Biomedical Engineering Reference
In-Depth Information
10.5
Variation of relative viscosity of different nanofluids as a function
of dispersed particle size summarized from the available literature
(Table 10.1).
where [
] is the intrinsic viscosity with a value of 2.5 for mono-dispersed
hard spheres and equation 10.1 is applicable for concentrations
f <
η
0.01.
0.01, the hydrodynamic interactions
between particles are considered as the disturbance of fluid around one
particle interacting with that around other particles. The viscosity of
colloidal suspensions in such a condition was predicted by Batchelor (1977)
as:
For particle concentrations
f >
Z
Z
0
¼
2
3
1
þ½Zf þ
k
H
ð½ZfÞ
þ
O
ðfÞ
½
10
:
2
where k
H
is the Huggin's coefficient and can be considered as the interaction
parameter characterizing the colloidal interactions between particles.
Equation 10.2 is valid for
f
= 0.1 for flows dominated by particle-pair
microstructures (shown in Fig. 10.6(b)).
At higher concentrations (
f >
0.01), multi-particle collisions (Fig. 10.6
(c)) become more prominent and hence the third and higher order terms
have to be rigorously analyzed. Considering such factors, Kreiger and
Dougherty (1959) derived a semi-empirical relationship for viscosity as a
function of the volume fraction of dispersed particles:
½Zf
m
Z
Z
0
¼
f
f
m
1
½
10
:
3
where
f
m
is the maximum particle packing fraction varying in the range of
0.495 to 0.540 under quiescent conditions and is approximately 0.605 at high
