Phase Field Methods

Phase field methods consist of a class of equations that have seen widespread use to model the dynamics of density fields that form patterns. From phase transitions to the representation of moving interfaces in fluids and solids, phase field equations are now prominent in materials physics and biophysics. Coupled formulations combining phase field models with other physics, including elasticity, fluid flow, heat conduction, and electrochemistry, play an increasingly important role in computational studies. This chapter is an introduction to the most prominent phase field models used in them. As with the introduction to nonlinear elasticity in Chap. 2 , the treatment is meant to center the reader on the perspective and approach adopted to phase field models here. It is rigorous but not formal, and sufficient as an introduction to phase field methods for the purposes of this monograph. Details relevant to specific applications are filled in as needed in subsequent chapters.