Biomedical Engineering Reference
In-Depth Information
Figure 4.5
Alterations in viscosity: (a) non-Newtonian fl uids, (b) apparent viscosity, and (c) the
Fahraeus-Lindqvist effect.
Many of the biological fluids are non-Newtonian. Although non-Newtonian be-
havior has a low effect on flow resistance, its effect on flow separation is more
significant near the boundaries. Non-Newtonian fluids can be grouped into two
subgroups, one where properties are independent of time under shear and the other
dependent on time.
The viscosity of non-Newtonian fluids changes with shear rate. Thus, experi-
mental parameters such as the shear rate affect the measured viscosity while mea-
suring the viscosity of these solutions. To distinguish from Newtonian viscosity, the
measured viscosity is called the apparent viscosity (
μ
app
). It is calculated using the
local slope of a
curve and accurate when explicit experimental parameters are
adhered to. For example,
τ
−
γ
C is highly sensitive to shear rates less
than 100 s
−1
[Figure 4.5(b)] and decreases with an increase in shear rate. Apparent
viscosity of synovial fluids is around 10 kg/m-s at 0.1 s
−1
shear rate (a rate resem-
bling knee flexes during very slow walking), which decreases to ~ 0.1 kg/m.s at
10 s
−1
(very fast running). Similarly,
μ
app
of blood at 37
°
μ
app
of respiratory tract mucus is 1 kg/m-s at
0.1-1 s
−1
shear rates, which decreases to ~ 0.01 kg/m-s at 100-1,000 s
−1
shear rates.
Normal blood and some deoxygenated sickle cell blood are classified into
shear-thinning (non-Newtonian) fluids, and can be described by Casson's equation
[1], an empirical relationship for fluids deviating from the ideal Bingham plastic
behavior.
τ
=+
τ
μγ
(4.18)
0
C
where
μ
c
is the Casson viscos-
ity, which is the viscosity at high shear rates. Casson's equation suffices for time-
dependent, one dimensional simple stream patterns. For complicated flow patterns,
τ
0
is the yield stress (0.04 dyne/cm
2
at 37
°
C) and
