JOURNAL OF APPLIED PHYSICS 107, 054317 共2010兲

Effects of shear rate and temperature on viscosity of alumina

polyalphaolefins nanofluids
Sheng-Qi Zhou,1,2,a兲 Rui Ni,2 and Denis Funfschilling2,3
1
Laboratory of Tropical Marine Environmental Dynamics, South China Sea Institute of Oceanology,
Chinese Academy of Sciences, Guangzhou 510301, China
2
Department of Physics, The Chinese University of Hong Kong, Satin, Hong Kong, China
3
LSGC CNRS—GROUPE ENSIC, BP 451, 54001 Nancy Cedex, France
共Received 24 September 2009; accepted 9 January 2010; published online 15 March 2010兲
In this paper, the shear rate and temperature dependencies of viscosity of alumina nanofluids have
been investigated experimentally. The alumina nanofluids are suspensions of alumina nanospheres
or nanorods in polyalphaolefins 共PAO兲 lubricant. The base fluid PAO has a Newtonian behavior. To
the first approximation, nanofluids of volume fractions ␾ = 1% and 3% nanospheres as well as
nanofluid of ␾ = 1% nanorods can be considered as Newtonian fluids because their viscosity shows
very weak shear rate dependence. However, our measurement clearly indicates that these nanofluids
demonstrate certain non-Newtonian feature due to the addition of nanoparticles. Moreover, the
relative viscosity 共the ratio of viscosity of nanofluid to that of PAO兲 of these nanofluids has been
measured to be independent of temperature. Nanofluid of a higher volume fraction ␾ = 3% nanorods
has an apparent non-Newtonian shear thinning viscosity and a strong temperature dependence of its
relative viscosity. By reviewing the previous studies, the approximation that the viscosity is
Newtonian and the relative viscosity is independent of temperature seem to hold for most nanofluids
of low volume fraction ␾ and low aspect ratio nanoparticles. © 2010 American Institute of Physics.
关doi:10.1063/1.3309478兴

I. INTRODUCTION ratio 共the ratio between the length and the diameter of the
particle兲, and aggregate size if aggregation occurs.1–3,8–12 In
Nanofluids are the suspensions where the nanosize me- this paper, we would address two other important issues of
tallic, metal-oxide, or nonmetallic particles are dispersed in nanofluid. The first one is: what is the shear-rate dependence
the base fluids 共BFs兲. The BFs are common-used cooling of the viscosity of nanofluid? In other words, is the viscosity
liquids, such as water, water and ethylene glycol mixture, of nanofluid Newtonian or non-Newtonian? The second is:
engine oil 关e.g., polyalphaolefins 共PAO兲兴, and so on. Because what is the temperature dependence of viscosity of nano-
of their remarkable higher thermal conductivity compared to fluid? As reviewed below, both issues are very important for
the BFs, nanofluids have attracted more and more attention the fundamental understanding of nanofluids as well as their
since the first study in 1995.1–3 For example, it has been heat transfer applications.
reported that nanofluids of a small amount 共the volume frac- Newtonian and non-Newtonian fluids have completely
tion ␾ ⬍ 1%兲 of copper nanoparticles in ethylene glycol and different rheological behaviors. The viscosity is independent
carbon nanotubes in oil can increase the thermal conductivity of shear rate in the case of a Newtonian fluid. Whereas for a
of the liquid by 40% and 161%, respectively.4–6 In compari- non-Newtonian fluid, the viscosity does depend on the shear
son to the thermal application of fluids with micrometer size rate, so that the viscosity is sometimes a complicated func-
particles, these nanofluids are very stable 共within 1 month7兲 tion of the shear rate. Similar to many colloidal suspensions
and almost free from problems of sedimentation, erosion, where micrometer-size particles are dispersed in a Newton-
and pressure drop. All these novel features enable nanofluids ian fluid,13–16 some nanofluids have been observed to exhibit
to potentially meet the increasing demand for high thermal non-Newtonian behaviors.17–22 However, other nanofluids
conductive working fluids. Also nanofluids will have a sig- have been concluded to have Newtonian viscosities.8–10,23–30
nificant impact on energy conservation and pollution reduc- What is the main reason or factor for such different behav-
tion if they can be successfully applied in the thermal appli- iors? This is one motivation of this work.
cation. The study of the temperature dependence of viscosity of
In the actual thermal management, the nanofluids are nanofluids is very important because it influences the hydro-
expected to be used under the flow conditions, so the rheo- dynamics and, through that, influences the heat transfer of
logical properties of nanofluid would affect its heat transfer cooling system. In this study, one concern is whether the
performance, in which the viscosity surely plays a vital role. temperature dependence of viscosity of nanofluids is domi-
The viscosity of nanofluids is affected by many factors, such nated by BF or influenced by nanoparticles. This can be rep-
as the volume fraction ␾, the particle size, the particle aspect resented by the relative viscosity between nanofluid and
based fluid, which is defined as ␮r = ␮nf / ␮ f , where ␮ is the
a兲
Author to whom correspondence should be addressed. Electronic mail: dynamic viscosity and the subscripts nf and f refer to the
sqzhou@phy.cuhk.edu.hk. nanofluid and BF, respectively. By reviewing the previous

