Rheological and volumetric properties of TiO2-ethylene glycol nanofluids
© Cabaleiro et al.; licensee Springer. 2013
Received: 15 April 2013
Accepted: 19 May 2013
Published: 13 June 2013
Homogeneous stable suspensions obtained by dispersing dry TiO2 nanoparticles in pure ethylene glycol were prepared and studied. Two types of nanocrystalline structure were analyzed, namely anatase and rutile phases, which have been characterized by scanning electron microscopy. The rheological behavior was determined for both nanofluids at nanoparticle mass concentrations up to 25%, including flow curves and frequency-dependent storage and loss moduli, using a cone-plate rotational rheometer. The effect of temperature over these flow curve tests at the highest concentration was also analyzed from 283.15 to 323.15 K. Furthermore, the influence of temperature, pressure, nanocrystalline structure, and concentration on the volumetric properties, including densities and isobaric thermal expansivities, were also analyzed.
KeywordsNanofluid TiO2/EG Anatase Rutile Non-Newtonian Nanoparticles Density Thermal expansivity coefficient
Nowadays, it is well known that the novel proposal of nanofluids represents a valuable way for the development of the heat transfer fluids currently available. Thus, nanofluids have recently emerged with new potential applications in heat exchangers or cooling devices, being widely used in many engineering applications as electronics cooling, vehicle engines, nuclear reactors, energy efficiency enhancers, food industry, air conditioning, refrigeration, and biomedicine [1–4]. As an example, it has been shown that by using nanofluids in radiators, pumps, or compressors in cars, the aerodynamic charge could be reduced, producing fuel savings up to 6% . Therefore, with the aim to improve the heat transfer properties of nanofluids, a considerable amount of research efforts are being devoted to the analysis of their thermal conductivity and convective heat transfer properties. Although it is possible to tailor nanofluids exhibiting negative thermal conductivity enhancement, or a decrease in the effective thermal conductivity of the dispersion if compared with that of the base liquid , in most cases, nanofluids exhibit a significant enhancement in thermal conductivity. Therefore, nanofluids are expected to provide optimized convective heat transfer coefficients. However, this type of nanocolloidal dispersion affects also other thermophysical properties than thermal conductivity. Concerning the concentration dependence of nanofluids, a revision of the literature shows, besides the increase in thermal conductivity, decreases of heat capacity and a noticeable increase of density and viscosity, including the possibility of a non-Newtonian behavior. All these properties affect significantly the convective heat transfer coefficient. In addition, as the relation between this coefficient and the involved thermophysical properties could not follow classical laws, it is essentially required to determine accurately their trend with concentration, temperature, and/or pressure.
Recently, Huminic and Huminic  have reported a review on the application of nanofluids in various types of heat exchangers as plate, shell and tube, compact, and double pipe heat exchangers. The authors concluded that both the thermophysical properties and type of flow inside the heat exchanger played important roles in the efficiency of the nanofluid as a coolant. Moreover, in most practical applications, the heat transfer fluid is not stationary , and consequently, the analysis of the rheological properties is also essential to appropriately determine the increments on the average heat transfer coefficient of the flowing system, which generally increases with the concentration of nanoparticles as well as with the Reynolds number . Numerical results  indicate that high-concentration nanofluids of TiO2 or Al2O3 in water exhibit higher heat transfer enhancements and also higher pressure drops. On the other hand, Peyghambarzadeh et al.  have experimentally demonstrated, using water- and ethylene glycol (EG)-based nanofluids as cooling agents inside flat aluminum tubes of a car radiator, that the heat transfer behaviors of the nanofluids were highly dependent on particle concentration and flow conditions and otherwise weakly temperature dependent. From the results of Huminic and Huminic , it can be concluded that homogeneously dispersed and stabilized nanoparticles enhance the forced convective heat transfer coefficient of the base fluid in a range of 3% to 49%, observing a greater increase with increasing temperature and nanoparticle concentration. Therefore, a proper balance between the heat transfer enhancement and the pressure drop penalty, together with viscosity behavior, should be taken into account when seeking an appropriate nanofluid for a given application.
