The Solid–Liquid Phase Interface Dynamics in an Undercooled Melt with a Solid Wall

Ekaterina A. Titova and Dmitri V. Alexandrov ()
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Ekaterina A. Titova: Laboratory of Multi-Scale Mathematical Modeling, Department of Theoretical and Mathematical Physics, Ural Federal University, Lenin Ave., 51, Ekaterinburg 620000, Russia
Dmitri V. Alexandrov: Laboratory of Multi-Scale Mathematical Modeling, Department of Theoretical and Mathematical Physics, Ural Federal University, Lenin Ave., 51, Ekaterinburg 620000, Russia

Mathematics, 2024, vol. 12, issue 2, 1-11

Abstract: A new boundary integral equation for the interface function of a curved solid/liquid phase interface propagating into an undercooled one-component melt is derived in the presence of a solid wall in liquid. Green’s function technique is used to transform a purely thermal boundary value problem to a single integro-differential equation for the interface function in two- and three-dimensional cases. It is shown that a solid wall represents an additional source of heat and melt undercooling can be negative in the vicinity of the wall. The new boundary integral equation has a limiting transition to previously developed theory in the absence of a solid wall.

Keywords: boundary integral equation; Green’s function technique; phase transitions; propagation of curved solid–liquid interfaces; undercooled melts; dendrites (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2024
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