Instabilities and turbulence in polymeric fluids

The presence of polymers in a viscous fluid confers elasticity to it, resulting in unexpected flow phenomena. The consequences are most startling under conditions when the flow of the viscous fluid is unstable or turbulent. For instance, turbulence in wall-bounded flows of viscous liquids causes additional energy losses because of increased drag relative to laminar flow. Minute quantities of polymer molecules added to this flow can reduce turbulent drag by upto 70%. We analyze and re-interpret the phenomenology of polymer turbulent drag reduction compiled by Virk (1975). Building upon the viscous and elastic theories of drag reduction, we construct a one parameter model that fits quantitatively the mean velocity profiles from experiments and numerical simulations of drag-reduced wall-bounded flows of dilute solutions of polymers and non-Brownian fibers in the low and modest drag reduction regime. We then investigate the near-wall coherent structures of wall-bounded turbulence that are the most dominant contributors to turbulent drag in viscous fluids. Exact coherent structures that appear at Reynolds numbers far below turbulence form the backbone around which turbulent coherent structures are organized. We analyze low-dimensional models developed earlier to describe the exact coherent structures and conclude that the 9-dimensional model of Moehlis, Faisst and Eckhardt (2004) best describes the spatial form as well as the self-sustaining process of the underlying exact coherent structures. Using a retarded-motion expansion to describe the polymer stress, we investigate the effect of polymer elasticity on the 9-dimensional model of exact coherent structures and arrive at a mechanism for polymer drag reduction in wall-bounded flows. Finally, we show from experiments that the effect of polymers on flows of viscous liquid filaments and sheets can be equally dramatic' and consisin drag reduction, in that polymers reduce or reverse flow instabilities. Increased elasticity due to polymers can force a polymeric fluid filament fixed at its ends to rise against its own weight, when the ends are suddenly brought closer together. Starting from the governing equations of motion, we use perturbation method to derive an equation for the centerline of the filament to explain our observations in some simple settings.