Pseudospectral calculations of stress-induced concentration changes in viscometric flows of polymer solutions
We investigate the flow of dilute polymer solutions in viscometric devices where the polymer concentration is allowed to vary due to the existence of nonzero stress gradients. A spectral collocation method is used in order to solve for the axisymmetric steady-state solution of the full set of the governing equations. Two alternative continuum formulations are considered based on a single- and two-fluid concept, respectively. For the parallel-plate flow problem and for the two-fluid model, the analytical solution obtained by Brunn (1984) is recovered. This solution describes a polymer migration toward the centerline that depends solely on the Weissenberg number. The results obtained for the single-fluid model are qualitatively similar; however, they also depend on additional molecular parameters. Variations in the geometry which initiate even a small secondary recirculation are found to result in a significant decrease in the concentration gradients, as shown in the analysis of the cone-and-plate flow for a small angular inclination and a large centerline gap thickness. When the centerline gap thickness decreases, the results are dominated by the ideal, purely azimuthal cone-and-plate flow behavior, according to which substantial variations in the radial concentration are observed mainly close to the centerline. This is in agreement with the predictions of Aubert et al. (1980) and Brunn (1984).