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On the Multiscale Formulation and the Derivation of Phase-Change Moving Interfaces

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Abstract

A closed-form analytical solution for transient solidification of multicomponent alloys is proposed by analytically solving the microscale solidification to feed the local conditions, such as surface energy, surface tension, nucleation radius, interface temperature, and solute concentration, necessary to the evolution of macroscopic solidus, liquidus, and eutectic interfaces. Expressions for the critical radius, total free energy, and nucleation rate are derived for homogeneous and heterogeneous nucleation based on recent propositions for nucleation and surface energy. A general solution for interface evolution is proposed, encompassing local temperature and concentration conditions to provide the proper integration of the macroscopic temperature necessary for latent heat release in the solid–liquid phase.

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Data Availability

The data that support the findings of this study are available from the corresponding author upon reasonable request.

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Funding

The authors acknowledge the financial support provided by FAPERJ (The Scientific Research Foundation of the State of Rio de Janeiro—Brazil) and CAPES (Coordenação de Aperfeiçoamento de Pessoal de Nível Superior—Brazil—Finance Code 001) and CNPq—Brazil (National Council for Scientific and Technological Development).

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Authors and Affiliations

  1. Faculty of Mechanical Engineering, Federal University of Pará, UFPA, Augusto Corrêa Avenue 1, Belém, PA, 66075-110, Brazil

    I. L. Ferreira & A. L. S. Moreira

  2. Department of Manufacturing and Materials Engineering, University of Campinas – UNICAMP, Campinas, SP, 13083-860, Brazil

    A. Garcia

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Contributions

ILF developed the formalism, derived equations proposed, performed computations, and wrote the text. ALSM wrote the Introduction section, performed the literature review, and improved the text. AG helped with the comparison with his model and proposed improvements in the English text and the figures layouts.

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Correspondence to I. L. Ferreira.

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Ferreira, I.L., Garcia, A. & Moreira, A.L.S. On the Multiscale Formulation and the Derivation of Phase-Change Moving Interfaces. Int J Thermophys 44, 2 (2023). https://doi.org/10.1007/s10765-022-03099-6

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