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

Author

Listed:
  • 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)

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.

Suggested Citation

  • Ekaterina A. Titova & Dmitri V. Alexandrov, 2024. "The Solid–Liquid Phase Interface Dynamics in an Undercooled Melt with a Solid Wall," Mathematics, MDPI, vol. 12(2), pages 1-11, January.
    • Handle: RePEc:gam:jmathe:v:12:y:2024:i:2:p:327-:d:1322302
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