J. Phys. Chem. C 2010, 114, 18825–18833
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Synthesis of Aqueous and Nonaqueous Iron Oxide Nanofluids and Study of Temperature Dependence on Thermal Conductivity and Viscosity P. D. Shima, John Philip,* and Baldev Raj SMARTS, NDED, Metallurgy and Materials Group, Indira Gandhi Centre for Atomic Research, Kalpakkam 603 102, Tamilnadu, India ReceiVed: August 7, 2010; ReVised Manuscript ReceiVed: October 1, 2010
We investigate the temperature-dependent thermal conductivity (k) of aqueous and nonaqueous stable nanofluids with average particles size of 8 nm stabilized with a monolayer of surfactant. Iron oxide (Fe3O4) nanoparticles are synthesized by a coprecipitation technique and are characterized by powder X-ray diffraction (XRD), transmission electron microscopy (TEM), vibrating sample magnetometry (VSM), dynamic light scattering (DLS), and theromogravimetric analysis (TGA). The particles are functionalized with suitable surfactants and dispersed in aqueous and nonaqueous base fluids. The thermal conductivity and viscosity measurements are carried out using a transient hot wire and a rotational rheometer, respectively. The thermal conductivity of aqueous nanofluids increases with temperature while it shows a decrease in nonaqueous nanofluids. Interestingly, the ratio of thermal conductivity of both nanofluids with respect to base fluids (k/kf) remains constant with an increase in temperature, irrespective of the nature of the base fluid. This observation is in sharp contrast to microconvection theory predictions of an increase in thermal conductivity with a rise in temperature. These results unambiguously confirm the less dominant role of microconvection on thermal conductivity enhancement. Although the viscosity of nanofluids decreases with increases in temperature, the viscosity ratio with respect to base fluid remains constant. These results show that the viscosity and thermal conductivity of nanofluids simply tracks those properties of the base fluids. Measurement of particle size with temperature shows that the average particle size remains constant with temperature. 1. Introduction Advances in nanotechnology have led to miniaturization and increased operating speeds that warrant the need for new and innovative cooling concepts with improved performance.1 Thermal properties of nanofluids have been a hotly debated topic during the last two decades due to their promising applications in heat transfer.2-27 In addition to nanoengineered coolants, new promising applications of nanofluids are emerging in the area of mass transport,28 improved critical heat flux, in-vessel retention capability in light-water reactors,9 optical devices,29,30 etc. Some of the papers report unusual thermal conductivity (k) enhancement in nanofluids that cannot be explained by classical effective medium theory.31-38 However, recent reports show that thermal conductivity enhancement is within the predictions of effective medium theory.8,20,39-45 Recent systematic studies, led by Buongiorno of MIT, and thirty research groups around the globe, on a series of stable nanofluids produced by the same manufacturer using a similar protocol show modest enhancement in thermal conductivity in polyalphaolefin lubricant (PAO)-based alumina nanofluids at low and high particle concentrations.7 Several possible mechanisms such as Brownian motion of the nanoparticles, fluid convection at the microscales, liquid layering at the particle-fluid interface, cluster agglomeration, or a combination of above mechanisms have been proposed to explain the anomalous enhancement in thermal conductivity.6 Unfortunately, none of the heat transport models could explain the wide spectrum of thermal conductivity data reported in various nanofluids. After detailed investigations, Brownian motion-induced convection and effective conduction through * Corresponding author. Phone: 00-91-94 431 51 536. Fax: 00-91-4427480356. E-mail:
[email protected].
