Modeling of human blood rheology in transient shear flows

Abstract

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.