Flows with moving contact lines are encountered in many applications involving wetting phenomena such acid gas treatment with contacting devices, film coatings, and microfluidics. Numerically simulating flows with moving contact lines under realistic conditions is a computational challenge, because a large range of length scales is involved, and the fluid/fluid interface is generally strongly curved close to the contact line. This is due to the different physical behavior in the near vicinity of a moving contact line: a conventional no-slip formulation would lead to a singularity in the wall stress at a moving contact line. Several models have been proposed to account for the physical behavior in the near vicinity of contact lines – herein we adopt a slip formulation, which involves a slip length parameter that is typically estimated to be nanometric, which is much smaller than the dimensions of an entire flow, even for a millimetric droplet. Direct numerical simulations (DNS) of such flows wherein the entire flow is resolved not being feasible, it is proposed here to numerically resolve the large-scale flow and part of the intermediate-scale flow whilst using a subgrid-scale model, which originates from hydrodynamic theories, to represent the unresolved part of the flow. We have developed a methodology for such large-scale simulations in 3D in the context of level-set methods.

Results will be presented first for axisymmetric droplet spreading (simulated in 3D) in a regime dominated by viscous and capillary effects, with a comparison against results of DNS available in the literature. This is followed by results for axisymmetric droplet spreading (simulated in 3D) for more rapid flows, wherein inertial effects enter the contact-line region, for which excellent agreement with experimental data was obtained, both qualitatively and quantitatively.

A second part of the work investigates whether such a model can be used for more complex evolution of contact lines, including effects of contact-angle hysteresis in 3D, which are also represented by our computational method. For this purpose, we consider next three-dimensional drops sliding down an inclined plane; numerical results will be demonstrated to be in good agreement with experiments.

The subgrid-scale model used herein is restricted to flows with moving contact lines on planar substrates with small gravity effects compared to capillary effects. Further complexities may now be considered, involving heterogeneous substrates or higher Bond numbers, which calls for further DNS and theoretical development.