Using detailed asymptotic analyses of the dynamics of the phase-field model, we show that the major sharp-interface models (Stefan, modified Stefan, Hele-Shaw, etc.) all arise as limiting cases of the phase-field equations. The scaling of the physical parameters in the microscopics leads to distinct macroscopic models with critical differences.

• Received 28 November 1988

DOI:https://doi.org/10.1103/PhysRevA.39.5887