2000/11/01 by K. R. Elder, Martin Grant, Nikolas Provatas +1 · 1 citation
Physics and Astronomy · #cond-mat.soft
paper · pdf · doi:10.1103/physreve.64.021604
17 pages, 9 figures
arxiv created 2000/11/01 · arxiv updated 2009/11/30
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 ξ. In particular,phase-field equations are mapped onto sharp interface equations in the limits ξκ≪ 1 and ξv/D ≪ 1, where κ 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.