Contact line motion from molecular dynamics, the diffuse interface model and the sharp interface model.

In the context of the sharp interface model Huh and Scriven wrote “not even Herakles could sink a solid if the physical model were entirely valid”. The resolution of this paradox has occupied a large number of investigators, however a popular fix is to assume a Navier boundary condition for the tangential fluid velocity on the solid surface, which introduces a slip length $\lambda$. Nevertheless realistic molecular models show no slip of the first water layer on the SiO2 substrate. Alternate models of the contact line motion involve a dissipative relaxation of the order parameter at the boundary. This relaxation towards contact angle equilibrium involves a contact line friction $\mu_f$. We thus compare interface shapes obtained from a phase-field diffusive-interface model with the results of molecular dynamics (MD) simulation using the GROMACS code. The setup is a simple Couette flow between two plates, with a vapor droplet sheared in the middle of the domain. Another com parison is performed between MD and the sharp-interface model with a slip length and a Generalized Navier Boundary Condition. The sharp interface model is implemented using a VOF method. The role of diffusion across the interface, which is possible in the diffuse interface model, is given particular attention.