The microstructure resulting from the solidification of alloys can greatly affect their properties, making the prediction of solidification phenomena under arbitrary conditions a very important tool in the field of computer-aided design of materials. Although considerable attention has been allocated to the understanding of this phenomenon in cases in which the solidification front advances freely into the liquid, the actual microstructure of solidification is strongly dependent of interfacial interactions. Over the past decade, the phase-field approach has been proved to be a quite effective tool for the simulation of solidification processes. In phase-field models, one or more phase fields o (conserved and/or non-conserved) are introduced to describe the microstructure of a complex system. The behavior of a given microstructure over time is then simulated by solving evolution equations written in terms of the minimization of the free energy of the entire system, which is written as a functional of the field variables as well as their gradients and materials' constitutive equations. With the given free energy functional, the governing equations (phase-field equation, diffusion equation, heat equation and so on) are solved throughout the entire space domain without having to track each of the interfaces formed or abrupt changes in the topology of the microstructure. In this work I will present phase-field models for solidification processes, solid/liquid interactions as well as their applications.
