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Investigations on electrical conductivity of stabilized water - Al2O3 nanofluids
Alina Adriana MINEA, Razvan Silviu LUCIU Technical University Gheorghe Asachi Iasi Bd. D. Mangeron 61, code 700050, Iasi, ROMANIA E-mail:
[email protected] Tel: 00 40 723 455071
Abstract The electrical conductivity is an important property of nanofluids that has not been widely studied. To study both the effects of temperature and concentration, the electrical conductivity of water based Al2O3 nanofluids with 12 nm diameter particles is measured. Conventional models, such as the Maxwell Model and Bruggemann correlation, were considered for comparison and disagreement were noticed. Experimental results showed the Al2O3 nanofluids increased their electrical conductivity with increasing volume fraction compared to that of the base fluid, as well as with temperature increasing. A stronger influence on volume fraction was noticed. Electrical conductivity measurements for these nanofluids indicate an enormous enhancement (390.11%) at 60 °C for a volume fraction of 4%in distilled water. Furthermore, at higher volume fractions, the electrical conductivity enhancement begins to level off, which is attributed to ion condensation effects in the high surface charge regime. A 3D statistical analysis was also considered in order to obtain an empirical correlation.
Keywords: nanofluid, alumina, volume fraction, temperature, electrical conductivity
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1. Introduction There is a great need to enhance heat transfer in a lot of industrial areas.Usual methods to enhance heat transfer rates such as active and passive techniques [1, 2] have the disadvantage to increase the required pumping power of the cooling fluid. The development of advanced fluids with improved electrical and thermal characteristics is of dominant importance to achieve higher flux densities. Electrical and thermal conductivities of solids may be orders of magnitude greater than that of fluids and it is therefore expected that dispersion of solid particles will significantly improve the thermal and electrical behavior of fluids. The use of solid particles as an additive suspended in the base fluid is a technique to augment the heat transfer. Choi [3] found that the particles of nanometer size, suspended in conventional fluids, enhance the heat transfer. These innovative heat transfer fluids consisting of suspended nanometer-sized solid particles are called “nanofluids.” Nanofluids can be considered to be the next generation heat transfer fluids as they offer exciting new possibilities to enhance heat transfer performance compared to pure liquids. The much larger relative surface area of nanoparticles, compared to those of conventional particles, not only significantly improves heat transfer capabilities, but also increases the stability of the suspensions. Suspended nanoparticles in various base fluids can alter the fluid flow and heat transfer characteristics of the base fluids. Necessary studies need to be carried out before wide application can be found for nanofluids. Various investigations have been carried out for the physical mechanism and mathematical modeling to describe and predict the thermal conductivity and heat transfer phenomena. Some models like Maxwell–Garnett [4] and Hamilton–Crosser [5] do not take particle motion into consideration. Xuan et al.[6] developed a dynamic model that takes into account the effects of Brownian motion of nanoparticles and fractals. But all the static and dynamic models developed with conduction-based mechanisms still fail to predict the magnitude and trends of the experimental data. Even though there are lack of theoretical models to explain the enhancement in conductivity in nanofluid, studies are going on in
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the experimental side with different nanoparticles to enhance conductivity. Al2O3 is the most well-known nanoparticle used by many researchers in their experimental works. Even when the size of the particles and type of base fluids are different, all the experimental results showed the enhancement of the thermal conductivity [7, 8]. It can be noted here that most of the above-mentioned studies have typically investigated the mechanism for augmentation of heat transfer by nanofluids, the stability of the suspensions and their superior thermal performance over the conventional heat transfer medium. The major focus of the research work, so far, has been on the estimation of thermophysical properties, primarily on the effective thermal conductivity. Despite the vast scientific and technological importance of electrical conductivity characteristics of nanoparticle suspensions, studies concerning the issue of the effective electrical conductivities of nanofluids have largely been ignored. Also, there is very few data published when it comes to the electrical properties of nanofluids [9 – 15]. On the other hand, among the transport properties, electrical conductivity might bring information on the state of dispersion