percolating nanoparticle paths are considered as the two most probable mechanisms responsible for the enhanced heat conduction in nanofluids.4,46 More recent systematic studies reveal that the conduction path through the agglomerates is one of the most significant factors responsible for the dramatic enhancement of k.8,47 A recent study using nanofluids of different particle sizes in the range 3-10 nm shows that the thermal conductivity decreases with a decrease in particle size, indicating the less important role of Brownian motion on heat transport.48 Among various issues, one of the areas that lacks consensus is the exact dependence of temperature on the thermal conductivity of nanofluids.5,8,10,20,22,35,36,40,49-73 There are conflicting reports of temperature-dependent thermal conductivity in nanofluids. Some of the studies show an enhancement in k/kf with temperature10,22,35,36,49-65 while others reports invariant k/kf with rise in temperature.5,8,20,40,66-72 Also, a decrease in k/kf with temperature is reported.74 Contradictory temperature-dependent k results are reported both for metal and metal oxide nanofluids even in the same base fluids.5,8,10,20,22,35,36,40,49-74 Most of the studies in water-based alumina nanofluids show an enhancement in k/kf with temperature.10,36,50-58 An enhancement in k/kf with temperature is also reported in ethylene glycol (EG)-based alumina nanofluids.10 A few reports show temperature independent thermal conductivity of water-, EG-, and hexadecanebased alumina nanofluids where the k of nanofluids simply follows that of the base fluids.5,8,66,67 An enhancement in k/kf51,52,56 and a constant67 k/kf ratio are reported for water-based copper oxide nanofluids with increase in temperature. Similarly, both an enhancement59 and a constant67 k/kf with increase in temperature is reported for water-based TiO2 nanofluids. These conflicting reports warrant a systematic study on temperature-
10.1021/jp107447q 2010 American Chemical Society Published on Web 10/19/2010
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dependent k in stable aqueous and nonaqueous nanofluids. This was the main motivation behind the present study. Another important and intriguing question that remained unanswered in the domain of thermal properties of nanofluids is the effect of temperature on nanoparticle clustering and viscosity. Dynamic light scattering (DLS) and viscosity (η) measurements are the two widely accepted tools to probe the effect of aggregation in nanofluids.13,17,20,27,40,75-86 We investigate the role of temperature on clustering of nanoparticles using the DLS technique. Agglomeration and clustering of nanoparticles will cause viscosity increase in nanofluids, which is not a desirable effect for practical applications. This is the third aspect discussed in this paper. Some of the recent systematic studies on viscosity measurements in nanofluids show that the shear viscosity increase is much more dramatic than that predicted with the Einstein model.49,75,76,87-92 The viscosity was found to increase with particle loading in both metal and metal oxide nanofluids.10,13,27,40,49,53,59,71,75,77,78,87-99 Several studies show Newtonian nature of viscosity in nanofluids (viscosity does not vary with shear rate).13,75,88,93,94,100 However, there are some reports of non-Newtonian nanofluid viscosity as well.13,27,60,77,78,89,97,101-103 Dynamic light scattering is recognized as a powerful technique to determine the size distribution of small particles in solution.104 There are many studies on aggregation in nanofluids using DLS.13,20,40,84,85,17,78,86 Past studies showed discrepancies and a lack of consensus on the effect of temperature on k, viscosity, and cluster size. The purpose of this systematic study was to obtain insight into the exact dependence of temperature on k, particle agglomeration, and viscosity in well tailored ‘stable’ nanofluids. 2. Experimental Section We prepared magnetite nanoparticles of average size of about 8 nm for our study by chemical coprecipitation.105 Details of the preparation procedure are provided in the Supporting Information. Sample Characterization. The samples were characterized for phase identity by X-ray diffraction using a MAC Science MXP18 X-ray diffractometer. The 2θ values were from 20° to 80° using Cu KR radiation (λ value is 1.5416 Å). The average particle size was obtained from the most intense peak (311) by using the Debye-Scherrer formula. d ) 0.9λ/βcos θ, where d is the particle size, β is the full width at half maxima, λ is the incident copper kR wavelength of 1.546 Å, and θ is the maximum peak position. The obtained patterns were verified by comparing with the JCPDS data. A Tecnai F30 instrument with an acceleration voltage of 200 kV was used to record TEM images. The samples were prepared by slowly evaporating a drop of nanoparticle suspension in acetone on amorphous carbon-coated copper grids at room temperature. A Setsys Evolution-1750 Setarm instrument was used for TGA measurements. Weight loss measurements were taken from 50 to 600 °C in an inert atmosphere of argon. A heating rate of 5 °C/min was maintained for the entire measurement. Vibrating sample magnetometry (VSM) (Lake Shore Model: 7404) was used for magnetization measurements with the applied magnetic field in the range of -15 to 15 kG. The size distribution of nanoparticles was determined by dynamic light scattering using a Zetasizer-Nano (Malvern Instrument). The rheological behavior of dispersions was studied with a rotational rheometer (Anton Paar Physica MCR 301). Thermal conductivity was measured using a transient hot wire (KD2-pro). The accuracy in the k measurement is within 5%.
