Boundary conditions for the moving contact line problem
Weiqing Ren, NYU

Contact lines refer to the intersection of the a fluid-fluid interface with a solid  surface. Boundary conditions at the moving contact line have for many years
remained an issue of controversy and debate. The difficulty stems partly from the fact  that classical hydrodynamic equation (e.g. the Navier-Stokes equation) coupled with the no-slip boundary condition predicts a singularity for the stress that results in a  non-physical divergence for the energy dissipation rate.
In this talk, I will discuss a contact line model derived based on principles of  non-equilibrium thermodynamics and molecular dynamics simulations.
Macroscopic thermodynamic is used to place constraints on the form of the boundary conditions;  the detailed constitutive relations are then computed from molecular dynamics. The contact line model consists of the Navier-Stokes equation, a boundary condition for the slip  velocity, and a relation between the dynamic contact angle and the contact line velocity. In the second part of the talk, I will discuss numerical methods for the contact line model  and its application to the contact line dynamics on a chemically patterned solid surface.