The use of continuum phase-field models to describe the motion of well-defined interfaces is discussed for a class of phenomena that includes order–disorder transitions, spinodal decomposition and Ostwald ripening, dendritic growth, and the solidification of eutectic alloys. The projection operator method is used to extract the “sharp-interface limit” from phase-field models which have interfaces that are diffuse on a length scale $\xi .$ In particular, phase-field equations are mapped onto sharp-interface equations in the limits $\xi \kappa \ll 1$ and $\xi v/D\ll 1,$ where $\kappa$ and $v$ are, respectively, the interface curvature and velocity and D is the diffusion constant in the bulk. The calculations provide one general set of sharp-interface equations that incorporate the Gibbs–Thomson condition, the Allen–Cahn equation, and the Kardar–Parisi–Zhang equation.

• Received 25 October 2000

DOI:https://doi.org/10.1103/PhysRevE.64.021604