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

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.