Shima et al. The thermal conductivity of the nanofluid was measured by monitoring of heat dissipation from a line heat source. The KD2 works on the assumption that the probe is an infinitely long heat source and that the material (fluid or solid) being measured is homogeneous and isotropic and of a uniform initial temperature. An electric heating probe was applied to the fluid, and the rise in temperature was calculated using the equation
T - T0 =
[( )(
( ))]
q r2 ln(t) - γ - ln 4πλh 4k
(1)
where T is the temperature (K), T0 is the initial temperature (K), q is the heat produced per unit length per unit time (W m-1), λh is the thermal conductivity of the medium (W m-1 C-1), t is the time (s), γ is Euler’s constant (0.5772), r is the radial distance (m), and k is thermal diffusivity (m2 s-1). By plotting ∆T against ln(t), the thermal conductivity is then simply calculated from the gradient of the slope, m, which is equal to q/4πλh. A measurement cycle consists of a 30 s equilibration time, a 30 s heat time, and a 30 s cool time. Temperature measurements were made at 1s intervals during heating and cooling. Measurements are then fit with exponential integral functions using a nonlinear least-squares procedure. A linear drift term corrects for temperature changes of the sample during the measurement, to optimize the accuracy of the readings. To measure the thermal conductivity at different temperatures, the sample vial with the thermal conductivity probe was immersed in a circulating water bath and the temperature of the water bath was maintained within (0.1 °C. The entire sample assembly was insulated for temperature gradient and vibrations. The thermal conductivity measurements were made 10 min after achieving the desired temperature for better temperature equilibrium. 3. Results and Discussion 3.1. XRD, TEM, TGA, VSM, and DLS Analysis. Figure 1a shows XRD patterns of uncoated Fe3O4 nanoparticles at room temperature. The diffraction peaks of (220), (311), (400), (422), (511), and (440) can be indexed to cubic spinel structure with the Fe3O4 phase. It is known that maghemite also shows all the peaks of magnetite, in addition to the low intensity peaks (with intensity 20kBT) prevents the particles from crossing the barrier. Further, the presence of surfactant monolayer leads to complete wetting of the particle by the liquid medium, which has a major role on the interfacial resistance. In such stable nanofluids, the aggregation is negligible at higher temperatures. 3.4. Effect of Temperature on Viscosity of Nanofluids. Figures 8 and 9 show the variation of viscosity of kerosenebased nanofluids and its ratio (with respect to base fluid), respectively, for three different volume fractions of nanopar-
Figure 9. The variation of viscosity ratio with temperature for kerosenebased ferrofluids with φ ) 0.027, 0.05, and 0.095.