and stability of the particulate suspension. Wong and Kurma [9] investigated electrical conductivity of alumina nanofluids and recorded an enormous increase for small volumetric concentrations compared with the base fluid (water). These results are in correlation with the present study. Teng et al [10] studied electrical conductivity of carbon nanofluids and shows a considerable underestimation while comparing calculation results with experimental data. Apart from the concentration and electric conductivity of particles and fluids, the effective electrical conductivity of nanofluids exhibits a complex dependence on the electrical double layer (EDL) interactions, ionic concentrations and other physicochemical properties which is not effectively captured by the Maxwell’s model. Also in the study, the electric conductivity of carbon/water nanofluids had a high enhancement. Sikdar et al [11] studied water based titanium oxides and found a monotonically increasing trend of electrical conductivity with the increase in temperature. Silver nanofluids are found to have a similar behavior [12]. More studies in this area and for different nanoparticles, like aluminum oxide, silicon
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oxide, zinc oxide [13], copper oxide decorated graphene [14] are converging to the same idea of an increasing electrical conductivity of the nanofluid compared to the base fluid. An interesting study is performed by Shen et al [15] with a new kind of nanofluid, ZnO-insulated oil nanofluid. Electrical property measurement showed that the electrical conductivity increases by 973 times after adding 0.75% volumetric fraction of ZnO nanoparticles into the insulated oil. Although some preliminary studies with similar objective have been reported [16-19], a systematic study addressing this extremely significant issue is yet to be found in the literature. In this context, the present work has been undertaken to explore the electrical transport property of nanofluids. This is accomplished by conducting experiments at different volume fractions of water-based alumina (Al2O3) nanofluids.
2. Theoretical models The Maxwell model [20] was the first model developed to determine the effective electrical or thermal conductivity of liquid–solid suspensions. This model is applicable to statistically homogeneous and low volume fraction liquid–solid suspensions with randomly dispersed, uniformly sized and noninteracting spherical particles. The Maxwell equation predicts that the effective conductivity of the suspension (keff), is a function of the conductivity of the particles (kp), conductivity of the base fluid (kbf) and the volume fraction ( ) of the particles, and is given by: .
k eff k bf
3 2
1
1 1
(1)
where α=kp/kbf, is the conductivity ratio of the two phases. Generalization of the Maxwell's model leads to the following cases depending on the conducting nature of the particles and the base fluid [21] a)
k eff k bf
1
3 , for kp≪kbf (insulating particles) 2
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b)
k eff k bf
1 , for kp=kbf (equal conductivity)
c)
k eff k bf
1 3 , for kp≫kbf (highly conducting particles)
Cases (a)–(c) show the theoretical effect, as predicted by the Maxwell's model, of the particle volume fraction on the relative conductivity (keff /kbf ) for a constant value of conductivity ratio (kp/kbf). The applicability of the Maxwell's model has been successfully verified by experimental data [22] for dilute suspensions ( ≪1%) with large particles (particle size larger than tens of micrometers). The present experimental situation corresponds to Case (a) in the Maxwell's model (alumina particles have very poor electrical conductivity characteristics). Therefore, it is expected that the mixture's electrical conductivity is reduced. Moreover, the experimental study is based on
1% suspension with very small
particles (nanoparticles). Another important model used for conductivity estimation is The Bruggeman Model. Effective medium approximations or effective medium theory (sometimes abbreviated as EMA or EMT) are physical models that describe the macroscopic properties of a medium based on the properties and the relative fractions of its components. They can be discrete models such as applied to resistor networks or continuum theories as applied to elasticity or viscosity but most of the current theories have difficulty in describing percolating systems. Indeed, among the numerous effective medium approximations, only Bruggeman’s symmetrical theory is able to predict a threshold. This characteristic feature of the latter theory puts it in the same category as other mean field theories of critical phenomena. There are many different effective medium approximations [23], each of them being more or less accurate in distinct conditions. Nevertheless, they all assume that the macroscopic system is homogeneous and typical of all mean field theories; they fail to predict the properties of a multiphase medium close to the percolation threshold due to the absence of long-range correlations or critical fluctuations in the theory.
