Rheological Behavior of Nanofluid

5 Rheological Behavior of Nanofluid 5.1 Introduction Rheological properties define the flow characteristics of a fluid. A knowledge of rheology is necessary in fluid mechanics, polymer science, mining, food and chocolate processing, and many other applications. Rheology is one of the most important properties that describe the flow and/or deformation of matter under the influence of extremely imposed mechanical forces. It can be defined as the properties of matter determining its behavior, that is, its reaction to deformation and flow. Different types of flow behaviors are demonstrated in Fig. 5-1. In general, fluid flow is either Newtonian or non-Newtonian. If the viscosity of a fluid or suspension remains constant with different applied shear rates, the fluid is considered as Newtonian; if viscosity changes with the applied shear rates, it is non-Newtonian; if viscosity increases with shear rates, it is dilatant or shear thickening; conversely, if viscosity decreases with increasing shear rates, it is pseudoplastic or shear thinning behavior. In oil recovery and refinery industries, drilling muds, food and additive processing industries, their rheological properties are very important for handling. Rheological behaviors give an idea about flow characteristics, which is significant to design required pumping power and pressure drop. Nanofluids are the colloidal suspension of nanograde (1029) solid particles into a base fluid. Nanofluids are promising fluids for solar collector (Faizal, Saidur, Mekhilef, Hepbasli, & Mahbubul, 2015), heat exchanger (Elias et al., 2013), electronics coolant (Khaleduzzaman et al., 2014), refrigeration (Mahbubul, Saidur, & Amalina, 2013), and many other applications (Saidur, Leong, & Mohammad, 2011), which are related to the flow of fluids. Therefore, for the practical implementation of nanofluids, it is essential to analyze their rheological properties. In most cases, an addition of a small amount of solid particles changes the flow characteristics of suspensions. Most of our surrounding fluids have a yield point, which requires a small amount of stress to flow (Bonn & Denn, 2009). Below this stress limit, a fluid acts like a solid (does not flow), and the it starts to flow after this critical level of the stress is termed the yield stress. Nevertheless, there are controversies among researchers, even in dictionary form for the definition of yield stress (Barnes, 1999). Mostly, nanofluids are considered to be used under flow conditions (Kwak & Kim, 2005). Therefore, flow characteristics of nanofluids are necessary for their practical applications. Different fluids have various flow characteristics and even for the same base fluid, various types of results (both Newtonian and nonNewtonian) have been reported in the literature (Chen, Witharana, Jin, Kim, & Ding, 2009). Many analytical models (e.g., thermal conductivity, viscosity, density) related to Newtonian fluids are using for non-Newtonian nanofluids have been observing in the literature (Banerjee, 2013), which will not give a proper approximation. For example, Einstein’s equation (Einstein, 1906) is improper to assume the viscosity of nanofluids in most cases, as it is Preparation, Characterization, Properties, and Application of Nanofluid. DOI: https://doi.org/10.1016/B978-0-12-813245-6.00005-8 © 2019 Elsevier Inc. All rights reserved.

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Shear thickening (dilatant) Newtonian

Shear thinning (pseudo plastic)

Shear stress (τ),N/m2

Viscosity (μ),Pa·s

Shear thickening (dilatant)

.

Shear rate (γ),s–1

Newtonian

Shear thinning (pseudo plastic)

.

Shear rate (γ),s–1

FIGURE 5-1 Types of flow behaviors of fluids or suspensions.

