Generalized Navier Boundary Condition for the Moving Contact Line∗

From molecular dynamics simulations on immiscible flows, we find the relative slipping between the fluids and the solid wall everywhere to follow the generalized Navier boundary condition, in which the amount of slipping is proportional to the sum of tangential viscous stress and the uncompensated Young stress. The latter arises from the deviation of the fluid-fluid interface from its static configuration. We give a continuum formulation of the immiscible flow hydrodynamics, comprising the generalized Navier boundary condition, the Navier-Stokes equation, and the CahnHilliard interfacial free energy. Our hydrodynamic model yields near-complete slip of the contact line, with interfacial and velocity profiles matching quantitatively with those from the molecular dynamics simulations.