498
Chapter 11
Table 11.6. Viscosity of some fluids (Adapted from Johnson, 1999).
Fluid
Temperature (°C)
r}
(kg m'1
s'1)
Water
0
1.793 10j
21
9.84 10*4
100
5.59
{O'4
Ethanol
20
1.20 10'3
Glycerol
60
0.98
Sucrose solution (20 wt%)
21
1.916 10'3
Sucrose solution (60 wt%)
21
6.02 10'2
Olive oil
30
8.40 10'2
Molasses
21
»6.6
A typical functional relationship for shear rate dependent viscosity is the so-called
power law model
(or
Ostwaldde Waele model):
ri = K \y\-'
(
11
.
21
)
K is the
consistency index
and
n
is the
power law index
. In accordance with previous definitions, it
can be seen that if
n >
1, the fluid is dilatant, and if n < 1, it is pseudoplastic. For a Newtonian fluid
n=
1.
For Bingham fluids, the shear stress is given by
r = r 0
- rtf
(11.22)
where T0 is the yield stress. A material which exhibits both a yield stress and pseudoplasticity is
often described by an empirical model named after Casson:
MftS=|r0f
+ K c\y\°'s
(11.23)
The different kinds of shear-rate dependent rheological behaviors are schematically shown in Fig.
11
.
8
.
The viscosity may also change with time. A
decrease o f viscosity with time
is called
thixotropy
,
whereas
an increase o f viscosity with time
is call
rheopexy.
Thixotropy, as well as pseudoplastisticy,
is often observed in polymer solutions. It is caused by irreversible breaking of bonds between long
macromolecules, or breakdown of hyphae. Rheopectic behavior is rather unusal, but clotting blood
can be named as one example.
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