suitable for Newtonian fluids with spherical particles. Even this model has been used to estimate the viscosity of tubular shape particles (carbon nanotubes (CNTs), titanate nanotubes) suspended in nanofluids, which is not appropriate. It has been observed that even for a small concentration of nanoparticles, typical Newtonian fluids often become non-Newtonian (Banerjee, 2013). (This paragraph is adapted from Mahbubul, Saidur, Hepbasli, and Amalina (2016a), copyright (2015), with permission from Elsevier.) Various parameters, such as material type, base fluid type, percentage of concentration, size and shape of particles, surfactants, temperature, shear stress, shear rate (applied force), and time have an effect on rheology. Specifically, in the case of rheological properties of nanofluid, researchers analyze viscosity as a function of volume concentration, temperature, and shear rate (to check the flow characteristics, whether they are Newtonian or non-Newtonian). Even rheological knowledge is required to understand the interactions of fluid
particles and particles
particles in the fluid. Furthermore, it gives an idea of the microstructure under both static and dynamic conditions (Kwak & Kim, 2005). Wang and Guo (2006) suggest preparing colloidal suspensions in different methods as the aggregate size of particles proportionally affects the shear stress and viscosity of a sample (Leong, Scales, Healy, Boger, & Buscall, 1993). Due to the significance of rheology in fluid mechanics, extensive investigations of rheological properties of nanofluids are necessary. Although it is a colloidal property (also considered as thermophysical property), due to the importance of this property (in fluid mechanics and mechanical engineering), rheology deserves extra attention. That is why a separate chapter is included on the rheology of nanofluid.

5.2 Measurement Method Different types of rotational rheometers are used, which are classified based on the cylinder shape: (A) concentric (or Couette) cylinder, (B) cone and plate, and (C) parallel plate, as

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199

FIGURE 5-2 Schematic diagrams of typical rheometers: (A) concentric (or Couette) cylinder, (B) cone and plate, and (C) parallel plate. The associated description of cylinder types are adapted from Kim, Y., Kim, K., & Park, Y. (2012). Measurement techniques for red blood cell deformability: Recent advances. In Blood cell-An overview of studies in hematology, InTech.

Parallel plate

Underfilled

Correct

Overfilled

FIGURE 5-3 The precise amount of loaded sample into the parallel plate geometry. Reprinted from MuñozSánchez, B., Nieto-Maestre, J., Veca, E., Liberatore, R., Sau, S., Navarro, H. . . . García-Romero, A. (2018). Rheology of Solar-Salt based nanofluids for concentrated solar power. Influence of the salt purity, nanoparticle concentration, temperature and rheometer geometry. Solar Energy Materials and Solar Cells 176, 357
373, copyright (2017), with permission from Elsevier.

shown in Fig. 5-2. Two concentric cylinders are used in Couette types, where one is a rotational inner cup and the other is a stationary outer cylinder. The time-independent shear rate can be precisely measured by concentric cylinders (Nguyen & Boger, 1987). In cone and plate types, an inverted cone with a very shallow angle (B5 degrees) rotates; the shear rate under the plate is maintained consistently and independent of the flow curve. A parallel plate type is a simplified version of the cone and plate viscometer and has the advantage of flexible space between two parallel plates (Kim, Kim, & Park, 2012). The viscous fluid can be confined and rotated in a narrow space between two circular parallel plates (Gent, 1960). Filling of the sample is important in rheometers, especially cone and plate, and parallel plate types. Underfilling the container may lead to errors and overfilling may cause the loss of fluid (Leo, Mohamed, Karen, Alexander, & Marcus, 2015; Muñoz-Sánchez et al., 2018). An example of the precise amount of sample in a parallel plate rheometer is portrayed in Fig. 5-3 from Muñoz-Sánchez et al. (2018). A detailed example of nanofluid rheology measurement is adapted from Mahbubul, Saidur, Amalina, and Niza (2016b) where a concentric (or Couette) type rheometer was used. This type of rheometer was used in many other nanofluid rheology analyses (Mahbubul, Saidur, Hepbasli, & Amalina, 2016a; Mahbubul, Saidur, Amalina, & Niza, 2016b;

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Temp. display USB Cable Computer

LVDV-III Rheometer

Spindle Ultra low adapter

Outlet pipe Nanofluid

Digital refrigerated circulator bath

Inlet pipe FIGURE 5-4 Schematic illustration of rheology measurement. Reprinted from Mahbubul, I.M., Khaleduzzaman, S.S., Saidur, R., and Amalina, M.A. (2014). Rheological behavior of Al2O3/R141b nanorefrigerant. International Journal of Heat and Mass Transfer 73, 118
123, copyright (2014), with permission from Elsevier.