In addition to the knowledge of the cited rheological behavior, the volumetric properties including the isobaric thermal expansivity coefficient play as well an important role in many heat removal systems involving natural convection. The thermal expansivity coefficient is needed to apply nanofluids in engineering-scale systems [8, 9], and this property is usually negligible for metallic oxide particles if compared to that of the base fluids as EG or water. Hence, it is often presumed that this coefficient should decrease with rising concentration of nanoparticles as we have previously reported . Nevertheless, some works [8, 9] have found the opposite behavior of the one resulting from considering the fluids to behave separately in the mixture for the case of water-based Al2O3 nanofluids. This is one of the singular properties of nanofluids that would find a remarkable application in many heat extraction systems using natural convection as a heat removal method . Therefore, more attention should be paid to this magnitude with the goal to understand the complex interaction of nanoparticles with the base fluid molecules, and it could be also a powerful additional tool to characterize nanofluids.
In this work, we focus our attention on the volumetric and rheological behaviors of the suspension of two nanocrystalline forms of TiO2 nanoparticles, anatase and rutile, dispersed in pure EG as the base fluid. The influence of the nanocrystalline phase, temperature, pressure, and concentration on the isobaric thermal expansivity coefficient is also analyzed, looking for a verification of the surprising results for different nanofluids found by Nayak et al. [8, 9]. In addition to the reasons cited, the selection here of TiO2/EG nanofluids is inspired also on several other arguments. First, EG can be used over a wide temperature range. Then, an enhancement in the overall heat transfer coefficient of up to 35% in a compact reactor-heat exchanger, with a limited penalty of increase in pressure drop due to the introduction of nanoparticles, has been reported for TiO2/EG nanofluids . Moreover, TiO2 is a safe and harmless material for human and animals if compared with other nanomaterials . From a production perspective, these nanoparticles are easily obtained because they are readily produced in large industrial scales. Concerning their physicochemical profile, they have an excellent stability when dispersed in a fluid even without stabilizer addition, and metal oxide nanoparticles are chemically more stable than their metallic counterparts . Finally, remarkably few works are found in the literature [3, 14, 15] devoted to the study of thermal or rheological properties of TiO2/EG nanofluids, and up to our knowledge, their volumetric and viscoelastic properties have never been reported.
The experimental density of stable and homogeneous TiO2/EG nanofluids at percent mass concentrations (wt.%) of 1.00, 1.75, 2.50, 3.25, and 5.00, which correspond in percent volume (vol.%), respectively, of 0.29, 0.51, 0.74, 1.04, and 1.51 for anatase and 0.26, 0.47, 0.67, 0.94, and 1.36 for rutile, in wide pressure (from 0.1 to 45 MPa) and temperature (from 283.15 to 343.15 K) ranges was analyzed. From these density data for anatase titanium dioxide-EG nanofluids (A-TiO2/EG, from now on, for the sake of brevity) and rutile titanium dioxide-EG nanofluids (viz. R-TiO2/EG) , the derived thermal expansion and thermal compressibility coefficients were studied. Moreover, we have carried out a rheological study on samples of A-TiO2/EG and R-TiO2/EG nanofluids at mass concentrations of 5.00, 10.00, 15.00, 20.00, and 25.00 wt.%, which correspond to 1.51, 3.13, 4.88, 6.77, and 8.83 vol.% for A-TiO2/EG and to 1.36, 2.83, 4.43, 6.16, and 8.08 vol.% for R-TiO2/EG, respectively. The effect of the structure of nanoparticles, rutile and anatase, on linear and non-linear tests was analyzed on these samples, and the influence of the temperature was carried out over a temperature range of 283.15 to 333.15 K for the 25 wt.% concentration in both structures.
Several works in the literature have focused on water- or water + EG-based TiO2 nanofluids [13, 17–24]. Bobbo et al.  and Penkavova et al.  studied the viscosity of TiO2/water nanofluids observing a Newtonian behavior for all compositions, while He et al.  concluded that aqueous TiO2 nanofluids, with anatase phase and a small amount of rutile phase, show a shear thinning behavior where the shear viscosity tends to be constant at shear rates above 100 s−1 and also that the pressure drop of these nanofluids is very close to that of the base liquid. Nevertheless, Tseng and Lin  have investigated the rheological behavior of suspensions of anatase TiO2 nanoparticles in water (0.05 to 0.12 vol.%), reporting a pseudoplastic flow for most of the shear rates examined, from 10 to 1,000 s−1. Moreover, their tests suggest a time-dependent phenomenon, attributing to these suspensions a thixotropic response . Several authors [19–23] have studied thermal conductivity enhancements, higher than 20% , increasing the nanoparticle concentration. Concerning volumetric studies in TiO2/water nanofluids, only the work by Setia et al.  can be cited, where the specific volume for several concentrations up to 0.75 vol.% of TiO2 nanoparticles for several temperatures is reported, finding significant deviations from the additive rule  for the samples with volume fractions higher than 0.5 vol.%.
