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Phase-field modelling of the effect of density change on solidification revisited: Model development and analytical solutions for single component materials

journal contribution
posted on 07.01.2020 by Gyula Toth, Wenyue Ma
In this paper the development of a physically consistent phase-field theory of solidification shrinkage is presented. The coarse-grained hydrodynamic equations are derived directly from the N-body Hamiltonian equations in the framework of statistical physics, while the constitutive relations are developed in the framework of the standard Phase-field Theory, by following the variational formalism and the principles of non-equilibrium thermodynamics. To enhance the numerical practicality of the model, quasi-incompressible hydrodynamic equations are derived, where sound waves are absent (but density change is still possible), and therefore the time scale of solidification is accessible in numerical simulations. The model development is followed by a comprehensive mathematical analysis of the equilibrium and propagating 1-dimensional solid-liquid interfaces for different density-phase couplings. It is shown, that the fluid flow decelerates/accelerates the solidification front in case of shrinkage/expansion of the solid compared to the case when no density contrast is present between the phases. Furthermore, such a free energy construction is proposed, in which the equilibrium planar phase-field interface is independent from the density-phase coupling, and the equilibrium interface represents an exact propagating planar interface solution of the quasi-incompressible hydrodynamic equations. Our results are in excellent agreement with previous theoretical predictions.

History

School

  • Science

Department

  • Mathematical Sciences

Published in

Journal of Physics: Condensed Matter

Volume

32

Issue

20

Publisher

IOP Publishing

Version

AM (Accepted Manuscript)

Rights holder

© IOP Publishing Ltd

Publisher statement

This is the Accepted Manuscript version of an article accepted for publication in Journal of Physics: Condensed Matter. IOP Publishing Ltd is not responsible for any errors or omissions in this version of the manuscript or any version derived from it. The Version of Record is available online at https://doi.org/10.1088/1361-648x/ab670e

Acceptance date

02/01/2020

Publication date

2020-02-18

Copyright date

2020

Notes

18 pages, 5 figures, submitted to the Journal of Physics: Condensed Matter

ISSN

0953-8984

eISSN

1361-648X

Language

en

Depositor

Mr Gyula Toth Deposit date: 2 January 2020

Article number

205402

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