  The dynamics of thin films on a horizontal solid substrate is investigated in
the case of non-Newtonian fluids exhibiting normal stress differences, the
rheology of which is strongly non-linear. Two coupled equations of evolution
for the thickness of the film and the shear rate are proposed within the
lubrication approximation. This framework is applied to the motion of an
advancing contact line. The apparent dynamic contact angle is found to depend
logarithmically on a lengthscale determined solely by the rheological
properties of the fluid and the velocity of the contact line.