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The properties under consideration are usually the conductivity σ or the dielectric constant of the medium. These parameters are interchangeable in the formulas in a whole range of models due to the wide applicability of the Laplace equation. The problems that fall outside of this class are mainly in the field of elasticity and hydrodynamics, due to the higher order tensorial character of the effective medium constants. In this article, it shall generalize Bruggeman effective medium theory (EMT) [24, 25] to investigate the effective electrical conductivity in alumina – water nanofluid. It considers an alumina nanofluid in which the nano particles with volume fraction
and alumina particles with conductivity kp are randomly mixed.
For simplicity, it assumes that particles are spherical. Since nanoparticles are randomly oriented, the effective conductivity keff is isotropic. For such a nanofluid, the EMT gives [24],
1
kp
k eff
kp
kp
k bf
k eff
1/ 3
(2)
The theoretical results on effective electric conductivity of the nanofluid suspensions are found to be in disagreement with experimental data. This disagreement appears mainly because the alumina electrical conductivity is very low (10−8 μS/cm) and it was expected a decrease in effective conductivity. Further, the experiment is described along with its interpretation.
3. Experimental observation -Al2O3 nanoparticles in 20% wt. aqueous solution (Nanostructured and Amorphous Material, Inc., USA) were used for this investigation. The base fluid was distilled water. The suspensions of nanoparticles in water were subjected to ultrasonic vibration for about 1 h to ensure uniform nanoparticle dispersion was obtained. Then, appropriate amounts of distilled water were added to the suspensions and thoroughly mixed to achieve the desired concentration of nanofluids. It should be noted that the suspension stability of nanoparticles within the base fluid, distilled water, has been found to be very good even after a
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relatively long resting period, even few months. To investigate the effect of nanoparticle concentration, nanofluids of 1, 2, 3 and 4% by volume were prepared. Table 1 contains the nanofluid properties.
Table 1. Main characteristics of the tested nanofluids Al2O3 - water Structure
gamma
purity
99.9%
average particle diameter
10 5 nm
structure percentages of original solution
79% water + 20.3% Al2O3 + 0.003 % Fe
surfactant
none
For a better description of the nanofluid, few imagistic techniques were employed. Fig. 1 shows the field emission of a TEM microscope Tesla BS 613 at a tension U=100kV and an intensity I=100 A. The image was obtained from an aqueous suspension of Al2O3 particles with volume fraction of 1%. It can be observed that although there are signatures of agglomeration present in the micrograph, the particles are truly nanometric. Major part of the agglomeration seen in the image occurred during drying of the base liquid. However, since the photographs were taken only after drying the nanofluid, the intrinsic dispersion of nanoparticles in the fluid cannot be clearly ascertained from the figure.
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Figure 1. TEM image of the alumina nanoparticles after dispersion
Moreover, information about particle dimension distribution was obtained and in Table 2 is presented. Fig. 2 is the histogram of the dimensions frequency.
Table 2. Dimensions and frequency of particles appearance Nr.crt.
Dimension
Frequency
[nm]
[%]
1
6 – 7.5
3.32
2
7.5 – 9
6.88
3
9.0 – 10.5
11.46
4
10.5 -12
34.08
5
12.0-13.5
20.06
6
13.5 – 15.0
8.65
7
15.0 – 16.5
6.82
9
8
16.5 – 18.0
5.84
9
18.0 - 19.5
2.86
Figure 2. Particle dimension distribution
Analyzing Fig. 2 and Table 2 it results a medium diameter dm = 12 nm and a standard deviation σ=2.67 nm. Moreover, an ESEM analysis was done to see the nanofluid uniformity. The environmental scanning electron microscope or ESEM is a scanning electron microscope (SEM) that allows for the option of collecting electron micrographs of specimens that are "wet," uncoated, or both by allowing for a gaseous environment in the specimen chamber. Although there were earlier successes at viewing wet specimens in internal chambers in modified SEMs, the ESEM with its specialized electron detectors and its differential pumping systems to allow for the transfer of the electron beam from the high vacuums in the gun area to the high pressures attainable in its specimen chamber make it a complete and unique instrument designed for the purpose of imaging specimens in their natural state. The analysis was performed on a Microscope with scanning in medium Quanta 200 3D and it is in Fig. 3.
