Continuum Models for the Contact Line Problem

Abstract Continuum models are derived for the moving contact line problem through a combination of macroscopic and microscopic considerations. Macroscopic thermodynamic argument is used to place constraints on the form of the boundary conditions at the solid surface and the contact line. This information is then used to set up molecular dynamics to measure the detailed functional dependence of the boundary conditions. Long range molecular forces are taken into account in the form of a surface potential. This allows us to handle the case of complete wetting as well as the case of partial wetting. In particular, we obtain a new continuum model for both cases in a unified form. Two main parameters and different spreading regimes are identified from the analysis of the energy dissipations for the continuum model. Scaling laws in these different regimes are derived. The new continuum model also allows us to derive boundary conditions for the lubrication approximation. Numerical results are presented for the thin film model, and the effect of the boundary condition is investigated.