0021-8979/2010/107共5兲/054317/6/$30.00 107, 054317-1 © 2010 American Institute of Physics

054317-2 Zhou, Ni, and Funfschilling J. Appl. Phys. 107, 054317 共2010兲

experimental works on temperature dependence of viscosity

in nanofluid,8–11,22–25,28–35 we find there are only few reports
on the temperature dependence of relative viscosity 共␮r兲 of
nanofluid. In some cases, ␮r decreases with the increasing
temperature,28,30 but recently, it has been observed for sev-
eral nanofluids of low volume fraction particles that ␮r is
independent of temperature.8,9,25,32 It is the other motivation
to elucidate these conflicting results as well as to obtain a
better understanding of temperature dependence of viscosity
of nanofluids.
To our knowledge, the viscosity of metallic or metallic
oxide nanoparticles nanofluids has been mostly measured for
FIG. 1. Dynamic viscosities as a function of shear rate at temperature of
water based and ethylene glycol based nanofluids, but not 25 ° C for the BF 共solid diamonds兲, nanofluids of volume fraction 1% 共solid
too much for oil 共PAO is a synthetic engine oil兲 based ones. squares兲 and 3% 共open squares兲 alumina nanospheres, and nanofluids of
Given its importance on the heat transfer, we measured the volume fraction 1% 共solid circles兲 and 3% 共open circles兲 alumina nanorods.
viscosity of the PAO based alumina nanofluids. Their shear
rate and temperature dependencies were measured by using the stress stepwise. For each shear rate, the measurements
an ARG2 rheometer and a capillary viscometer, respectively. were performed under steady-shear conditions after a waiting
The experimental results were employed to characterize the period of 120 s.
rheology of nanofluids as well as to resolve the issues men- An Ubbelohde capillary viscometer 共inner diameter 1.2
tioned above. The rest of the paper is organized as follows. mm, ShenLi Glass Labware, Shanghai, China兲 was em-
In Sec. II we describe the sample and the measurement ployed to measure the viscosities of samples at different tem-
equipments in details. The results and discussions are pre- peratures. The capillary tube was placed into a temperature-
sented in Sec. III. We first discuss the shear rate dependence controlled water bath so that the temperature stability could
of viscosity of nanofluids. After comparison to the previous be maintained within 0.1 ° C. With this capillary viscometer,
literature, aggregation of nanoparticles has been considered we measured the time taken for a known amount of liquid to
to understand the rheology of nanofluid. Then we present the pass through the constant length of capillary, and then Poi-
results of the relative viscosity ␮r as a function of tempera- seuille equation was applied to determine the viscosity val-
ture. By reviewing the previous work, we discuss whether ues. We compared the viscosities measured with the ARG2
there is a general relationship between relative viscosity of and capillary rheometer and found a good agreement be-
nanofluid and temperature. A brief summary of the results is tween them within experimental uncertainty 共as shown in
given in Sec. IV. Fig. 4 below兲.

