We report an experimental study on the dynamics of a thin film of polymer
solution coating a vertical fiber. The liquid film has first a constant
thickness and then undergoes the Rayleigh-Plateau instability which leads to
the formation of sequences of drops, separated by a thin film, moving down at a
constant velocity. Different polymer solutions are used, i.e. xanthan solutions
and polyacrylamide (PAAm) solutions. These solutions both exhibit shear-rate
dependence of the viscosity, but for PAAm solutions, there are strong normal
stresses in addition of the shear-thinning effect. We characterize
experimentally and separately the effects of these two non-Newtonian properties
on the flow on the fiber. Thus, in the flat film observed before the emergence
of the drops, only shear-thinning effect plays a role and tends to thin the
film compared to the Newtonian case. The effect of the non-Newtonian rheology
on the Rayleigh-Plateau instability is then investigated through the
measurements of the growth rate and the wavelength of the instability. Results
are in good agreement with linear stability analysis for a shear-thinning
fluid. The effect of normal stress can be taken into account by considering an
effective surface tension which tends to decrease the growth rate of the
instability. Finally, the dependence of the morphology of the drops with the
normal stress is investigated and a simplified model including the normal
stress within the lubrication approximation provides good quantitative results
on the shape of the drops.Comment: Accepted in Journal of Fluid Mechanic
