Capillary levelling of thin liquid films of power-law rheology

We find solutions that describe the levelling of a thin fluid film coating a substrate, comprising a non-Newtonian power law fluid, under the influence of surface tension. We consider the evolution from both periodic and localised initial conditions. These solutions exhibit the generic property that the profiles are weakly singular (that is, higher order derivatives do not exist), at points where the pressure gradient vanishes. Numerical solutions of the thin film equation are shown to approach one of the two cases for appropriate initial conditions.