Nonisothermal Diffuse Interface Model for Phase Transition and Interface Evolution

Source abstract

Abstract. In this paper, we derive a thermodynamically consistent nonisothermal diffuse interface model for phase transition and interface evolution involving heat transfer. This model is constructed by integrating concepts from classical irreversible thermodynamics and the energetic variational approach. By making specific assumptions about the kinematics of the temperature, we derive a nonisothermal Allen–Cahn equation. Through both asymptotic analysis and numerical simulations, we demonstrate that in the sharp interface limit, the nonisothermal Allen–Cahn equation converges to a two-phase nonlinear Stefan type problem, under a certain scaling of the melting/freezing energy. In this regime, the motion of the liquid-solid interface and the temperature interface coincides and is governed by the mean curvature flow, at least for a short time. The result provides a justification for the classical Stefan problem within a certain physical regime.