Phase-field model: Boundary layer, velocity of propagation, and the stability spectrum

We present a study of a phase-field model for diffusion-limited growth. A boundary-layer approximation is used to show that for sharp interface, the first approximation to the phase-field model is the free boundary model, which includes surface tension and a linear kinetic term. The velocity of propagation and the stability spectrum are calculated for a steady-state flat interface. In the case where the phase and the field have similar variation lengths, a stable growth regime is found above a critical value of driving force. We discuss the application of phase-field-like models in the description of the ensemble-average pattern.