Nevertheless, as pointed out above, few studies were focused on the thermophysical or rheological behavior of TiO2/EG nanofluids [3, 14, 15]. Fan et al.  determined the thermal conductivity at 303 K for the concentrations 0.5, 2.0, and 4.0 wt.% (corresponding respectively to 0.10, 0.43, and 0.86 vol.%) for TiO2/EG nanofluids and their corresponding viscosity in the shear rate range of 1 to 3,000 s−1, confirming a Newtonian behavior and the expected increase of viscosity with nanoparticle concentration. Chen et al.  have also found a Newtonian behavior for TiO2/EG nanofluids containing 0.5, 1.0, 2.0, 4.0, and 8.0 wt.% spherical nanoparticles at 293.15 to 333.15 K and a relative viscosity dependent on particle concentration in a non-linear manner without temperature dependence. On the other hand, Lee et al.  have determined temperature-independent thermal conductivity enhancements up to 16% for 5.5 vol.% TiO2/EG nanofluids constituted by nanoparticles with rutile and anatase phases. On the other hand, to our knowledge, no evidence on non-Newtonian behavior for TiO2/EG nanofluids, or studies about their volumetric behavior, including densities, isothermal compressibility, and isobaric thermal expansivity coefficients, have been reported so far in the literature. Hence, there is a key need to address this issue.
Mass purity (%)
Medium size (nm)
Anatase titanium dioxide (A-TiO2)
35 ± 17
Rutile titanium dioxide (R-TiO2)
47 ± 18
The preparation of the nanofluid was carried out using the two-step method at the mass concentrations of 1.00, 1.75, 2.50, 3.25, and 5.00 wt.% for volumetric measurements, whereas 5.00, 10.00, 15.00, 20.00, and 25.00 in wt.% concentrations were used for rheological tests, without adding any surfactant, in order to study the effect of nanoparticle aggregation. The uncertainty in the mass compositions for the different studied nanofluids ranges from 0.003% to 0.02%, increasing with the mass concentration. Subsequently, the nanofluids were dispersed by ultrasonic homogenization using a Bandelin Sonoplus HD 2200 (Bandelin Electronic, Berlin, Germany) for 16 min to prevent aggregation. More details about sonication methods have been previously published .
Concerning the characterization of the volumetric behavior of the cited R-TiO2/EG and A-TiO2/EG nanofluids, density measurements were experimentally carried out at concentrations up to 5% in mass fraction from atmospheric pressure up to 45 MPa and from 278.15 to 363.15 K. Temperature and pressure were measured within uncertainties of 0.02 MPa and 0.02 K for pressure and temperature, respectively. Density data were obtained from the period values measured using a commercially available vibrating tube densimeter (Anton Paar DMA 512P, Graz, Austria) with an estimated uncertainty of 5 × 10−4 g cm−3 over the whole pressure and temperature range. More details about the procedure, calibration, temperature, and pressure control can be found in our previous works [10, 30, 31].
Rheological properties of R-TiO2/EG and A-TiO2/EG nanofluids were determined using a rotational Physica MCR 101 rheometer (Anton Paar, Graz, Austria), equipped with a cone-plate geometry with a cone diameter of 25 mm and a cone angle of 1°. The cone went down to an imposed gap of 0.048 mm from the plate and covered the whole sample for all tests. The measurement consists of imposing the shear stress to the sample and recording the related shear rate. Temperature is controlled with a Peltier P-PTD 200 (Anton Paar, Graz, Austria), placed at the lower plate, with a diameter of 56 mm without groove. The linear and non-linear tests were developed from torques of 0.1 μNm in the temperature range of 283.15 to 323.15 K, each 10 K. A constant amount of 110 μl of sample was considered  for the analysis and was placed on the Peltier plate. Non-linear and linear viscoelastic experiments were carried out with the objective to analyze both relatively large deformations and small-amplitude oscillatory shear. Thus, the flow curves of the samples studied and the frequency-dependent storage (G’) and loss (G”) moduli were determined. More details about the experimental setup and operating conditions can be found in our previous papers [10, 32, 33].
