Nanoscale sheared droplet : volume-of-fluid, phase-field and no-slip molecular dynamics

The motion of the three-phase contact line between two immiscible fluids and a solid surface arises in a variety of wetting phenomena and technological applications. One challenge in continuum theory is the effective representation of molecular phenomena close to the contact line. Here, we characterize the molecular processes of the moving contact line to assess the accuracy of two different continuum two-phase models. Specifically, molecular dynamics (MD) simulations of a two-dimensional droplet between two moving plates are used to create reference data for different capillary numbers and contact angles. We use a simple-point-charge/extended (SPC/E) water model with particle-mesh Ewald electrostatics treatment. This model provides a very small slip and a more realistic representation of the molecular physics than Lennards-Jones models. The Cahn-Hilliard phase-field model and the Volume-of-Fluid model are calibrated against the drop displacement from MD reference data. It is demonstrated that the calibrated continuum models can accurately capture droplet displacement and droplet breakup for different capillary numbers and contact angles. However, we also observe differences between continuum and atomistic simulations in describing the transient and unsteady droplet behavior, in particular, close to dynamical wetting transitions. The molecular dynamics of the sheared droplet provide insight of the line friction experienced by the advancing and receding contact lines and evidence of large-scale temporal "stick-slip" like oscillations. The presented results will serve as a stepping stone towards developing accurate continuum models for nanoscale hydrodynamics.
45 pages, 23 figures, 4 tables, 1 supplementary PDF, 2 supplementary movies, 1 supplementary archive, accepted for publication in "Journal of Fluid Mechanics"