Tensorial formulations for improved thixotropic viscoelastic modeling 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, yield stress, and thixotropy. There is renewed interest in the modeling of human blood with thixo-elasto-visco-plastic rheological models. Previous work [Armstrong and Tussing, Phys. Fluids 32, 094111 (2020)] has led to the development of the enhanced thixotropic viscoelastic model for blood (ethixo-mHAWB; called here, after a minor modification, ETV) that incorporates viscoelasticity to a thixotropic model for the stress contributed by the rouleaux aggregates, in addition to describing using a nonlinear viscoelastic model the stress contributed by the individual red blood cells deforming under the action of the flow. This model has shown superior performance in fitting human blood steady state and transient rheological data from a strain-controlled rheometer [Horner et al., J. Rheol. 62, 577–591 (2018); 63, 799–813 (2019)] as compared to other alternate models. In the present work, we first develop another variant of the ETV model, the enhanced structural stress thixotropic-viscoelastic (ESSTV) model, and the modification patterned following an elastoviscoplastic model developed recently [Varchanis et al., J. Rheol. 63, 609–639 (2019)]. We develop full tensorial stress formulations of the rouleaux stresses for both the above-mentioned models, resulting in the t-ETV and t-ESSTV models. We use steady state and step-ups, and step-downs in shear rate data to independently fit the parameters of all before-mentioned models. We compare predictions against experimental data obtained on small, large, and unidirectional large amplitude oscillatory shear conditions. We find that the full tensor stress formulations t-ETV and t-ESSTV significantly improved the predictive capability of the earlier ETV model.

Recent Advances in Biofluid Mechanics and Bio- and Hemorheology Collating Recent Advances in Predicting Complex Behavior of Human Blood With Thixo-Elasto-Visco-Plastic Models and Sequence of Physical Process

“…where τ break is the characteristic time of shear breakage, τ aggr is the characteristic time of shear aggregation, and d is set to ½ for human blood, an optimum value from the literature [8-10, 40, 41, 43] (Previous work has incorporated the characteristic time of shear aggregation outside the absolute value; we note this is for convenience and does not change the mathematics of structure evolution [41,46]). We note here that _ γ p is the plastic shear rate and the portion of the total shear rate that is associated with plastic deformation of the microstructure derived from: [8, 9, 33, 33-35, 41, 45, 46].…”

“…The demonstrated behavior of rouleaux under evolving force conditions, are the descriptions of rouleaux breakdown and agglomeration over time per τ break and τ aggr respectively [46]. These each present the breakdown and agglomeration of rouleaux in a comparative ratio to the Brownian microstructure aggregation constant.…”

“…The developments were accompanied by the parallel development of the viscoelastic enhanced Modified Delaware Thixotropic (VE-MDTM) in incorporating a viscoelastic evolution timescale into the total stress term produced by rouleaux module of the original MDTM system. In this, the presence of a unique timescale associated with the viscoelastic stress contribution of suspended rouleaux was successfully demonstrated [45][46][47][48][49]. Per the Armstrong-Frederick kinematic hardening rule, KH and IH approaches can be applied to currentgeneration TEVP models, allowing for enhanced model step-test performance when used in conjunction with other thixotropic and viscoelastic terms [36,37,43,44].…”

“…The ETV, and ESSTV [46] performance in fitting steady state and transient data to observed blood rheology was substantially improved compared to earlier-generation models; however, the most recent modifications of ETV have applied a novel viscoelastic module to apply recently published approaches to plasticity to better express both the plastic and elastic contributions to stress from the rouleaux microstructure [31,36,37,[46][47][48][49]. In understanding the rheology, and mechanical properties of blood, it is useful to analyze its response under a few experimental shear conditions due to the dynamic nature of blood viscoelasticity.…”

“…where, Gc is the elastic modulus of the plasma and individual RBCs and μ C (σ ve,xx ) is mathematically described below in Table 1 [8,9,46]. The equations have been derived previously, using a White-Metzner approach, with a Cross model substituting for the viscosity:…”