  A homogeneous thin polymer film with a stepped height profile levels due to
the presence of Laplace pressure gradients. Here we report on studies of
polymeric samples with precisely controlled, spatially inhomogeneous molecular
weight distributions. The viscosity of a polymer melt strongly depends on the
chain length distribution; thus, we learn about thin-film hydrodynamics with
viscosity gradients. These gradients are achieved by stacking two films with
different molecular weights atop one another. After a sufficient time these
samples can be well described as having one dimensional viscosity gradients in
the plane of the film, with a uniform viscosity normal to the film. We develop
a hydrodynamic model that accurately predicts the shape of the experimentally
observed self-similar profiles. The model allows for the extraction of a
capillary velocity, the ratio of the surface tension and the viscosity, in the
system. The results are in excellent agreement with capillary velocity
measurements of uniform mono- and bi-disperse stepped films and are consistent
with bulk polymer rheology.
