An immersed boundary-phase field fluid-surfactant model with moving contact lines on curved substrates

In this study, we propose an immersed boundary-phase field fluid-surfactant model that incorporates moving contact lines on complex geometries. To accurately capture the interface, we introduce an additional phase field variable to represent the solid phase, which remains fixed throughout the process. The modified Cahn–Hilliard equations are utilized to describe the interface. In order to address stiffness issues, a stabilization technique is incorporated into the calculations. To prevent streamlines from penetrating into solid obstacles, a boundary condition-enforced immersed boundary method is applied at the solid boundaries. The desired contact angle is ensured using the characteristic moving contact line method. All variables are treated independently in the computations, and the numerical results demonstrate the accuracy and excellent performance of our model on curved substrates with surfactants.