Incompressible two-phase flow: Diffuse interface approach for large density ratios, grid resolution study, and 3D patterned substrate wetting problem

We subsequently perform exhaustive numerical tests to determine the minimal resolution of spatial discretization required and showcase the robustness of our framework. We illustrate the accuracy of the framework using the analytical results of Prosperetti for a damped oscillating interface between two fluids with various density contrasts as well as a benchmark Rayleigh-Taylor instability problem. We also showcase the framework by modeling the crown ring effect during droplet impact, and the spread of a droplet on a wetting surface. Finally, we explore the affects of surface patterns on the droplet spreading process. Specifically, we investigate formations of wetting spots and air entrapment on grooved and checker-patterned surfaces. These results have implications for the design of tuned wettability surfaces for the manufacture of thin film devices.