Results and discussion
Density ( ρ ), isobaric thermal expansivity ( α p ), and isothermal compressibility ( κ T ) of A-TiO 2 /EG and R-TiO 2 /EG nanofluids
104·α p (K−1)
104·κ T (MPa−1)
T= 283.15 K
T= 313.15 K
T= 343.15 K
T= 283.15 K
T= 313.15 K
T= 343.15 K
T= 283.15 K
T= 313.15 K
T= 343.15 K
Base fluid (EG)
A-TiO2/EG (1.75 wt.%)
A-TiO2/EG (5.00 wt.%)
R-TiO2/EG (1.75 wt.%)
R-TiO2/EG (5.00 wt.%)
Density correlation coefficients and standard deviations ( σ ) for the base fluid (EG) and the nanofluids
104·σ (cm3 g−1)
−c (MPa °C−1)
102·d (MPa °C−2)
− 103·f (MPa−1)
104·σ* (cm3 g−1)
The values of B(pref,Tref), c, d, e, and f were determined by fitting Equation 1 to all the experimental data at pressures different than pref by a least squares method using a Marquardt-Levenberg-type algorithm. For the base fluid and all the studied nanofluids, the standard deviations obtained with this correlation are lower than or equal to 1.4 × 10−4 cm3 g−1, and the coefficients are given in Table 3.
In Table 2, the values calculated for α p and κ T are reported for some temperatures and pressures for the base fluid (EG) and both nanofluids at two different concentrations (1.75 and 5.00 wt.%). The estimated uncertainties for α p and κ T are 4% and 2%, respectively. The α p values for both the base fluid and R-TiO2/EG and A-TiO2/EG nanofluids decrease when pressure rises (up to 9.8% for the base fluid) and increase with temperature (up to 6.6% for the base fluid). Concerning the concentration dependence, first, we have found that the α p values of nanofluids are very similar to or lower than those of EG, achieving decreases up to 1.0% and 1.9% for A-TiO2/EG and R-TiO2/EG nanofluids, respectively. These results are opposite to those previously found by Nayak et al. [8, 9], reporting a significant increase in this property compared to the base fluid for water-based Al2O3, CuO, SiO2, and TiO2 nanofluids. It should be mentioned that Nayak et al. have determined the isobaric thermal expansivities by measuring the bulk variation with temperature for the samples in a glass flask with a long calibrate stem. Consequently, further studies about this property are still needed on EG- or water-based nanofluids. On the other hand, the κ T values of the studied samples do not exhibit evident concentration or nanocrystalline structure dependence (or these differences are within the uncertainty). The κ T values decrease when the pressure rises and increase with the temperature along the isobars for both the base fluid and nanofluid samples, as can be seen in Table 2.
where the adjustable parameters K and n are the flow consistency factor and the flow behavior index, respectively. Good adjustments are obtained for all studied nanofluid samples, reaching percentage deviations in shear dynamic viscosity around 3%. At the same mass concentration, the flow behavior index values for R-TiO2/EG nanofluids are higher than those for A-TiO2/EG, as shown in Figure 6c. These n values range from 0.27 to 0.72 for A-TiO2/EG and from 0.33 to 0.83 for R-TiO2/EG, decreasing near-exponentially when the volume fraction increases, which evidences that the shear thinning behavior is more noticeable when the nanoparticle concentration increases. The n values are similar to those typically obtained for common thermoplastics . It must also be pointed out that although this model offers a simple approximation of the shear thinning behavior, it does not predict the upper or lower Newtonian plateaus .
where R is the universal gas constant and A and E a are the fitting parameters of the pre-exponential factor and energy of activation to fluid flow, respectively. This equation describes adequately the temperature dependence of the shear viscosity of the studied nanofluids. Figure 7c shows the obtained E a values vs. shear rate for the 25 wt.% concentration of A-TiO2/EG and R-TiO2/EG nanofluids. It is generally accepted that higher E a values indicate a faster change in viscosity with temperature and high temperature dependency of viscosity . Thus, lower E a values found for A-TiO2/EG indicate an inferior temperature influence on viscosity for this nanofluid. Moreover, at shear rates around 6 s−1 for A-TiO2/EG and around 8 s−1 for R-TiO2/EG, a minimum of the energy of activation was detected, as can be observed in Figure 7c. The values obtained here for A-TiO2/EG and R-TiO2/EG are similar to those obtained by Abdelhalim et al.  for gold nanoparticles in an aqueous solution.
