Effective perpendicular boundary conditions in phase-field models using Dirichlet boundary conditions

초록

The primary objective of this study is to present the temporal and spatial evolution dynamics of two- and three-dimensional phase-field models with Dirichlet boundary conditions on arbitrary shaped domains. We consider the Allen-Cahn (AC), Cahn-Hilliard (CH), nonlocal Cahn-Hilliard (nCH) equations among the phase-field models in this study. The AC equation has been used to model various phenomena, such as motion by mean curvature flows. It can be derived from the Ginzburg-Landau free-energy functional. The CH equation has been applied to many conservative physical phenomena, such as phase separation dynamics. As for the nCH equation, a fourth-order nonlocal nonlinear PDE, it models the microphase separation of diblock copolymers. For these phase-field models, there are various boundary conditions available, such as Neumann, periodic, Dirichlet boundary conditions. In this study, we investigate the phase transformation dynamics of the phase-field models using different Dirichlet boundary conditions. Furthermore, complex-shaped domains can be handled straightforwardly, and a perpendicular boundary condition can be effectively imposed by applying the zero Dirichlet boundary condition. This approach proves to be highly useful and efficient in imposing the perpendicular boundary conditions for complex-shaped domains.

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