Elder K R, Grant M, Provatas N, Kosterlitz J M
Department of Physics, Oakland University, Rochester, Michigan 48309-4487, USA.
Phys Rev E Stat Nonlin Soft Matter Phys. 2001 Aug;64(2 Pt 1):021604. doi: 10.1103/PhysRevE.64.021604. Epub 2001 Jul 19.
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)<<1 and xi(v)/D<<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.
