Comparison of the Cahn-Hilliard-Navier-Stokes and Molecular Dynamics Approaches for the Simulation of Droplet Coalescence and Wetting Phenomena

Diffuse-interface/Cahn-Hilliard equations, coupled to Navier-Stokes (CHNS), have been used extensively over the last few years in fluid dynamics including interfacial phenomena in multiphase systems. Applications range from turbulent two-phase flows to rheological systems and microfluidic devices. But despite the considerable attention CHNS have received, little work has been undertaken to investigate the extent to which they agree with ``first-principles" physical models such as those provided by molecular dynamics (MD). Here we compare MD simulations with solutions of the CHNS system obtained numerically using an efficient and systematic finite-element methodology we have developed recently. For this purpose, we consider two paradigmatic model systems: droplet coalescence and droplet motion on a substrate with varying wettability.