PMID: 22587102May 17, 2012Paper

Onsager approach to the one-dimensional solidification problem and its relation to the phase-field description

Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics
Efim A Brener, D E Temkin

Abstract

We give a general phenomenological description of the steady-state 1D front propagation problem in two cases: the solidification of a pure material and the isothermal solidification of two-component dilute alloys. The solidification of a pure material is controlled by the heat transport in the bulk and the interface kinetics. The isothermal solidification of two-component alloys is controlled by the diffusion in the bulk and the interface kinetics. We find that the condition of positive-definiteness of the symmetric Onsager matrix of interface kinetic coefficients still allows an arbitrary sign of the slope of the velocity-concentration line near the solidus in the alloy problem or of the velocity-temperature line in the case of solidification of a pure material. This result offers a very simple and elegant way to describe the interesting phenomenon of a possible non-single-value behavior of velocity versus concentration that has previously been discussed by different approaches. We also discuss the relation of this Onsager approach to the thin-interface limit of the phase-field description.

References

Apr 1, 1996·Physical Review. E, Statistical Physics, Plasmas, Fluids, and Related Interdisciplinary Topics·A Karma, W J Rappel
Aug 11, 2001·Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics·K R ElderJ M Kosterlitz
Feb 9, 2005·Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics·Blas EchebarriaMathis Plapp
May 24, 2011·Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics·Alexander L KorzhenevskiiRudi Schmitz
Mar 10, 2012·Physical Review Letters·Alexander L KorzhenevskiiRudi Schmitz

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Citations

Jul 16, 2014·Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics·G Boussinot, Efim A Brener
Feb 2, 2013·Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics·Efim A Brener, G Boussinot
Jul 16, 2013·Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics·Alexander L KorzhenevskiiRudi Schmitz
Feb 16, 2013·Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics·Angbo Fang, Yongli Mi
Sep 17, 2013·Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics·G Boussinot, Efim A Brener

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