Modeling of the blood rheology in steady-state shear flows
Modeling of the blood rheology in steady-state shear flows
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DOI：
10.1122/1.4866296
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发表时间：
2014-05-01
影响因子：
3.3
通讯作者：
Beris, Antony N.
中科院分区：
文献类型：
--
作者：
Apostolidis, Alex J.;Beris, Antony N.
我们在这里进行一个系统的研究血液在稳态剪切流的流变学。由于血液是一种复杂的流体，我们试图回答的第一个问题是，即使在稳态剪切流中，我们是否可以将其建模为流变学简单的流体，即，我们可以通过仅涉及局部运动学量的本构模型来描述其行为。在肯定地回答了这个问题之后，我们接着探讨哪种非牛顿模型最适合现有的剪切应力与剪切速率的文献数据。我们表明，在生理条件下，血液通常是粘塑性的，即，其表现出作为流动的最小阈值的屈服应力。我们进一步表明，卡森模型自然出现的最佳近似，至少在低和中等剪切速率。然后，我们系统地开发一个参数依赖性的流变参数进入卡森模型的关键生理量，如红细胞体积分数（红细胞压积）。对于屈服应力，我们的描述是基于它的临界性和屈服起源的性质。因此，我们首先确定起始条件，即，红细胞压积必须具有的临界阈值，以便出现屈服应力。它表明，这是一个关键的红细胞结合蛋白，纤维蛋白原的浓度的函数。然后，我们建立了一个参数依赖的纤维蛋白原和红细胞压积从其临界值的差异的平方的函数。同样，我们提供了一个表达式的卡森粘度，在红细胞压积和温度。根据额外的实验文献数据成功验证了所提出的公式。所提出的表达式预计是有用的，不仅为稳态血流建模，但也提供了瞬态剪切，或更一般的流动建模的起点。(C)2014流变学学会。
We undertake here a systematic study of the rheology of blood in steady-state shear flows. As blood is a complex fluid, the first question that we try to answer is whether, even in steady-state shear flows, we can model it as a rheologically simple fluid, i.e., we can describe its behavior through a constitutive model that involves only local kinematic quantities. Having answered that question positively, we then probe as to which non-Newtonian model best fits available shear stress vs shear-rate literature data. We show that under physiological conditions blood is typically viscoplastic, i.e., it exhibits a yield stress that acts as a minimum threshold for flow. We further show that the Casson model emerges naturally as the best approximation, at least for low and moderate shear-rates. We then develop systematically a parametric dependence of the rheological parameters entering the Casson model on key physiological quantities, such as the red blood cell volume fraction (hematocrit). For the yield stress, we base our description on its critical, percolation-originated nature. Thus, we first determine onset conditions, i.e., the critical threshold value that the hematocrit has to have in order for yield stress to appear. It is shown that this is a function of the concentration of a key red blood cell binding protein, fibrinogen. Then, we establish a parametric dependence as a function of the fibrinogen and the square of the difference of the hematocrit from its critical onset value. Similarly, we provide an expression for the Casson viscosity, in terms of the hematocrit and the temperature. A successful validation of the proposed formula is performed against additional experimental literature data. The proposed expression is anticipated to be useful not only for steady-state blood flow modeling but also as providing the starting point for transient shear, or more general flow modeling. (C) 2014 The Society of Rheology.