Biomedical Engineering Reference
In-Depth Information
ditions invariably come from real, compliant vessels, and that care must be taken
when attempting to impose them onto rigid models. Out of these considerations, it
is worthwhile to consider incorporating the effects of compliance in an approximate
way that avoids the need for expensive and cumbersome fluid structure analyses,
which anyway may be inaccurate or imprecise.
1.4 Newtonian vs. non-Newtonian rheology
Blood is a complex fluid, comprised mainly of fluid-filled vesicles in a water-like
carrier. This carrier (plasma) is mostly water with some dissolved proteins, and is
widely considered to behave as a constant viscosity (Newtonian) fluid. The fluid
filled vesicles (erythrocytes or, literally, red blood cells) normally comprise 40-45 %
of the blood by volume. RBC are normally shaped like biconcave disks having an
8-
m height [28], although they can take on a variety of shapes
depending on the prevailing flow conditions. It is this concentrated suspension of mi-
croscopic, flexible cells that gives blood its most well known non-Newtonian prop-
erty: shear-thinning.
11
As shown in Fig. 1.5, at shear rates above about 100 s
−
1
blood viscosity asymp-
totes to a constant value, variously reported to be 3-4 cPoise.
12
For shear rates below
100 s
−
1
blood viscosity starts to increase exponentially, as the stagnating RBC as-
semble into stacks or rouleaux. For most large arteries under normal, fully-developed
μ
m diameter and 2-
μ
Fig. 1.5.
Shear-thinning behaviour of blood, approximated by the Carreau and generalized power
law (Ballyk) curve fits. Adapted from [30]
11
Although blood exhibits a variety of non-Newtonian properties, as briefly discussed later, in the
large artery hemodynamics literature the term “non-Newtonian” often explicitly or implicitly refers
to shear-thinning properties alone. Many shear-thinning models have been proposed, as recently
reviewed by [29].
12
Poise is the cgs unit of dynamic viscosity, named for Poiseuille. 1 Poise = 1 dyne-s/cm
2
=
0
.
1Pa-
s. The cgs unit for kinematic viscosity is the Stokes, equivalent to cm
2
/s, and is often calculated
from the dynamic viscosity assuming a blood density of 1.06 g/cm
3
.
