The viscosity measurement was taken 2 weeks after the nanofluid preparation. As seen in Figure , the viscosity decreases as the shear rate increases. At a certain shear rate, the nanofluid at 5 vol% has the largest viscosity while the viscosity value is the lowest in the 1 vol% nanofluid. The nanofluids behaved as non-Newtonian fluids. The effective viscosity, μeff
, of nanofluids increases up to about 38 × 10-3
Pa·S for the 5 vol% nanofluid. Figure shows that the relative viscosity, μeff
is the viscosity of the base fluid) increases from the above value for the 1 vol% nanofluid to about 43 for the 5 vol% nanofluid. However, the values are much higher than the those predicted from the conventional Einstein model, and those of the modified models by Brinkman, Batchelor, and Graham [6
]. The data of Xie et al. [18
] show a similar phenomenon also as shown in Figure . The nanoparticles were indicated to be prone to form agglomeration in a nanofluid suspension. The high viscosity observed is probably as a result of agglomeration that had occurred in the nanofluids after 2 weeks. Once agglomeration is formed, a larger stress is necessary to break the ligand structure among particles when shearing takes place; therefore, a high relative viscosity would be observed in the fluids as shown in Figures and . Zhou et al. [19
] also highlighted that the shear thinning behavior at high shear rate is likely due to aggregates being destroyed under shear. This can also explain that the non-Newtonian characteristics of nanofluids are more obvious at a higher volume fraction and a longer holding time since the chance of aggregation is higher. The aggregates are also verified in the following SEM images.
Viscosity as a function of shear rate in Al2O3-water nanofluids at the volume concentration from 1 to 5% (after 2 weeks).
Relative viscosity of Al2O3-water nanofluids as a function of volume con-centration (after 2 weeks).
Re-ultrasonication process was conducted on the 2-week Al2
-water nanofluids in order to disperse the aggregated nanoparticles before the viscosity was measured again. Figure demonstrates that the viscosity increases with the shear rate roughly linearly at the beginning before it reaches a constant value for each fluid. The nanofluids resume Newtonian. The nanofluid at 5 vol% has the largest viscosity while the value is the lowest in the 1 vol% nanofluid. Distinctively, it is seen that the relative viscosity is much lower than the relative nanofluid before re-ultrasonication, as illustrated in Figure . After re-ultrasonication, the effective viscosity gets back the values in the freshly prepared nanofluids [20
]. The relative viscosity increases as the volume concentration increases. It supports the hypothesis that a high viscosity might be due to nanoparticle agglomeration. The results reported by Masoumi et al. [4
] show a similar trend, too. From these experimental results, the measured relative viscosity of Al2
-water nanofluids is significantly 60% higher than those of the base fluid in the nanofluids after the non-Newtonian fluids were ultrasonically agitated again. The measures of Masoumi et al. and this research are much higher than those of the predicted values given by the Einstein and Graham equations [6
]. Clearly, the Einstein formula and the others have underestimated the nanofluid viscosities [6
]. For higher particle concentrations, the deviation of conventional models from the present experimental data is considerable. Even the Batchelor formula that considers the Brownian effects performs poorly [10
]. Chandrasekar et al. [21
] suggested that the significant difference between the experimental results and the predicted values might be because of the conventional models neglecting the hydrodynamic interactions between particles which become important, as the other disturbances of the fluid around one particle might interact with the surrounding particles at higher volume concentrations. The nanoparticle aggregation in the fluids would reinforce the effects.
Viscosity as a function of shear rate for Al2O3 nanofluids at the volume concentrations from 1 to 5% (after re-ultrasonication).
Relative viscosity of Al2O3 nanofluids as a function of volume concentration (after re-ultrasonication).
As illustrated in Figure , the microstructure of the nanoparticle distribution was measured after sampling and drying the drops at 5 vol% nanofluids which were held for 2 weeks and after re-ultrasonication. The nanoparticles accumulated together in a micron scale before re-ultrasonication of the 2-week nanofluids as seen in Figure , while the slight aggregation of nanoparticles was well dispersed after re-ultrasonication as seen in Figure .
SEM microstructure of the dried Al2O3-water nanofluids before re-ultrasonication (a) and after re-ultrasonication (b).
As suggested by Chen et al. [22
], the nanoparticles in the fluid are likely to form aggregates. We can apply the Krieger and Dougherty model to explain the relative viscosity, μeff/μf
, qualitatively [23
] is the intrinsic viscosity with a value of 2.5 for hard spherical particles, ϕm
is the volume fraction of densely packed spheres, ϕa
is the volume fraction of aggregates, expressed as
is the diameter of aggregates, d
is the nominal diameter of particle, df
is the fractal dimension of the aggregates, and ϕ
is the volume fraction of the well-dispersed individual particles. If there is no agglomeration, then Krieger and Dougherty model can be reduced to the ideal Einstein model [6
]. However, it is impossible to eliminate the agglomeration in nanofluids completely. Thus, the magnitude of da/d
in the nanofluids is larger than 1. As the size of the aggregates increases, the relative viscosity will increase. In addition, as the shape of the aggregate is no longer spherical due to aggregation, the intrinsic viscosity should be greater than 2.5 for other shapes [24
]. This can also account for the increase in the viscosity as the nanoparticle aggregate size is larger in the 2-week nanofluids before re-ultrasonication than that after re-ultrasonication. It might also partially explain as to show a higher concentration nanofluid has a larger relative viscosity because the 5 vol% nanofluid has a higher possibility for forming agglomerates in comparison with the 1 vol% nanofluid.