  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 length-scale 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.
