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

Abstract

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.