III. RESULTS AND DISCUSSIONS

II. EXPERIMENT SETUP A. Shear rate-dependence
There are five samples in our work. The samples were As done in Refs. 9, 17, 19, 20, 23–26, and 28, the dy-
supplied by Sasol Inc. as part of an international nanofluid namic viscosities of different samples have been plotted to-
property benchmark exercise 共INPBE兲.36 The BF is PAO lu- gether in Fig. 1 for comparison. For the same volume frac-
bricant mixed with certain surfactant. The nanofluids are sus- tion, the viscosity in nanofluids of nanorods is larger than
pensions of alumina nanospheres or nanorods in the BF. It is that of nanospheres because the aspect ratio of rods are larger
claimed that the nominal diameter of the nanoparticles, that than that of nanoparticles, which is consistent with the pre-
can be considered as spheres with a good approximation, is vious work.37 While for the nanofluids of the same nanopar-
10 nm and that of nanorod size is 80⫻ 10 nm. However, the ticles, the viscosity of nanofluid increases with the increasing
dynamic light scattering measurement suggests that the av- volume fractions, which also agrees with the observations in
erage size of nanoparticles is around 100 nm,36 which may other studies.8–10,17–30 As shown in Fig. 1, it is clearly dem-
imply that aggregation occurs in these samples. Based on onstrated that the nanofluid of ␾ = 3% nanorods 共NF4兲 has a
various particle shapes and concentrations, the four samples non-Newtonian viscosity. It has a Newtonian plateau for
are 1% alumina nanospheres nanofluid 共NF1兲, 3% alumina shear rate ␥ lower than 1 s−1, and an obvious shear-thinning
nanospheres nanofluid 共NF2兲, 1% alumina nanorods nano- behavior for shear rate over this value. For the other samples
fluid 共NF3兲, and 3% alumina nanorods nanofluid 共NF4兲. 共BF, NF1, NF2, and NF3兲, at first approximation, their vis-
The rheological behavior of the BF and nanofluids was cosities vary little in the shear rate range under test, thus they
measured by a stress-controlled rheometer in a cone-plate appear to be Newtonian fluids.
configuration 共Model ARG2, TA Instruments, Delaware, However, in Fig. 1, the detailed trend of the viscosity
USA兲. In this rheometer, the magnetic thrust bearing tech- data of samples BF, NF1, NF2, and NF3 cannot be well
nology is used so that ultralow torque 共the torque resolution discerned due to the compressed scale coming from the large
of the ARG2 is 0.1 nN m兲 can be detected. During the mea- viscosity of NF4 共␾ = 3.0% nanorods兲. The viscosities of
surement, the working temperature was set at 25 ° C, the these four samples have been plotted again in the individual
shear rate decreased from 500 to 0.01 s−1 with decreasing figures in Fig. 2. Figure 2共A兲 shows the dynamic viscosity of
054317-3 Zhou, Ni, and Funfschilling J. Appl. Phys. 107, 054317 共2010兲

FIG. 3. 共a兲 Dynamic viscosities of the ethanol suspensions when suspended

FIG. 2. Dynamic viscosities as a function of shear rate at temperature of with silica particle of different sizes and different volume fractions. Data
25 ° C for 共a兲 the BF; 共b兲 nanofluid of volume fraction 1% alumina nano- come from Fig. 2 of Ref. 27. 共b兲 Dynamic viscosities as a function of shear
spheres; 共c兲 nanofluid of volume fraction 3% alumina nanospheres; and 共d兲 rate for ␾ = 6.12% copper oxides nanofluid at −35 ° C, which come from
nanofluid of volume fraction 1% alumina nanorods. Fig. 3 of Ref. 30.