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Figure 3. ESEM analysis of the 1% nanofluid
From these two analyses one can notice the particle good sphericity, the solution stability and its homogeneity. To measure the electrical conductivity of nanofluids, a precision conductivity cell (Multiparameter Consort C 831) with an application range of 1 μS/cm– 200 mS/cm has been used. The resolution is 0.01 μS/cm. The electrical conductivity of Al2O3-water nanofluid was measured at different temperatures starting with the room temperature (25°C) until 70°C and subsequent measurements were conducted to examine the effects of volume fractions (1- 4%) on the effective electrical conductivity of the nanofluid. For each case, five to six measurements were performed, and the mean value was reported. Table 3 contains the mean experimental data.
Table 3 Experimental for electrical conductivity at 25 °C volume concentration,
electrical conductivity,
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[%]
k [ S/cm]
distilled water
5
1
638
2
1081
3
1474
4
1903
4. Results and discussions 4.1. Electrical conductivity The electrical conductivity of alumina is reported as 10−8 μS/cm in the literature [26, 27]; conductivity of the base fluid (distilled water) used in the present study varies from 5 μS/cm to 11 μS/cm in the present experimental temperature range. Table 3 shows the measured electrical conductivity of water and of the nanofluid at room temperature. It can be seen that the conductivity values obtained from the experiment agree well with the reference values available in literature [28, 29], in an order of magnitude sense. Fig. 4 shows the effective electrical conductivity of alumina nanofluid at different volume fractions and temperatures. The temperatures considered are from 25 to 70°C. It is seen that the electrical conductivity of alumina nanofluid increases almost linearly with increase in the volume fraction of the alumina nanoparticles and temperature. The highest value of electrical conductivity, 4210 μS/cm, was recorded for a volume fraction of 4% at a temperature of 70°C.
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a.
b. Figure 4. Measured electrical conductivity: a. variation with temperature; b. variation with volume fraction
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It is of interest to examine the enhancement in electrical conductivity of the alumina nanofluid with respect to the base fluid. For this purpose, the rate of enhancement of the effective electrical conductivity, defined as the difference between the electrical conductivity of the nanoparticle suspension and the electrical conductivity of the base fluid, divided by the electrical conductivity of the base fluid, is plotted as a function of temperature, at volume fractions of 1, 2, 3 and 4% and as a function of volume fraction for different temperatures. As illustrated in Fig. 5a, the rate of electrical conductivity enhancement is almost constant on different temperatures for the same volume fraction. Some minor increases are for 3% and 4% volume fractions. In Fig. 5b, the rate of enhancement increases with respect to increase in the nanoparticle volume fraction, which indicates a dependence on volume fraction, the greater is the enhancement.
a.
