Sharp interface limits of phase-field models - art. no. 021604

The use of continuum phase-field models to describe the motion of well-defi ned interfaces is discussed for a class of phenomena that includes order-di sorder 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 mode ls which have interfaces that are diffuse on a length scale. In particular, phase-field equations are mapped onto sharp-interface equations in the lim its xi kappa<<1 and xi nu /D << 1, where kappa and nu are, respectively, th e interface curvature and velocity and D is the diffusion constant in the b ulk. 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.