Phase-field model for solidification of a monotectic alloy with convection

In this paper we discuss two phase-field models for solidification of monot ectic alloys, a situation in which a liquid phase L-1 may simultaneously tr ansform into both a new liquid phase L-2 and a solid phase S via the reacti on L-1 --> L-2 + S. The first model uses three different phase-fields to ch aracterize the three phases in the system and, in addition, a concentration field. This construction restricts the validity of the model to describe p hase transitions within the vicinity of the monotectic temperature. In cont rast, the second model distinguishes the two liquid phases by their concent ration using a Cahn-Hilliard type model and employs only one phase-field to characterize the system as solid or liquid. This formulation enables the s econd model to represent a wider temperature range of the phase diagram inc luding the miscibility gap where the spinodal decomposition L --> L-1 + L-2 occurs. Both our models permit the interfaces to have temperature-dependen t surface energies which may induce Marangoni convection at L-1-L-2 interfa ces in non-isothermal systems. By deriving a generalized stress tensor incl uding stresses associated with the capillary forces on the diffuse interfac e, we extend the two monotectic phase-field models to account for convectio n in both liquid phases. Together with a generalized set of Navier-Stokes e quations, we give a complete set of dynamic field equations to describe mon otectic systems with fluid flow. Finally, we present numerical simulations of lamellar monotectic growth structures which exhibit wetting phenomena as well as coarsening and particle pushing. (C) 2000 Elsevier Science B.V. Al l rights reserved.