Influences on Pattern Formation During Non-Isothermal Phase Separation in Local and Nonlocal Phase-Field Models

The classical phase-field model represents a coupling of an Allen-Cahn type nonlinear equation with a standard diffusion equation and has been proposed to describe uniform phase separation in a pure substance. This research considers an extension of that model which incorporates a more accurate approximation to the diffuse interface between states of matter through the use of a nonlocal operator. Results of simulations under this model are compared with those of the classical model in order to understand the effects of the nonlocal contribution. Attention has been given to the behavior of the underlying temperature field during early phase separation. We use the tools of computational homology to quantitatively compare patterns in the phase field under both models. Simulations show that the complicated patterns in the phase field persist longer during the solidification process in the nonlocal extension of the classical model.