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b. Figure 5. Electrical conductivity enhancement of Al2O3-water nanofluid: a. variation with temperature; b. variation with volume fraction
A maximum of 390.11 % increase in the electrical conductivity was observed for 4% ( =4) volume concentration of alumina nanoparticles in water at a temperature t=60 °C. Also, one can notice a stronger dependence of the electrical conductivity enhancement on volume fraction and a lower one on temperature variation. If it refers to Case (a) in the Maxwell's model (alumina particles have very poor electrical conductivity characteristics), it is expected that the mixture's electrical conductivity is reduced. However, from Fig. 4, it can be seen that the measured electrical conductivity of the suspension increases with volume fraction of the nanoparticles. Therefore, the theoretical models [20, 24], which compared well with the
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measurements of dispersions with large size (micrometer or larger) particles, under predicts the conductivity increase in nanoparticle- fluid mixtures. This is due to the fact that, apart from the physical properties of fluid and conductivity of particles and fluids, the effective electrical conductivity of colloidal nanosuspensions in a liquid exhibits a complex dependence on the EDL (electric double layer) characteristics, volume fraction, ionic concentrations and other physicochemical properties, which is not effectively captured by the standard models. When alumina particles are suspended in a polar liquid (water in the present case), electric charges develop on their surfaces. Ions of charge opposite to that of the particle surface are attracted, causing the development of a charged diffuse layer surrounding the particle. With an increase in particle volume fraction, the availability of conducting pathways increases in the solution, which in turn increases the overall electrical conductivity of the solution. If it refers to Figure 5b, obvious deviation in linearity dependence of electrical conductivity enhancement with temperature is observed when the concentration becomes higher. One possible reason is that the direct contact of the nanoparticles aggregates in the nanofluid is activated by the increased temperature. That means at higher temperature, the electrons are more easily to transport through the short conducting paths among the aggregates. The dependence of electrical conductivity on the aggregation of the particles was studied by Chakraborty et al. [30]. They concluded that aggregation has both positive and negative effects on the electrical conductivity of the colloidal suspensions, which depends on the volumetric fraction of the particles. In this study, it is interesting to observe that the aggregation only enhance the electrical conductivity in the nanofluid. This difference might be due to the conducting property of Al 2O3 in the insulated fluid system. Since the experimental data demonstrated an almost linear relationship between the enhancement factor and both the temperature and nanoparticle volume fraction (Fig. 5a and b), a two-factor regression analysis [31], using Table Curve3D commercial code [32], was employed to develop an empirical relationship for the electrical conductivity at different volume fractions as a function of temperature. Data analysis starts with the most trustable equations and through computing were obtained more than 300
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equations. The most convenient regression is a polynomial one, depicted as Eq. (3) with an R2 value of 0.9975. Moreover, its details are presented in table 4, along with the statistical parameters (in table 5). k = 176.69 +588.41 + 11.06
– 13.64 t - 86.31
2
– 1.01 t
2
3
- 0.003 t3+ 0.18 t2
+ 0.36 t2+ 1.07 t
+ (3)
where: k is the electrical conductivity t is the temperature of nanofluid is the volume fraction
Figure 6. Regression surface
Fig. 6 is the 3D representation of the experimental points, which stood at the bases of this work, along with the regression surface. All the statistical data along with their graphical representation were obtained with the Table Curve 3D commercial code.
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It may be noted that Eq. (3) indicates the relative importance of the impact of volume fraction, , on electrical conductivity of alumina nanofluid. The coefficients for the volume fraction are large (see table 4: coefficients a, b, c, d, g), indicating a strong dependence of the effective electrical conductivity on volume fraction and less on the temperature, as one can notice from table 4 (coefficients e, f, h and j).
