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In theoretical analyses of the moving contact line, an infinite force alongthe solid wall has been reported based off the non-integrable stress along asingle interface. In this investigation we demonstrate that the stresssingularity is integrable and results in a finite force at the moving contactline if the contact line is treated as a one-dimensional manifold and all threeinterfaces that make up the moving contact line are taken into consideration.This is due to the dipole nature of the vorticity and pressure distributionaround the moving contact line. Mathematically, this finite force is determinedby summing all the forces that act over an infinitesimally small cylindricalcontrol volume that encloses the entire moving contact line. With this finiteforce, we propose a new dynamic Young's equation for microscopic dynamiccontact angle that is a function of known parameters only, specifically theinterface velocity, surface tension, and fluid viscosity. We combine our modelwith Cox's model for apparent dynamic contact angle and find good agreementwith published dynamic contact angle measurements.

Theoretical model of a finite force at the moving contact line