ticles. Although the absolute viscosity decreases with an increase in temperature in both the base fluids and the nanofluids, the viscosity ratio remains almost constant with an increase in temperature, which is a clear indication for the absence of aggregation with temperature. A similar viscosity behavior with temperature was reported for other nanofluids also.40,70,93,94 A constant viscosity ratio is observed with an increase in temperature in water and hexadecane-based nanofluids in our study. Almost all the existing theoretical formulas which are used for the determination of a particle suspension viscosity was derived from Einstein analysis of infinitely dilute suspensions of hard spheres.113 In the Einstein model, the particles are assumed to be rigid, uncharged, and without attractive forces; they are small enough so that the dilatational perturbation of the flow is unbound and is able to decay to zero. A particle moves at the velocity of the streamline in line with the particle center in such a suspension. The Einstein equation describes the dependence of viscosity increase on the concentration of particles in the simplest case of dilute suspensions (φ e 0.01) as
η ) 1 + 2.5φ η0
(6)
φ is the particle volume fraction, η is the nanofluid dynamic viscosity, and η0 is the base fluid dynamic viscosity. When φ g 0.01, hydrodynamic interactions between particles become important, as the disturbance of the fluid around one particle interacts with that around other particles. The viscosity in such a case is given by the Batchelor equation114
η ) 1 + 2.5φ + 6.5φ2 η0
(7)
For φ g 0.1, where multiparticle collisions become increasingly important, a semiempirical relationship for the shear viscosity covering the full range of particle volume fraction was obtained by Krieger and Dougherty.115
(
η φ ) 1η0 φm
)
-[η]φm
(8)
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Figure 12. The variation of viscosity with shear rate at different temperatures for kerosene-based ferrofluids with φ ) 0.05 and φ ) 0.095. Figure 10. The variation of viscosity ratio with volume fraction for kerosene-based ferrofluids at 25 °C together with the Einstein and Krieger-Dougherty (KD) fit.
Figure 11. The variation of viscosity with shear rate at different temperatures for kerosene and kerosene-based ferrofluid with φ ) 0.027.
where [η] is the intrinsic viscosity, which is 2.5 for hard spheres and φm is the maximum packing fraction. For randomly monodispersed spheres, the maximum close packing fraction is approximately 0.64. Functional dependence of the viscosity on the fluid temperature can be expressed by an Arrhenius-type equation.116
η ) η∞T e
Ea
/RT
(9)
where η is the viscosity from experimental tests, η∞T is the viscosity at infinite temperature, Ea is the activation energy to fluid flow, R is the universal gas constant, and T is the temperature in Kelvin. The activation energy and infinite temperature viscosity can be extracted from experimental data. Figure 10 shows variation of viscosity ratio with volume fraction for kerosene-based ferrofluids together with Einstein and Krieger-Dougherty (KD) fit. The results show that the enhancement in viscosity ratio with φ is much more than the values predicted by Einstein and KD models. Some of the studies show a moderate viscosity enhancement10,40,59,76,88,93,99 while others reports a very high viscosity enhancement49,75,87,89,90 in nanofluids compared to the Einstein model. We have also measured the viscosity of the nanofluid as a function of the shear rate (10-1000 s-1) at different temperatures. Figures 11 and 12 show the variation of viscosity with shear rate at different temperatures for kerosene-based ferrofluids with φ ) 0 (base fluid), φ ) 0.027, φ ) 0.050, and φ )0.095. Our results show that the viscosity is independent of shear rate
Figure 13. The variation of viscosity with shear rate at different temperatures for hexadecane and hexadecane-based ferrofluid with φ ) 0.0608.
from 25 to 50 °C, indicating that the nanofluids are stable and possess Newtonian nature. Such Newtonian nature of viscosity was reported for both metal- and metal oxide-based nanofluids. Figure 13 shows the variation of viscosity with shear rate at different temperatures for hexadecane and hexadecane-based ferrofluid with φ ) 0 (base fluid) and φ ) 0.0608. The viscosity did not appreciably vary, indicating Newtonian behavior, over the shear rate and temperature studied. The effectiveness of nanofluid coolants depends on the flow mode (laminar or turbulent) and can be estimated based on fluid dynamics equations. Lower viscosity implies lower pumping power that is advantageous from an industrial application standpoint. A quantitative expression derived for fully developed laminar flow that compares the relative coefficients of viscosity and k enhancements shows that the use of nanofluid will be beneficial if the increase in the viscosity is less than four times of the increase in k.93 Viscosity and thermal conductivity enhancements can be described by linear dependence on the particle volume fraction in our studies.
k ) 1 + Ckφ kf
(10)
η ) 1 + Cηφ η0
(11)
where Ck and Cη are constants. At low volume fractions, for the nanofluid to be beneficial, the ratio of coefficients (Cη/Ck)
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should be