the BF. The viscosity data measured at very small shear rate published results are very scattered. In some studies, the res-
共⬍0.1 s−1兲 must be discarded because of the experimental olution of the rheometer was not high enough to reveal the
uncertainty, where the torque is so small that the steady flow non-Newtonian behavior. For example, the data represented
state cannot be reached in the 120 s waiting time. When the in Fig. 3共A兲 are obtained from Fig. 2 of Ref. 27 and they
shear rate is larger than 0.1 s−1, the viscosity is constant and seem to fluctuate around 10% in the shear rate range of the
has a value of 0.1181 Pa s with fluctuation within 0.8%. measurements. In some studies, the measurements were done
Thus, it can be concluded that the BF shows a perfect New- on a narrow shear rate range.26,30 Figure 2 of Ref. 26 has
tonian behavior in the shear rate range under test, which is shown that both copper oxides and alumina nanofluids are
consistent with previous study.38 treated as Newtonian fluid at concentration up to 3%. It is
The dynamic viscosity of nanofluid with alumina nano- partially correct because the viscosity has been measured
spheres of ␾ = 1% 共NF1兲 is represented in Fig. 2共B兲. Due to within a narrow shear rate range, 500– 1100 s−1. Figure 3共B兲
the addition of spherical nanoparticles, the viscosity has in- is extracted from Fig. 3 of Ref. 30. It shows a clear shear-
creased to 0.1494 Pa s. This fluid can be approximately thinning behavior of the nanofluid in the shear rate range
treated as a Newtonian fluid too because the variation of between 1 and 8 s−1, even though the fluid was considered
viscosity is within 2.2%. However, NF1 exhibits a Newton- as Newtonian. In some studies, the conclusion that nano-
ian plateau for shear rate between 0.1 and 20 s−1, and there fluids show Newtonian behavior may be plausible when the
may eventually be a small shear thinning effect at higher viscosity data of each sample were exhibited in the indi-
shear rate. For nanofluid of larger volume fraction, ␾ = 3%, vidual figure.8,9,23–25
alumina spherical nanoparticles 共NF2兲, as shown in Fig. In the colloidal suspension study, the reason that the
2共C兲, the dynamic viscosity varies within 7.9%. A small Newtonian viscosity of a fluid is mostly modified to be non-
shear thinning trend can be seen when the shear rate is larger Newtonian comes from the complex interactions between the
than 20 s−1. For nanofluid with alumina nanorods, an obvi- fluid and particles and between particles.13 Recently, it has
ous shear thinning tendency appears even at lower volume been pointed out that there are possible particle aggregations
fraction 共␾ = 1%, NF3兲, as shown in Fig. 2共D兲. The dynamic and formation of extended structures of linked nanoparticles
viscosity keeps constant when shear rate is smaller than in nanofluid.8,9,11,39 As explained in Refs. 8 and 9, the vis-
20 s−1, afterward it decays to a value of 12.3% smaller till cosity of nanofluids has been affected by the aggregations
the shear rate reaches 500 s−1. At larger volume fraction, where the sizes of aggregates are between 3 and 4 times the
␾ = 3%, as shown in Fig. 1, the dynamic viscosity varies up diameter of nanoparticles. It seems that the existence of ag-
to 32%, it is totally a non-Newtonian fluid. gregation process can be responsible for the present results.
Looking through the literature where the nanofluids have 共i兲 The aggregation can explain the non-Newtonian viscosity
been claimed to be Newtonian, it can be observed that some of nanofluids, that is, the presence of a Newtonian plateau is
054317-4 Zhou, Ni, and Funfschilling J. Appl. Phys. 107, 054317 共2010兲

followed by a shear-thinning behavior at high shear rate

where the aggregate are possibly destroyed under shear. 共ii兲
It can explain why the non-Newtonian character of the nano-
fluids is more obvious at higher volume fraction where the
chance of aggregation is higher. 共iii兲 It can also explain why
nanorods nanofluids which have an aspect ratio higher than
spherical nanoparticles have a higher viscosity and a much
more pronounced non-Newtonian character—rods are much
more subject to form aggregates or superstructures.
To summarize, it can be stated that a non-Newtonian
rheological behavior appears when the nanoparticles are sus-
pended into the Newtonian BF even when the volume frac-
tion of nanoparticles is low. This is similar to that of the
colloidal suspensions of larger size particles.13–16 The rheol-
ogy of nanofluid can be explained by the mechanism of ag-
gregation of nanoparticles. Nevertheless, because non-
Newtonian rheological behavior is relatively weak, as shown
in Fig. 1, from an engineering point of view, it may be taken
as a good approximation that nanofluids of such a low or
moderate volume fractions can be considered most of the
time as Newtonian fluid.8–10,23–30

