Consistent modeling of scalar transport coupled with two-phase flows using phase-field models

Phase field models have emerged as a competitive alternative to sharp-interface models for simulating two-phase flows due to their simplicity in implementation, cost-efficiency, scalability, and regularity. Phase field methods like the Cahn-Hilliard equation and second-order conservative phase field models are particularly attractive, as they enforce mass conservation on the continuous level. However, any equation coupled to the phase field must consistently account for the conservative right-hand side terms in the phase field equations. For example, a consistency modification of momentum equations achieves robust simulations of high Re numbers and high-density ratios for phase-field methods. Additionally, it also ensures thermodynamic consistency in the case of Cahn-Hilliard-based phase-field models. In this study, we present consistency modifications to scalar transport PDEs when coupled with phase-field models for two-phase flows. In addition, an efficient numerical strategy for solving coupled scalar and two-phase flow phase field equations is presented. We use the numerical framework to demonstrate the effect of the consistency terms on accuracy and robustness.