Flow Enhancement due to Elastic Turbulence in Channel Flows of Shear Thinning Fluids

We explore the flow of highly shear thinning polymer solutions in straight geometry. The strong variations of the normal forces close to the wall give rise to an elastic instability. We evidence a periodic motion close the onset of the instability, which then evolves towards a turbulentlike flow at higher flow rates. Strikingly, we point out that this instability induces genuine drag reduction due to the homogenization of the viscosity profile by the turbulent flow. Viscoelastic polymer solutions are characterized by a relaxation time λ required by the polymer molecules to adjust to changes in the flow conditions. This time is at the origin of purely elastic instabilities observed at very low Reynolds numbers with no counterpart in pure Newtonian fluids. In shear flows, purely elastic instabilities arise due to stress tensor anisotropy inducing a destabilizing net force perpendicularly to curved streamlines [1–3]. These instabilities can lead to purely elastic turbulence [4–6]. In straight channels, theoretical studies demonstrate that the viscosimetric properties of the fluid play a major role in the stability of the flow. Plane Couette flows [7] and Poiseuille flows [8] of Oldroyd-B fluids exhibit a nonlinear subcritical elastic instability although the base flow is linearly stable [9]. Recent experiments [10,11] have shown that finite amplitude perturbation creates curved stream-lines that drive the instability. In contrast, channel flows of highly shear thinning fluids [12–14] are theoretically linearly unstable. The instability is driven in this case by the strong variations of both normal stress and viscous dissipation in the shear direction. An extreme situation is obtained with shear banding fluids, where the interface bears an unbalanced normal stress [14]. This leads to an interfacial instability which has been observed experimen-tally [15]. A similar mechanism is theoretically expected without shear banding but requires a strong gradient of shear rate [13]. At this stage, channel flow stability of such liquids has not been studied experimentally, although shear thinning is a very common feature of elastic fluids. In this Letter, we focus on highly shear thinning elastic polymer solutions with no shear banding flowing in straight channels. At low flow rates, no velocity fluctuations are observed. At higher flow rates, the power spectrum density of the velocity fluctuations displays a distinct peak indicat-ing the onset of instability. The position of the peak is in agreement with theoretical predictions for highly shear thinning fluids [13]. At even higher flow rates, the fluctuations occur at all scales and the spectrum becomes broadband with a power law decay. This instability induces genuine drag reduction: viscous losses are smaller than expected from the fluid rheology. This is a remarkable result since one expects additional energy losses due to the enhancement of velocity fluctuations. We study the flow of high molecular weight polymer solutions (18 × 10 6 g=mol partially hydrolyzed polyacry-lamide) in water at different concentrations in the semi-dilute regime. The global flow curves of these solutions are determined using the shear-rate-imposed mode of a rheometer (TA Instruments ARG2) in a sanded cone-and-plate geometry of angle θ ¼ 2°. Figure 1 reports both the shear stress σ and the Weissenberg number Wi ¼ N 1 =2σ a