Onset of transition in the flow of polymer solutions through deformable tubes

Experiments are performed to investigate laminar-turbulent transition in the flow of Newtonian and viscoelastic fluids in soft-walled microtubes of diameter ∼400 μm by using the micro-particle image velocimetry technique. The Newtonian fluids used are water and water-glycerine mixtures, while the polymer solutions used are prepared by dissolving polyacrylamide in water. Using different tube diameters, elastic moduli of the tube wall, and polymer concentrations, we probe a wide range of dimensionless wall elasticity parameter Σ and dimensionless fluid elasticity number E. Here, Σ = (ρGR²)/η², where ρ is the fluid density, G is the shear modulus of the soft wall, R is the radius of the tube, and η is the solution viscosity. The elasticity of the polymer solution is characterized by E = (λη₀)/R²ρ, where λ is the zero-shear relaxation time, η₀ is the zero-shear viscosity, ρ is the solution density, and R is the tube radius. The onset of transition is detected by a shift in the ratio of centerline peak to average velocity. A jump in the normalized centerline velocity fluctuations and the flattening of the velocity profile are also used to corroborate the onset of instability. Transition for the flow of Newtonian fluid through deformable tubes (of shear modulus ∼50 kPa) is observed at a transition Reynolds number of Re_t ∼ 700, which is much lower than Re_t ∼ 2000 for a rigid tube. For tubes of lowest shear modulus ∼30 kPa, Re_t for Newtonian fluid is as low as 250. For the flow of polymer solutions in a deformable tube (of shear modulus ∼50 kPa), Re_t ∼ 100, which is much lower than that for Newtonian flow in a deformable tube with the same shear modulus, indicating a destabilizing effect of polymer elasticity on the transition already present for Newtonian fluids. Conversely, we also find instances where flow of a polymer solution in a rigid tube is stable, but wall elasticity destabilizes the flow in a deformable tube. The jump in normalized velocity fluctuations for the flow of both Newtonian and polymer solutions in soft-walled tubes is much gentler compared to that for Newtonian transition in rigid tubes. Hence, the mechanism underlying the soft-wall transition for the flow of both Newtonian fluids and polymer solutions could be very different as compared to the transition of Newtonian flows in rigid pipes. When Re_t is plotted with the wall elasticity parameter Σ for different moduli of the tube wall, by taking Newtonian fluids of different viscosities and polymer solutions of different concentrations, we observed a data collapse, with Re_t following a scaling relation of Re_t ∼ Σ^0.7. Thus, both fluid elasticity and wall elasticity combine to trigger a transition at Re as low as 100 in the flow of polymer solutions through deformable tubes.