A methodology for adding thixotropy to Oldroyd-8 family of viscoelastic models for characterization of human blood

Recent work modeling the rheological behavior of human blood indicates that blood has all the hallmark features of a complex material, including shear-thinning, viscoelastic behavior, a yield stress, and thixotropy. After decades of modeling only the steady state blood data, steady state models, such as the Casson, Carreau-Yasuda, and Herschel-Bulkley models, have been developed. The advancement and evolution of blood modeling to transient flow conditions now has renewed interest. Using recently collected human blood rheological data from a strain-controlled rheometer, we show and compare a new modeling effort using the Oldroyd-8 viscoelastic framework as a foundation. This foundation is enhanced with the application of a recent thixotropic framework recently published to model elastic and viscoelastic contributions from the microstructure to three Oldroyd-8 families of models: the corotational Jeffreys model, the convected Maxwell model, and the Oldroyd 4-constant model. The elastic and viscoelastic stress contributions from the microstructure are then linearly superimposed with the viscoelastic backbone solution for stress given by the Oldroyd-8 family of models. Demonstrated here is a parametric analysis, model comparison, and a comparison of the new approaches made using the ability to predict large amplitude oscillatory shear and uni-directional large amplitude oscillatory shear flow. The new family of models can solve components of the full stress tensor, making them ideal for use with a future conformation tensor to evolve, model, and better understand the effects of the microstructure of human blood. In addition, there is now a methodology to model the normal forces of blood.