Table 4. Experimental data fitting k=a+b +c t+d
2
+e t2+f
t+ g
3
+h t3+i
t2+ j
2
t 99% Conf 99% Conf
Eqn # R2 DF Adj R2 Fit Std Err F-stat
Parameters
Values
Std Error
T Value
Lim
Lim
a
176.6919
568.5105
0.310798
-1013.21
1366.598
b
588.4183
150.8045
3.901862
272.7809
904.0558
c
-13.6448
38.91081
-0.35067
-95.0861
67.79645
d
-86.3048
53.45654
-1.61448
-198.191
25.58105
e
0.364499
0.846337
0.430678
-1.40691
2.135904
f
1.067322
4.994135
0.213715
-9.38552
11.52017
g
11.05885
8.140367
1.358519
-5.97914
28.09683
h
-0.003
0.005911
-0.50681
-0.01537
0.009376
i
0.176213
0.047628
3.699816
0.076528
0.275899
j
-1.01056
0.503384
-2.00754
-2.06416
0.043029
50 0.99745 0.996 71.8638 826.011
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Table 5. Statistical of experimental results t
k
k predict
Residual
residual, % 95% confindence limit
95% prediction limit
1
1
25
638
684.1611 -46.1611
-7.23528
561.5001
806.8221
487.7371 880.5852
2
1
30
730
733.0993 -3.09929
-0.42456
641.9024
824.2962
554.6236 911.5749
3
1
40
880
865.464
771.931
958.997
685.7834 1045.145
4
1
50
1030 1027.241 2.758717 0.267837
934.8508
1119.632
848.1528 1206.33
5
1
60
1200 1198.545 1.454907 0.121242
1101.668
1295.423
1017.101 1379.989
6
1
70
1390 1359.489 30.51073 2.195017
1224.493
1494.486
1155.135 1563.844
7
2
25
1081 1052.844 28.15605 2.60463
951.7383
1153.95
869.1076 1236.58
8
2
30
1230 1143.212 86.78834 7.055963
1061.291
1225.133
969.2929 1317.131
9
2
40
1450 1388.228 61.77183 4.260126
1305.25
1471.207
1213.809 1562.648
10
2
50
1690 1702.381 -12.381
-0.7326
1624.707
1780.055
1530.422 1874.34
11
2
60
1940 2065.784 -125.784
-6.48371
1977.267
2154.301
1888.663 2242.906
12
2
70
2420 2458.551 -38.5512
-1.59302
2350.202
2566.901
2270.731 2646.371
13
3
25
1474 1501.858 -27.8579
-1.88995
1400.752
1602.964
1318.122 1685.594
14
3
30
1540 1617.176 -77.1756
-5.01141
1535.255
1699.097
1443.257 1791.094
15
3
40
1910 1941.885 -31.8851
-1.66938
1858.906
2024.864
1767.466 2116.305
16
3
50
2330 2375.455 -45.4545
-1.95084
2297.781
2453.129
2203.495 2547.414
17
3
60
3010 2897.998 112.0021 3.721
2809.481
2986.515
2720.877 3075.119
18
3
70
3560 3489.629 70.37097 1.976713
3381.28
3597.979
3301.809 3677.449
19
4
25
1903 1848.87
1726.209
1971.531
1652.445 2045.294
20
4
30
1950 1972.658 -22.6579
-1.16194
1881.461
2063.855
1794.182 2151.134
21
4
40
2310 2344.101 -34.1013
-1.47625
2250.568
2437.634
2164.421 2523.782
22
4
50
2920 2864.129 55.8715
1.913408
2771.738
2956.519
2685.04
14.53603 1.651822
54.13053 2.844484
3043.217
19
23
4
60
3520 3512.853 7.14671
0.203032
3415.976
3609.731
3331.409 3694.297
24
4
70
4210 4270.39
-1.43443
4135.393
4405.386
4066.035 4474.744
-60.3896
5. Conclusion This paper presents the electrical conductivity measurements carried out with Al2O3–water (1 – 4% particle volume fraction) nanofluids at atmospheric pressure and different temperatures. Aluminum oxide nanoparticles were dispersed in distilled water to form stable nanofluids. Systematic experiments were carried out to investigate the effects of nanoparticle volume fraction on the effective electrical conductivity of Al2O3-water nanofluid. The experimental results show that the electrical conductivity of alumina nanofluid is significantly greater than the base fluid. The increase in electrical conductivity is a function of volume fraction of nanoparticles and temperature. At room temperature (25°C), an increase of 379.6 % in effective electrical conductivity of nanofluid is observed for a volume fraction of 4%. The electrical conductivity of the nanofluid increases almost linear with increase in the volume fraction. Later on, a polynomial regression analysis based on volume fraction and temperature has been applied to develop an empirical relationship for the electrical conductivity, k. The present analysis indicates the relative influence of volume fraction on the electrical conductivity values. Al2O3–water nanofluid seems to be promising as electrical medium.
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