B. Temperature dependence
As is mentioned above, temperature is one of the key
FIG. 4. 共a兲. Dynamic viscosities, measured by the capillary tube, as a func-
factors that influences the rheological characteristics of nano- tion of temperature 共in Celsius兲 for the BF 共solid diamonds兲, nanofluids of
fluid. Dynamic viscosities measured by the capillary vis- volume fraction 1% 共solid squares兲 and 3% 共open squares兲 alumina spheres,
cometer are shown in Fig. 4共A兲. First, we can observe that and nanofluid of volume fraction 1% 共solid circles兲 and 3% 共open circles兲a-
lumina nanorods. Viscosities 共at 25 ° C兲 measured by ARG2 rheometer are
data measured by capillary viscometer and ARG2 rheometer plotted for comparison 共cross兲. The fitting curve from Eq. 共1兲 of each data
are consistent. Second, as expected for most liquids, their set is plotted as solid line. 共b兲. The relative viscosity 共␮r兲 as a function of
viscosities decrease with an increase in temperature for all temperature for nanofluids of volume fraction 1% 共solid squares兲 and 3%
samples. In the literature, the dependence of viscosity on 共open squares兲 alumina nanospheres and nanofluids of volume fraction 1%
共solid circles兲 and 3% 共open circles兲 alumina nanorods.
temperature of nanofluids can be reasonably described by an
Arrhenius–Frenkel–Eyring equation,22,40 a Vogel–Fulcher–
Tammann equation,8,9,41 or other similar types of for the nanofluid NF4, the relative viscosity decreases with
equations28,30,33,35 or a simple polynomial fitting.34 In our an increase in temperature, such a trend has also been found
case, the data can be very well represented by the semithe- in the literature.28,30
oretical Vogel–Fulcher–Tammann equation,41 Our experimental results and the existing

冉 冊
literature8,9,25,28,30,32 inspire us to explore more about the re-
B lationship between the relative viscosity ␮r and temperature
␮共T兲 = A exp . 共1兲
T + T0 in nanofluids. We have reviewed the viscosity data in previ-
ous literature, where the ␮r has not ever been discussed. In
To some extent, parameter B is related to the free activation
Fig. 5, experimental results of alumina nanoparticles in
energy of fluid. Without any constraint, the experimental data
water-based fluids from the literature have been
were fitted by Eq. 共1兲. The fitting parameters and the discrep-
summarized.23,24,31,42 Due to the different particle sizes, deal-
ancy between the fitted data and measurements are listed in
ing processes, and other factors, the data from different
Table I. In this table, it can be found that nanofluids of the
groups do not agree with each other even for almost the same
same concentration 共NF1 and NF3 on one side, NF2 and
volume fraction. However, it is generally observed that the
NF4 on the other side兲 have almost the same parameters A
␮r seems independent of temperature within the measure-
and To, which means that both parameters are the function of
volume fraction and independent of particle shape. On the
TABLE I. The empirical constants of Eq. 共1兲 and the mean deviation 共Dm兲
contrary, the parameter B depends on both the volume frac- between the equation and measurements.
tion and particle shape.
According to the recent observations,8,9,25,32 the relative Sample A B T0 Dm
viscosity is independent of temperature when nanofluids are
BF 共base fluid兲 37.08⫻ 10−6 1233.66 126.23 1.24%
of relatively low volume fraction. Figure 4共B兲 shows the
NF1 共sphere, ␾ = 1%兲 39.38⫻ 10−6 1285.04 130.57 0.51%
relative viscosity ␮r of our nanofluids. It seems constant for
NF2 共sphere, ␾ = 3%兲 90.16⫻ 10−6 1120.85 119.97 2.87%
nanofluids NF1, NF2, and NF3, where ␮r = 1.18⫾ 0.02, NF3 共rod, ␾ = 1%兲 42.10⫻ 10−6 1305.54 131.24 0.41%
1.37⫾ 0.03, and 1.59⫾ 0.07, respectively. These results are NF4 共rod, ␾ = 3%兲 81.93⫻ 10−6 1223.92 119.79 1.23%
in agreement with the results in literature.8,9,25,32 However
054317-5 Zhou, Ni, and Funfschilling J. Appl. Phys. 107, 054317 共2010兲

