Driving forces for interface kinetics and phase field models

Phase field models for applications in physics and materials science are typically written in variational form starting from a free energy functional, and sharp interface descriptions for moving boundary problems can be formulated similarly. Here we discuss why and under which circumstances this postulate for deriving the equations of motion is justified, and what are limitations for specific cases. We investigate this in particular for alloys, systems with elastic, viscoelastic and plastic effects, mainly based on analytical and numerical investigations in one dimension. We find that the naturally guessed equations of motion, as derived via partial functional derivatives from a free energy, are usually reasonable, only for materials with plastic effects this assumption is more delicate due to the presence of internal variables.