Timofeeva et al., 2010; Namburu, Das, Tanguturi, & Vajjha, 2009; Namburu, Kulkarni, Dandekar, & Das, 2007; Mahbubul, Khaleduzzaman, Saidur, & Amalina, 2014; Mostafizur, Abdul Aziz, Saidur, Bhuiyan, & Mahbubul, 2014; Rudyak, Minakov, & Krasnolutskii, 2016; Agarwal, Vaidyanathan, & Sunil Kumar, 2015). An LVDV-III ultra-programmable rheometer (Brookfield, USA) was used to measure the viscosity and shear stresses of nanofluids at different shear rates from 12.23 to 305.75 s21. The rheometer was connected to a computer and Rheocalc 32 software was used for computer interfacing. An ultra-low adapter (ULA) was coupled with the main unit to use a lower amount of sample (about 16 mL is necessary). To maintain a constant temperature, an advanced programmable refrigerated water bath with a temperature stability of 6 0.01 C (Model AD07R-40-12E, Polyscience, USA) was linked to the water jacket of the ULA. The methodology is illustrated in Fig. 5-4. Viscosities and shear stresses of all samples were measured at shear rates from 36.69 to 305.75 s21, while the ULA spindle rotating was 30
250 rpm. It should be noted that there are two ways to change the spindle rotating speed in such kinds of programmable machines. Either the shear rate will be linearly changed with time or the ramp will stop at various rates for some time to be able to give steady-state values of viscosity/shear stresses. The second option is more reliable and involves manually adjusting the ramp speed with time. The first is a programmable option and may not give steady-state viscosity or be close to it, unless the operator is experienced enough with the device and sample, and knows how long it takes to reach steady state and the final steady-state viscosity for such samples. Only then can the operator set the speed change program with time accordingly. Specifically, in Mahbubul, Saidur, Amalina, and Niza (2016b), the speed ramp was changed by 10 rpm (12.23 s21 shear rate) and it was held for 20 s at each speed. A data point was taken just before the changing of each speed by using the built-in program and software of the device. Later, two samples were investigated again at 50, 100, 200, and 300 s21 shear rates and the ramp speeds were held constant at a point until it reached the final steady-state viscosity to study the variation of steady-state viscosity with the measured viscosity. It was observed that, in most cases, it took only 15 s to reach steady-state viscosity. Therefore, the measured viscosities of the study are very close to the viscosity at the steady state for each rate. Since torque range exceeds the limit of 100% at 300 s21 shear rates due to higher viscosity at 10 C temperature, therefore, in this purpose,

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201

250 s21 shear rates was used in lieu of 300 s21 shear rate for samples at 10 C. To get more precise values, each experiment was conducted at least four times and the average value was considered throughout the analysis. Viscosities and shear stresses were measured for the temperature range of 10
50 С with 10 С intervals and the precisions of temperatures were maintained in the range of 6 0.5 C. (Adapted from Mahbubul, Saidur, Amalina, and Niza (2016b), copyright (2016) with permission from Elsevier.)

5.3 Rheological Model Nanofluid is a new field in engineering and medicine; therefore, an appropriate rheological model needed to be identified based on experimental results for different nanofluids (Banerjee, 2013). There are some mathematical models developed to describe the flow behavior of fluids or suspensions. The most frequently applied model is the Power law (Ostwald) model (Ostwald, 1925), which has been used to analyze the flow characteristics expressed as: τ 5 K γn

ð5:1Þ

where, τ is the shear stress (N/m2), γ is the shear rate (s21), K is the consistency coefficient (mPa  s), and n is the Power law index or flow index (dimensionless). The types of fluid depend on the value of this Power law index n as n , 1 means pseudoplastic or shear thinning, n 5 1 means Newtonian fluid, and n . 1 means dilatant or shear thickening behavior (Mahbubul, Saidur, Amalina, & Niza, 2016b). The Bingham equation (Bingham, 1922) is expressed as: τ 5 τ 0 1 ηγ

