  The understanding of the spreading of liquids on solid surfaces is an
important challenge for contemporary physics. Today, the motion of the contact
line formed at the intersection of two immiscible fluids and a solid is still
subject to dispute. In this paper, a new picture of the dynamics of wetting is
offered through an example of non-Newtonian slow liquid movements. The
kinematics of liquids at the contact line and equations of motion are
revisited. Adherence conditions are required except at the contact line.
Consequently, for each fluid, the velocity field is multivalued at the contact
line and generates an equivalent concept of line friction but stresses and
viscous dissipation remain bounded. A Young-Dupr\'e equation for the apparent
dynamic contact angle between the interface and solid surface depending on the
movements of the fluid near the contact line is proposed.
