Biomedical Engineering Reference
In-Depth Information
sections, we first introduce the notion of non-Newtonian fluid, and present the
example of biological polymeric solutions.
2.2.2.2
ViscosityofNon-NewtonianFluids
The usual definition of the shear viscosity is
η τ = (2.15)
where τ is the shear stress (unit Pa) and γ is the shear rate (unit s -1 ). Usual liquids
like water and oil are said to be Newtonian because the relation between the shear
stress and the shear rate is linear. The viscosity η is a constant for a Newtonian fluid
(at a given temperature and pressure). Polymeric solutions behave differently. The
shear stress is not proportional to the shear rate and viscosity depends on the shear
rate. The rheological behavior of polymeric liquids depends on the conformation of
the polymeric chains (Figure 2.9).
It is obvious that the global rheological properties of the polymeric liquid will
be different if the chains are in majority stretched or coiled. In a shear flow the
polymeric chains stretch when the shear increases, resulting in a decrease of the vis-
cosity. Such a behavior is called shear-thinning . Typical shear-thinning behavior is
shown in Figure 2.10. In the case of blood, the red blood cells deform and elongate
under shear stress. Note that shear is not the only cause of change of polymer struc-
ture in the liquid. Elongational flows also modify the polymer's morphology [8].
Basically, the viscosity of a visco-elastic polymeric liquid depends on the con-
centration in polymers, the temperature, and the flow characteristics. Dropping the
pressure, we simplify the approach by writing
= (
)
η η γ
c T
,
,
(2.16)
2.2.2.3
SpeciicandIntrinsicViscosity:ViscosityasaFunctionofConcentration
In rheology of polymers, it is usual to define the specific viscosity as
η η
-
s
η
=
(2.17)
sp
η
s
Figure  2.9  Different morphologies of a polymeric chain calculated with a molecular dynamic
method(MD).(a)Atalowshearrate,thepolymeriscoiledinanearlysphericalshape,and(b)ata
highshearrate,thepolymerstretches(MDcalculationbyKatzetal.).
 
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