Droplet impact simulation with Cahn–Hilliard phase field method coupling Navier-slip boundary and dynamic contact angle model

As a highly promising interface capture tool, the phase field method (PFM) has gained fast development in the past 20 years or so including in the simulation of droplet impact. The mobility tuning parameter χ of PFM, however, is hard to determine since it ambiguously reflects the relative strength between advection and diffuse effects that are difficult to quantify. This problem becomes even more complex when it is coupled with the contact line movement modeling, i.e., the dynamic contact angle (DCA) model, which is closely related to the effective slip (Ls,e) and the Navier-slip (Ls). This study systematically investigated the factors that would take effect at the interface capture and the contact line movement in droplet impact simulation. The value and the scaling law of Ls,e as for its dependence on χ and interface thickness (ε) was first confirmed, and an approximation scheme for defining the DCA model was proposed based on the difference between the apparent contact line moving velocity (Ucl) and the Navier-slip velocity at the contact line (Ucl′), which is inherently determined by Ls,e and Ls, respectively. After validation with the experiments, the scaling law of χ with ε, i.e., the sharp-interface limit, was finally obtained, which provides improved droplet impact simulation.