Modeling and simulation of multi-component immiscible flows based on a modified Cahn–Hilliard equation

In this study, an efficient method will be developed for the phase-field model of multi-component immiscible phases. The formulation of surface tension requires the interfaces to satisfy the hyperbolic tangent property. However, the interfacial transitions between different phases are not hyperbolic tangent profiles. The enclosed area is not preserved although the total mass is conserved by the original Cahn–Hilliard equation. This study is an extended research based on our previous study (Li et al., 2016). This work aims to apply the modified Cahn–Hilliard model into the multi-phase system. The interface is forced to be hyperbolic tangent by the modified Cahn–Hilliard system. The computational accuracy of the surface tension is improved under our multiphase framework. The mass loss of each phase can be reduced and the enclosed area can be preserved by the proposed method. We show various numerical results to demonstrate the robustness of the proposed modified model.