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.

Blood rheology shows viscoelastic, thixotropic (using a structural parameterλ) and viscoplastic characteristics shown in steady stressvs.shear-rate data.

We offer here an extension of our previous work [Apostolidis and Beris, J. Rheol. 58, 607–633 (2014)] of modeling blood flow rheology in simple shear steady state flows to time-dependent conditions. The basis of our model is a scalar, structural, parameter thixotropic model. More specifically, we show that a modified version of the “Delaware model” [A. Mujumdar et al., J. Non-Newtonian Fluid Mech. 102, 157–178 (2002)] is capable of predicting the time-dependent shear flow rheology of blood at low and moderate values of shear rate. At steady state, the model reduces to the Casson constitutive model for low and moderate shear rate values consistent to the findings of our previously mentioned work. At high shear rates it reduces to a Newtonian model, correcting our previous model and consistent to data from the literature [Merrill and Pelletier, J. Appl. Physiol. 23, 178–182 (1967)]. Exploiting the existing parameterization developed before for the steady state Casson model and the Merrill and Pelletier steady state data, the transient thixotropic model introduces only three additional parameters. Each one of these parameters has a specific physical meaning: A zero-shear rate maximum strain, and two kinematic parameters governing the relaxation of the structural parameter and the elastic modulus, respectively. The model is able to naturally account for the additional yield strengthening effect attributable to the red blood cell rouleaux structures developed within blood. The proposed model can fit excellently the experimental data of Bureau et al. [Biorheology 17, 191–203 (1980)], on simple triangular steps in shear flow at low shear rates. The predictions of the present model are then validated comparing them against additional experimental data, collected on the same samples, either on triangular steps in shear flow but at higher shear rates or on rectangular step-up and step-down experiments. The model is further validated by comparing its predictions against recent large amplitude oscillatory shear data [P. C. Sousa et al., Biorheology 50, 269–282 (2013)]. In all these comparisons there is good, at least semiquantitative, agreement, with the observed discrepancies only appearing at the higher shear rates, where the isotropic description resulting from the use of a single scalar internal parameter to describe the blood microstructure naturally breaks down.

New in vitro measurements from two human donors for both steady and transient hemorheology are presented that are particularly suited for testing thixotropic and viscoelastic models for human blood and are made available to the community along with the relevant blood physiology. This more complete data set is analyzed within the context of recent thixo-elasto-visco-plastic models, and we improve upon the Horner-Armstrong-Wagner-Beris (HAWB) model to better model transient hemorheology. The improved model features an additional viscoelastic equation for the red blood cell rouleaux within blood, along with simplifications to the structure kinetics equation. The resulting model is fit to additional experimental data on human whole blood for a step shear change and steady shear experiments, and the corresponding parameter values are used to predict oscillatory shear moduli, transient large amplitude oscillatory shear, and unidirectional large amplitude oscillatory shear data. The modified HAWB model shows significant improvement in fitting and predicting the experimental data. Specifically, a significant overshoot is captured in step shear changes from a low shear rate to a moderate shear rate, and a plateau for the storage modulus is observed at low frequencies. Highly nonlinear behavior is observed for the third harmonic in unidirectional large amplitude oscillatory shear in the form of multiple extremum separated widely in frequency, which can be identified with the two dominant mechanisms for generating viscoelasticity in human blood, namely, rouleaux structuring and red blood cell deformation. We also discuss the potential applications and difficulties associated with the constitutive modeling of transient blood rheology and provide insight into microstructural sources of the stress contributions to the bulk flow behavior.

We present new dynamic rheological tests of human blood that motivate an improved model for the thixotropic shear rheology of human blood. Unidirectional large amplitude oscillatory shear (UD-LAOS) is proposed as a dynamic test relevant for understanding in vivo arterial pulsatile blood flow, and data are presented for two healthy donors studied previously using more traditional steady and step-rate experiments. The model analyzes the overall extra stress of the system in two components. A thixotropic component is represented by a structure-kinetics model coupled with a stress expression containing both viscoelastic and thixotropic elements to account for the presence of linear aggregates of red blood cells, known as rouleaux, which form at low shear rates. Another component is viscoelastic, described through an extend White–Metzner approach. It corresponds to the stresses that arise due to the isolated red blood cells, which deform at high shear rates. The combined model is fit to experimental steady she...