Viscoelastic fluids are a common subclass of rheologically complex materials that are encountered in diverse fields from biology to polymer processing. Often the flows of viscoelastic fluids are unstable in situations where ordinary Newtonian fluids are stable, owing to the nonlinear coupling of the elastic and viscous stresses. Perhaps more surprisingly, the instabilities produce flows with many of the hallmarks of turbulence—even though the effective Reynolds numbers may be $O\left(1\right)$ or smaller. We provide perspectives on viscoelastic flow instabilities by integrating the input from speakers at a recent international workshop: historical remarks, characterization of fluids and flows, discussion of experimental and simulation tools, and modern questions and puzzles that motivate further studies of this fascinating subject. The materials here will be useful for researchers and educators alike, especially as the subject continues to evolve in both fundamental understanding and applications in engineering and the sciences.

Additive manufacturing (AM) techniques and so-called 2D materials have undergone an explosive growth in the past decade. The former opens multiple possibilities in the manufacturing of multifunctional complex structures, and the latter on a wide range of applications from energy to water purification. Extrusion-based 3D printing, also known as Direct Ink Writing (DIW), robocasting, and often simply 3D printing, provides a unique approach to introduce advanced and high-added-value materials with limited availability into lab-scale manufacturing. On the other hand, 2D colloids of graphene oxide (GO) exhibit a fascinating rheology and can aid the processing of different materials to develop ‘printable’ formulations. This work provides an in-depth rheological study of GO suspensions with a wide range of behaviours from Newtonian-like to viscoelastic ‘printable’ soft solids. The combination of extensional and shear rheology reveals the network formation process as GO concentration increases from <0.1 vol% to 3 vol%. Our results also demonstrate that the quantification of ‘printability’ can be based on three rheology parameters: the stiffness of the network via the storage modulus (G′), the solid-to-liquid transition or flow stress (σ_f), and the flow transition index, which relates the flow and yield stresses (FTI = σ_f/σ_y).

In the current study, we report the results of a detailed and systematic numerical investigation of developing pipe flow of inelastic non-Newtonian fluids obeying the power-law model. We are able to demonstrate that a judicious choice of the Reynolds number allows the development length at high Reynolds number to collapse onto a single curve (i.e., independent of the power-law index $n$). Moreover, at low Reynolds numbers, we show that the development length is, in contrast to existing results in the literature, a function of power-law index. Using a simple modification to the recently proposed correlation for Newtonian fluid flows (Durst, F., 2005, “The Development Lengths of Laminar Pipe and Channel Flows ,” J. Fluids Eng., 127, pp. 1154–1160) to account for this low Re behavior, we propose a unified correlation for $XD∕D$, which is valid in the range $0.4<n<1.5$ and $0<Re<1000$.

The characteristics of convective heat transfer and fluid flow within a square cross-section serpentine channel are experimentally studied for two groups of polymeric viscoelastic fluids, shear-thinning and constant-viscosity Boger solutions. The elastic turbulence can be created by the non-linear interaction between elastic stresses generated within the flowing high-molecular-weight polymer solutions and the streamline curvature. In order to confirm elastic turbulence in this geometry, pressure drop across the serpentine channel was measured. The findings indicate that the measurements of non-dimensional pressure-drop increase approximately from 1.48 to 4.82 for viscoelastic solutions compared with the Newtonian fluid over a range of Weissenberg number from 4 to 211. The convective heat transfer enhances due to elastic turbulence by up to 200% for low polymer concentration (dilute) solutions and reaches up to 380% for higher polymer concentration (semi-dilute) solutions under creeping-flow conditions in comparison to that achieved by the equivalent Newtonian fluid flow at low Graetz number (up to 14.6). We propose a modified Weissenberg number which is able to approximately collapse the mean Nusselt number data for each solution group

In this study, we experimentally investigate the turbulent drag-reduction (DR) mechanism in flow through ducts of circular, rectangular and square cross-sections using two grades of polyacrylamide in aqueous solution having different molecular weights and various semidilute concentrations. Specifically, we explore the relationship between drag reduction and fluid elasticity, purposely exploiting the mechanical degradation of polymer molecules to vary their rheological properties. We also obtain time-resolved velocity data for various DR levels using particle image velocimetry and laser Doppler velocimetry. Elasticity is quantified via relaxation times determined from uniaxial extensional flow using a capillary breakup apparatus. A plot of DR against Weissenberg number ( $Wi$ ) is found to approximately collapse the data, with the onset of DR occurring at $Wi\approx 0.5$ and the maximum drag-reduction asymptote being approached for $Wi\gtrsim 5$ . Thus quantitative predictions of DR in a range of shear flows can be made from a single measurable material property of a polymer solution, at least for this particular flexible linear polymer.