  In theoretical analyses of the moving contact line, an infinite force along
the solid wall has been reported based off the non-integrable stress along a
single interface. In this investigation we demonstrate that the stress
singularity is integrable and results in a finite force at the moving contact
line if the contact line is treated as a one-dimensional manifold and all three
interfaces that make up the moving contact line are taken into consideration.
This is due to the dipole nature of the vorticity and pressure distribution
around the moving contact line. Mathematically, this finite force is determined
by summing all the forces that act over an infinitesimally small cylindrical
control volume that encloses the entire moving contact line. With this finite
force, we propose a new dynamic Young's equation for microscopic dynamic
contact angle that is a function of known parameters only, specifically the
interface velocity, surface tension, and fluid viscosity. We combine our model
with Cox's model for apparent dynamic contact angle and find good agreement
with published dynamic contact angle measurements.
