of Non-Newtonian Fluids
Please see published manuscript: "Stretching
and Mixing of Non-Newtonian Fluids in Time-Periodic Flows" by P.E.
Arratia, Greg A. Voth,and J.P. Gollub. Phys. Fluids, 17, 053102 (2005)
Abstract: The stretching of fluid elements and the dynamics of mixing are studied for a variety of polymer solutions in nearly two-dimensional magnetically driven flows, in order to distinguish between the effects of viscoelasticity and shear thinning. Viscoelasticity alone is found to suppress stretching and mixing mildly, in agreement with some previous experiments on time-periodic flows. On the other hand, the presence of shear thinning viscosity (especially when coupled with elasticity) produces a dramatic enhancement in stretching and mixing, compared to a Newtonian solution at the same Reynolds number. In order to understand this observation, we study the velocity field separately in the sheared and elongational regions of the flow for various polymer solutions. We demonstrate that the enhancement is accompanied by a breaking of time-reversal symmetry of the particle trajectories, on the average. Finally, we discuss possible causes for the time lags leading to temporal symmetry-breaking, and the resulting enhanced stretching.
Below, we present images of the dye field showing the changes in flow patterns and enhancement of mixing with a shear-thinning fluid. Left column: Newtonian fluid (Re=1.24). Right Column: a viscoelastic shear thinning solution (Polyacrylamide in water) (Re=1.45, Wi=1.09). Each row shows an image taken 10 periods after the one above it.
QuickTime format (.mpg) - the plugin needed to view QuickTime animations is free and available at www.apple.com.
Newtonian Fluid - Here we show the velocity field during one forcing period of a Newtonian fluid (Glycerol/water mixture, viscosity=90 cP, Re=1.92).