A novel Cahn–Hilliard–Navier–Stokes model with a nonstandard variable mobility for two-phase incompressible fluid flow

In this study, we present a novel Cahn–Hilliard–Navier–Stokes (CHNS) system with a nonstandard variable mobility for two-phase incompressible fluid flow. Unlike the classical constant mobility, the developed variable mobility has decreasing values nearby the interface and increasing values away from the interface, which minimizes the dynamics of the Cahn–Hilliard (CH) model nearby the interface. An unconditionally stable convex splitting method is used to solve the CH equation and the projection method is used to solve the NS equation. As benchmark tests, the Rayleigh–Taylor instability, drop deformation, and rising bubble are performed to show the accuracy and practicability of the proposed model. The computational results indicate that the proposed model accurately captures the interfacial position and keeps the interface region from being too much distorted.