Moving contact line with balanced stress singularities

A difficulty in the classical hydrodynamic analysis of moving contact-line problems, associated with the no-slip wall boundary condition resulting in an unbalanced divergence of the viscous stresses, is reexamined with a smoothed, finite-width interface model. The analysis in the sharp-interface limit shows that the singularity of the viscous stress can be balanced by another singularity of the unbalanced surface stress. The dynamic contact angle is determined by surface tension, viscosity, contact-line velocity and a single non-dimensional parameter reflecting the lengthscale ratio between interface width and the thickness of the first molecule layer at the wall surface. The widely used Navier boundary condition and Cox’s hypothesis are also derived following the same procedure by permitting finite-wall slip.