Comparison between numerical models for the simulation of moving contact lines

• We discuss different numerically models for the simulation of moving contact lines.
• The CSF method induces a grid dependence at the onset of the spreading.
• Static and dynamic models are compared to experiments of spreading drops.
• Dynamic models based on the Cox’s relation are able to reproduce experiments.
• Static and dynamic models difference increases with the Ohnesorge number.

The aim of this study is to discus different numerically models for the simulation of moving contact lines in the context of a Volume of Fluid–Continuum Surface Force (VoF–CSF) method. We focus on the particular situation of spreading drops. We first present the numerical methods used for the simulation of moving contact line i.e. static contact angle versus dynamic contact angle, no slip condition versus slip condition. A grid and time convergence is performed for the different models. We show that the integration of the Continuum Surface Force using the finite volume method results in a grid dependence at the onset of the spreading. The static and dynamic models are compared to experiments. It is shown that the dynamic models based on the Cox’s relation for the dynamic contact angle are able to reproduce experiments while static models overestimate the spreading time and are not able to reproduce the Tanner regime. The difference between static and dynamic models is shown to increase with the Ohnesorge number.