of most nanofluids is independent of temperature. This may

be explained by the fact that the rheological behavior of
nanofluids is mainly dominated by the BF even after the
addition of nanoparticles. Thus the temperature dependence
of viscosity of nanofluids follows that of BF, which results in
the constant relative viscosity at different temperatures. An
interesting phenomenon observed from the present work is
that the nanofluid either has Newtonian rheology and the
temperature independence of the relative viscosity 共NF1,
NF2, and NF3兲 or has non-Newtonian rheology and the tem-
perature dependence of the relative viscosity 共NF4兲. We are
not clear whether it is coincident or if there is some correla-
tion between them.
FIG. 5. The relative viscosity 共␮r兲 as a function of temperature 共in Celsius兲
in the water based alumina nanofluids. Some experimental data of Refs. 23, IV. CONCLUSION
24, 31, and 42 are included for comparison.
In summary, we have presented an experimental investi-
gation of the viscosity ␮ in the nanofluids where alumina
ment uncertainty when it is small 共usually for nanofluid of nanospheres or nanorods were suspended into PAO lubricant.
small volume fraction兲 within the measurement uncertainty, By measuring the viscosity in a wide shear rate range, the
and not for the case where ␮r is relatively large. As shown in PAO BF has been found to have a Newtonian behavior. At
Fig. 6共A兲 共reanalyzed from Fig. 8 of Ref. 23兲, the ␮r of relatively low volume fraction 共␾ = 1% and 3% of nano-
titanium dioxide nanofluid seems constant too within the ex- spheres and ␾ = 1% of nanorods兲, the addition of nanopar-
periment uncertainty. In some study, the ␮r is independent of ticles enables nanofluids to demonstrate non-Newtonian be-
temperature even when the volume fraction is large. Figure havior. However, from an engineering point of view, these
6共B兲 represents the relative viscosity ␮r of the water based nanofluids can be approximated as Newtonian fluid because
copper oxide nanofluid 共adopted from Fig. 6 of Ref. 33兲. they show only a very weak shear rate dependence of their
Here it can be seen that ␮r seems constant when ␾ ⬍ 10%. viscosity, which is consistent with the previous
Only for large ␾ 共13% and 15%兲, ␮r decreases with the literature.8–10,23–30 By reviewing the previous studies, that ␮r
increasing temperature. However, when the copper oxide or is independent of temperature seems hold for most nano-
the silicon dioxide nanoparticles have been added to the eth- fluids when their volume fraction ␾ and relative viscosity ␮r
ylene glycol and water mixture 共60:40% by weight兲,28,30 it is are small or aspect ratio is close to unity.8,9,23–25,31–33,42 How-
clearly shown that the relative viscosity ␮r diminishes as ever, nanofluid of volume fraction ␾ = 3.0% nanorods has an
temperature increases even at low volume fraction 共Fig. 5 of obvious non-Newtonian viscosity, and its relative viscosity
Ref. 30 and Fig. 4 of Ref. 28兲. decreases with an increase in the temperature. This observa-
Based on results from the literature8,9,23–25,31,32,42 and tion is in agreement with literature.28,30,33
present work, it may suggest that the relative viscosity 共␮r兲 We argue that the Newtonian rheology can be correlated
with the temperature independence of the relative viscosity
of the nanofluid. It may be suspected that the observations in
the present study are the common features of nanofluids
when their rheological properties are mainly dominated by
the BF. Inversely, it can also be suspected that the non-
Newtonian rheology can be correlated with the temperature
dependence of the relative viscosity of the nanofluid. How-
ever, further investigations are needed to explore this as-
sumption.

ACKNOWLEDGMENTS
We would like to thank J. Buongiorno for inviting us in
the international nanofluid property benchmark exercise 共IN-
PBE兲 program. Also we thank Z. Tong for providing AGR2
rheometer to take the viscosity measurement. Denis Funf-
schilling was supported by the CN Yang Visiting scholarship
共CUHK兲. The work was supported by Hong Kong GRF
共Grant No. 404808兲.
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