Biomedical Engineering Reference
In-Depth Information
10.6
(a-c) Schematic illustration of interactions of particles with shear
flow (Chen
et al
., 2007a).
shear rates. For f <
0.01, equation 10.3 reduces to Einstein's equation
(equation 10.1) if a monomial expansion is performed and to Batchelor's
equation (equation 10.2) if a binomial expansion is performed.
Cheng and Law (2003) utilized equation (equation 10.1) and used a
numerical expansion to predict the viscosity ratio of nanofluids for dilute
concentrations empirically as:
Z
Z 0 ¼
5
2 f þ
35
8 f 2
105
16 f 3
1155
128 f 4
3003
256 f 5
1
þ
þ
þ
þ
þ
½
10
:
4
As the dynamic effects of particles and fluid are not considered in the above,
the model is applicable for only dilute concentrations of nanofluids. Using
the above stated theories, Chen et al. (2007a) studied the effect of high shear
viscosity, shear thinning behavior, and temperature effect on the behavior of
viscosity and inferred that the rheological behavior of nanofluids can be
categorized into four categories: (a) dilute nanofluids where Einstein's
equation (equation 10.1) is applicable; (b) semi-dilute nanofluids with
aggregation of nanoparticles; (c) semi-concentrated nanofluids where
aggregation of nanoparticles and shear thinning behavior can be observed;
and (d) concentrated nanofluids with interpenetration of aggregation.
Lu and Fan (2008) used a molecular dynamics simulation to predict the
effect of particle concentration and size on the viscosity of nanofluids
assuming an NVT ensemble. The shear viscosity simulated using numerical
data quite accurately fitted with the experimental data for Al 2 O 3 dispersed
in water and EG based nanofluids (Fig. 10.7). Anoop et al. (2009) predicted
the viscosity ratio of electrostatically stabilized nanofluids by modifying
equation 10.1. It was considered that the electrical double layer introduces
an additional increase in viscosity brought about by electroviscous forces.
The intrinsic viscosity value was modified as:
￿ ￿ ￿ ￿ ￿ ￿
½Z EV ¼½Zð
1
þ
p
Þ
½
10
:
5
where [
] are the intrinsic viscosity values in the presence of
electroviscous forces and with uncharged particles respectively and p is the
η
] EV and [
η
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