Explicit Dynamics of Diffuse Interface in Phase-Field Model

Interfaces play an important role during phase transition and interfacial chemical reactions. In this paper, three different methods are introduced to analyze the explicit dynamics of the diffuse interface by means of phase-field model, and these methods are based on three independent perspectives: non-dispersive propagation of the interfacial waveform, the flux density and sources/sinks analysis of continuity equation, and the moving interfacial coordinate transformation. These theoretical derivations not only present the relationship between the diffuse interfacial velocity and the effect of driving force and interfacial curvature, but also clarify the equivalent method between the phase-field dynamics and the sharp-interfacial dynamics, which reveals the physical meaning of the diffuse interfacial dynamical equation from different perspectives. The present study advances the understanding of the interfacial phase transition and provides theoretical insights for the phase-field model and numerical simulation.