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

Brener, E.A.; Temkin, D.E.

doi:10.1103/PhysRevE.85.031601

Journal Article

PreJuSER-22906

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

Brener, E. A.FZJ* ; Temkin, D. E.

2012
APS College Park, Md.

Physical review / E 85(3), 031601 (2012) [10.1103/PhysRevE.85.031601]

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Please use a persistent id in citations: http://hdl.handle.net/2128/9262 doi:10.1103/PhysRevE.85.031601

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.

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Note: We thank M. Plapp for useful discussions. We acknowledge the support of the Deutsche Forschungs-gemeinschaft under Project No. SFB 917.

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