melt and solid material. We derive a generalized BIE for the thermal-concentration problem taking into account the nonlinear dependence of the crystallization temperature on solute concentration and the kinetics of atomic attachment at the interface. This equation determines the evolution of the interface function and the equation for crystallization driving force - the melt undercooling at the crystal surface. Our calculations carried out for a dendritic vertex in the form of a paraboloid of revolution have shown that the growth rate of the dendritic tip and its diameter substantially depend on the nonlinear effects under study. In particular, the velocity and diameter of the dendrite tip respectively become greater and narrower with increasing deviation of the liquidus equation from the linear relationship. Also, the dendrite tip velocity can be significantly affected by variations in the exponent of atomic kinetics.",

author = "E. Titova and A. Ivanov and L. Toropova",

note = "Ministry of Science and Higher Education of the Russian Federation (project 075‐02‐2023‐935 for the “Ural Mathematical Center”); Foundation for the Advancement of Theoretical Physics and Mathematics “BASIS”: 21‐1‐3‐11‐1. Funding information",

year = "2024",

month = may,

day = "30",

doi = "10.1002/mma.9520",

language = "English",

volume = "47",

pages = "6842--6852",

journal = "Mathematical Methods in the Applied Sciences",

issn = "0170-4214",

publisher = "John Wiley & Sons Inc.",

number = "8",

}

RIS

TY - JOUR

T1 - The boundary integral equation describing a curvilinear solid/liquid interface with nonlinear phase transition temperature

AU - Titova, E.

AU - Ivanov, A.

AU - Toropova, L.

N1 - Ministry of Science and Higher Education of the Russian Federation (project 075‐02‐2023‐935 for the “Ural Mathematical Center”); Foundation for the Advancement of Theoretical Physics and Mathematics “BASIS”: 21‐1‐3‐11‐1. Funding information

PY - 2024/5/30

Y1 - 2024/5/30

N2 - The boundary integral equation (BIE) describes the dynamics of a curved crystallization front separating liquid melt and solid material. We derive a generalized BIE for the thermal-concentration problem taking into account the nonlinear dependence of the crystallization temperature on solute concentration and the kinetics of atomic attachment at the interface. This equation determines the evolution of the interface function and the equation for crystallization driving force - the melt undercooling at the crystal surface. Our calculations carried out for a dendritic vertex in the form of a paraboloid of revolution have shown that the growth rate of the dendritic tip and its diameter substantially depend on the nonlinear effects under study. In particular, the velocity and diameter of the dendrite tip respectively become greater and narrower with increasing deviation of the liquidus equation from the linear relationship. Also, the dendrite tip velocity can be significantly affected by variations in the exponent of atomic kinetics.

AB - The boundary integral equation (BIE) describes the dynamics of a curved crystallization front separating liquid melt and solid material. We derive a generalized BIE for the thermal-concentration problem taking into account the nonlinear dependence of the crystallization temperature on solute concentration and the kinetics of atomic attachment at the interface. This equation determines the evolution of the interface function and the equation for crystallization driving force - the melt undercooling at the crystal surface. Our calculations carried out for a dendritic vertex in the form of a paraboloid of revolution have shown that the growth rate of the dendritic tip and its diameter substantially depend on the nonlinear effects under study. In particular, the velocity and diameter of the dendrite tip respectively become greater and narrower with increasing deviation of the liquidus equation from the linear relationship. Also, the dendrite tip velocity can be significantly affected by variations in the exponent of atomic kinetics.

UR - http://www.scopus.com/inward/record.url?partnerID=8YFLogxK&scp=85164606447

UR - https://gateway.webofknowledge.com/gateway/Gateway.cgi?GWVersion=2&SrcAuth=tsmetrics&SrcApp=tsm_test&DestApp=WOS_CPL&DestLinkType=FullRecord&KeyUT=001024144900001

U2 - 10.1002/mma.9520

DO - 10.1002/mma.9520

M3 - Conference article

VL - 47

SP - 6842

EP - 6852

JO - Mathematical Methods in the Applied Sciences

JF - Mathematical Methods in the Applied Sciences

SN - 0170-4214

IS - 8

ER -

ID: 56641599