Frequency sweep tests (for angular frequencies between 0.1 and 600 rad s−1) were performed for A-TiO2/EG nanofluids, and the evolution of each modulus with the oscillation frequency was obtained, as shown in Figure 8c,d. These experiments were carried out in the linear viscoelastic region using a constant strain value of 0.1% for all nanofluids. Both moduli increase with concentration at a given constant frequency which means that when the nanoparticle content is increased, the hydrodynamic interactions as well as the probability of collision become important, enhancing the aggregation processes. In all cases, the elastic modulus is higher than the viscous one at low frequencies, while the contrary occurs at high frequencies, where the suspensions behave like a liquid. Crossover frequencies, where G’ = G” and a change in the viscoelastic behavior is detected, increase with the concentration of nanoparticles from around 4 rad s−1 at a concentration of 10 wt.% to 15 rad s−1 at 25 wt.%. That is in agreement with the fact that the degree of agglomeration of the particles is more important at the highest concentrations, but the alignment with the flow of the aggregates is achieved in a shorter time for higher concentrations. This analysis was not carried out for the lowest nanofluid concentration (5 wt.%) due to the availability of the minimum torque of the used device. Moreover, it should be taken into account that those data at elevated frequencies in which problems of inertia of equipment appear were not considered. This was done by taking into consideration the relationship between the complex viscosity and the frequency. The loss and storage moduli increase with frequency especially at frequencies higher than 10 rad s−1. It can be also observed that the elastic modulus data fall on a straight line for the highest frequencies. Finally, we want to point out that the increase in nanoparticle concentration leads to an increase in the formation of agglomeration of the particle, but even the concentration of 5 wt.% for A-TiO2/EG nanofluid does not follow the conventional Cox-Merz rule , , η * being the complex viscosity η* ≡ (G´ + iG´´)/ω, which is often valid for Newtonian or non-structured fluids. Our data demonstrate the Cox-Merz rule to become more inapplicable as the concentration of nanoparticles increases. Moreover, it is illustrated that the addition of nanoparticles makes the difference |η*| − η increase as for all A-TiO2/EG concentrations. This behavior was previously found by Haleem and Nott  for suspensions of rigid spheres in semi-dilute polymer solutions. These authors attributed this anomalous behavior to the fact that an anisotropic particle microstructure can form at steady shear even in the limit , while it cannot reach it for small-amplitude oscillatory shear. Up to our knowledge, no previous results were published on the Cox-Merz rule of nanofluids, and therefore, more studies exploring other nanofluid types are necessary.
The density values for R-TiO2/EG are higher than those for the A-TiO2/EG nanofluid at the same temperature, pressure, and mass concentration. The enhancement of density in relation to the base fluid is also higher for rutile nanofluids, reaching values of 3.8% at the highest concentration. These increments with the concentration are almost temperature and pressure independent. The isobaric thermal expansivity values of A-TiO2/EG and R-TiO2/EG nanofluids decrease when the pressure rises and increase with temperature as the base fluid does, while we have found that these values for the nanofluids are very similar to or lower than those for the base fluid, achieving decreases up to 2%. The analyzed nanofluids present an expansive volumetric behavior which is more pronounced in A-TiO2/EG. This expansive behavior is also found for other EG-based nanofluids. Contrarily to what was previously published, a shear thinning non-Newtonian behavior was found for both sets of TiO2/EG nanofluids. As the concentration rises, Newtonian plateaus are found at the lowest shear rate and the shear thinning regions can be described using the Ostwald-de Waele model. At the same temperature and concentration conditions, A-TiO2 nanofluids show higher shear dynamic viscosity for all the shear rates. Minima in the energy of activation were found at shear rates around 6 s−1 for A-TiO2/EG and 8 s−1 for R-TiO2/EG when the shear dynamic viscosity data were fitted for the 25 wt.% concentrations using an Arrhenius-type equation. Finally, viscoelastic oscillatory experiments were performed for A-TiO2. The two-step decrease of the loss modulus present in the deformation tests evidence an attractive gel behavior of the studied nanofluids. Finally, the A-TiO2/EG nanofluid does not follow the conventional Cox-Merz rule. The differences between the viscosities determined in steady shear and the dynamic viscosities from the oscillatory rate are higher when the nanoparticle concentration increases.
This work was supported by the Ministerio de Economía y Competitividad (Spain) and the FEDER program through the project ENE2012-32908. The authors also acknowledge the financial support from Fundación Iberdrola and Universidad de Vigo. DC and LL acknowledge the financial support under the FPU and Ramón y Cajal Program provided by the ‘Ministerio de Educación, Cultura y Deporte’ and ‘Ministerio de Ciencia e Innovación’ (Spain), respectively.
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