Phase-field model with finite interface dissipation

In rapid phase transformations, interfaces are often driven far from equilibrium, and one or several intensive quantities (temperature or chemical potentials) may exhibit jumps across the interface. We develop a phase-field model for the description of such situations in the framework of the multi-phase-field formalism, with separate concentration fields in each phase. The key new feature of this model is that the two concentration fields are linked by a kinetic equation which describes exchange of the components between the phases, instead of an equilibrium partitioning condition. The associated rate constant influences the interface dissipation. For rapid exchange between the phases, the standard phase-field model is recovered, whereas in the opposite limit strong non-equilibrium behavior can be modeled. This is illustrated by simulations of a diffusion couple and of solute trapping during rapid solidification.