Multi-phase-field modeling using a conservative Allen–Cahn equation for multiphase flow

Abstract

The phase-field (PF) method is a method for interface tracking that can treat complex topological changes relatively easily because of its diffuse interface model. Therefore, as computational resources become increasingly powerful, it is a promising interface tracking method for multiphase flow problems. In this study, we developed a novel multi-PF (MPF) model for expressing flows that consist of an arbitrary number of phases. Here, we adopt the conservative Allen–Cahn (CAC) model instead of the Cahn–Hilliard model, which is often employed in multiphase flow problems, to reduce computational cost and increase the flexibility of the model for various problems. Six sets of two-dimensional simulations were performed to confirm the validity of the developed model for simulating the static and dynamic phenomena of the multiphase flow problem while conserving the volume of each phase. The results confirm that the developed CAC-type MPF model can accurately express the contact angle of a droplet placed on a solid substrate and the motion of bubbles interacting with liquid–liquid interfaces.