(117b) A Methodology for Adding Thixotropy to Maxwell and Oldroyd-8 Family of Viscoelastic Models for Characterization of Biomaterials | AIChE

(117b) A Methodology for Adding Thixotropy to Maxwell and Oldroyd-8 Family of Viscoelastic Models for Characterization of Biomaterials


Armstrong, M. - Presenter, United States Military Academy
Horner, J. S., University of Delaware
Corrigan, T., United States Military Academy
Tussing, J., United States Military Academy
Recent work modeling the rheological behavior of human blood indicates that blood has all of the hallmark features of a complex material, including shear-thinning, viscoelastic behavior, a yield stress and thixotropy. After decades of modeling steady state blood data, and the development of steady state models, like the Casson, Carreau-Yasuda, Herschel-Bulkley, etc. the advancement and evolution of blood modeling to transient flow conditions now has a renewed interest [1,2,5,11]. Using recently collected human blood rheological data from an ARESG2 rheometer we show and compare new modeling efforts. Starting with the recently published modified Horner-Armstrong-Wagner-Beris (mHAWB) model. We then enhance and apply the same thixotropic framework used in the mHAWB to model elastic and viscous contributions from the microstructure to the Giesekus model and two Oldroyd-8 family models: the Corotational Jeffries and the Convected Maxwell. The elastic and viscous stress contributions from the microstructure are then linearly superimposed with the viscoelastic backbone solution for stress of the Oldroyd-8 family of models. We will perform a parametric analysis, model comparison and then will compare the new approaches by ability to predict small and large amplitude and uni-directional oscillatory shear flow. The new family of models have the ability to 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. Following this we will show the results of a parametric analysis and statistical correlation between the rheological model parameters and physiological parameters of human blood and demonstrate the effect of aspirin on the rheology of human blood.

This effort is followed with a discussion of novel transient flow rheological experiments applied to human blood including for model fitting purposes including step-up/step-down, and triangle ramp experiments [7-10]. The family of models that can handle these transient flows

involve modifications to the recently published mHAWB model, and new modifications to the Oldroyd-8 family of viscoelastic models. We fist discuss the development of the scalar, structure parameter evolution models and we compare fitting results with our newly acquired transient blood data to the models [5,11], and make the case for future use of a conformation tensor to better model the effects of the microstructure at low shear rates. We also highlight our novel model fitting procedure by first fitting to steady state, and while keeping the steady state parameters constant fitting the remaining model transient parameters to a series of step up/down in shear rate experiments. With the full set of parameters determined with a global, stochastic optimization algorithm the SAOS, LAOS and unidirectional oscillatory shear flow is predicted and compared to the data. Model efficacy is then compared with cost function and number of model parameters. [12,13,14,15].


[1] Apostolidis et al. J. Rheol. (2015).

[2] Bautista et al. JNNFM (1999).

[3] S. Rogers. Rheol. Acta. (2017). DOI 10.1007/s00397-017-1008-1.

[4] Ewoldt, R. and G.H. McKinley. Rheol. Acta. (2017).

[5] M. J. Armstrong, A. N. Beris, S. Rogers, N. J. Wagner,J. Rheol. 60, 433 (2016).

[6] M. J. Armstrong, A. N. Beris, N. J. Wagner, AIChE Journal (2016).

[7] C.J. Dimitriou, R.H. Ewoldt and G.H. McKinley. J. Rheol. 571(1), 27-70.

[8] B.C. Blackwell and R.H. Ewoldt. JNNFM 208-209, (2014) 27-41.

[9] R.H. Ewoldt and N.A. Bharadwaj. Rheol. Acta. (2013) 52:201-219.

[10] N.A. Bharadwaj and R.H. Ewoldt. J.Rheol. 59(2), (2015) 557-592.

[11] Horner et al. J. Rheol.62(2), (2018) 577-591.

[12] Horner et al. J. Rheol. (2019).

[13] Ramya et al. POF (2020).

[14] Saengow et al. POF (2019).

[15] Bird et al. Dynamics of Polymeric Liquids (1987).