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Study of a system for the isothermal separation of components in a binary alloy with change of phase

Abstract : An isothermal model describing the separation of the components of a binary metallic alloy is considered. A process of phase transition is also assumed to occur in the solder; hence, the state of the material is described by two order parameters, i.e. the concentration c of the first component and the phase field ϕ. A physical derivation is provided starting from energy balance considerations. The resulting system of PDEs consists of a rather regular second-order parabolic equation for ϕ coupled with a fourth-order relation of Cahn-Hilliard type for c with constraint and solution-dependent mobility. Global existence of solutions is proved and several regularity properties are discussed under more restrictive assumptions on the physical parameters. Continuous dependence on data is shown in a special case. An asymptotic analysis of the model is also performed, yielding at the limit step a coupling of the original phase field equation with a Stefan-like system for c.
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https://hal.archives-ouvertes.fr/hal-00141794
Contributor : Jean-Francois Scheid <>
Submitted on : Friday, January 22, 2021 - 3:44:17 PM
Last modification on : Friday, February 26, 2021 - 3:22:01 AM

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Daniel Kessler, Jean-Francois Scheid, Giulio Schimperna, Ulisse Stefanelli. Study of a system for the isothermal separation of components in a binary alloy with change of phase. IMA Journal of Applied Mathematics, Oxford University Press (OUP), 2004, 69 (3), pp.233--257. ⟨10.1093/imamat/69.3.233⟩. ⟨hal-00141794⟩

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