Hydrodynamic model of steady movement of a solid/liquid/fluid contact line

Movement of the contact line over a solid surface violates the adherence, or “no slip,” boundary condition which is otherwise obeyed by flowing liquids. A flat fluid interface moving steadily over a flat solid is modeled with the creeping flow approximation, which turns out to be self-consistent. Adherence is required except at the contact line itself. Though the velocity field appears to be realistic, stresses and viscous dissipation are found to increase without bound at the contact line. The way the hydrodynamic model breaks down suggests that in reality there may be steep gradients, rheological anomalies, and discontinuous processes around the contact line. Slip and the role of long-range forces are explored with the aid of the lubrication flow approximation.