ð5:2Þ

where, τ is the shear stress (N/m2), τ 0 is the yield stress (N/m2), η is the plastic viscosity (mPa  s), and γ is the shear rate (s21). The Herschel
Bulkley mathematical model (Herschel and Bulkley, 1926) is expressed as: τ 5 τ 0 1 K γn

ð5:3Þ

where, τ is the shear stress (N/m2), τ 0 is the yield stress (N/m2), γ is the shear rate (s21), K is the consistency coefficient (mPa  s), and n is the flow behavior index (dimensionless). The Casson equation (Casson, 1959) was originally proposed for the shear thinning behavior of printer ink type fluids, expressed as: pffiffiffi pffiffiffiffiffi pffiffiffiffiffiffi τ 5 τ 0 1 ηγ

ð5:4Þ

where, τ is the shear stress (N/m2), τ 0 is the yield stress (N/m2), η is the plastic viscosity (mPa  s), and γ is the shear rate (s21).

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5.3.1 Rheogram of Different Base Fluids Some samples of base fluids and nanofluids were analyzed (in addition to the rheology measurement procedure stated in Section 5.2) by using Brookfield Rheocalc 32 software to observe the fitting parameters with rheology models. Fig. 5-5 shows the rheogram (shear stress versus shear rate curve) of R141 refrigerant. It can be seen in Fig. 5-5 that among the four models the raw data (measured) is best fitted with the Herschel
Bulkley model (refer to Fig. 5-5C). Moreover, the measured data are closely fitting with the Power law model (Fig. 5-5A). Fig. 5-6 shows the rheogram of water
ethylene glycol mixture (50:50 by volume) at 25 C. It can be seen in Fig. 5-6 that rheogram of water
ethylene glycol mixture fits with most of the models; it is best fitted with the Herschel
Bulkley model (refer to Fig. 5-6C) with 100% confidence of fitting.

FIGURE 5-5 Rheogram analysis of R141 refrigerant: (A) Power law, (B) Bingham, (C) Herschel Bulkley, and (D) Casson.

Chapter 5 • Rheological Behavior of Nanofluid

203

FIGURE 5-6 Rheogram analysis of water
ethylene glycol mixture (50:50 by volume): (A) Power law, (B) Bingham, (C) Herschel
Bulkley, and (D) Casson.

5.3.2 Rheogram of Different Nanofluids Fig. 5-7 shows the rheogram of 0.5 vol.% of Al2O3
water nanofluid at 25 C. It can be seen in Fig. 5-7 that among the four models the raw data (measured) are best fitted with the Herschel
Bulkley model (refer to Fig. 5-7C). Fig. 5-8 shows the rheogram of 0.5 wt.% of graphene oxide
water nanofluid at 30 C. It can be seen in Fig. 5-8 that among the four models the raw data (measured) are fitted only with the Herschel
Bulkley model (refer to Fig. 5-8C).

5.3.3 Effect of Temperature on Rheogram It is well known that the viscosity of a liquid is decreased with an increase in temperature due to weakening of the interparticle adhesion forces (Murshed, Tan, & Nguyen, 2008). Some samples were analyzed to see the effect of temperature on flow behavior. Table 5-1 shows the effect of temperatures from 10 to 50 C (with 10 C temperature intervals) on different parameters of rheological models for water
ethylene glycol mixture (50:50 by volume). It can be seen in Table 5-1 that at a lower temperature, the fluid has a higher fitting percentage with all the models. With an increase in temperature, the fitting percentages were decreased for the fluid.

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PREPARATION, CHARACTERIZATION, PROPERTIES, AND APPLICATION OF NANOFLUID

FIGURE 5-7 Rheogram analysis of 0.5 vol.% of Al2O3
water nanofluid at 25 C: (A) Power law, (B) Bingham, (C) Herschel Bulkley, and (D) Casson.

Table 5-2 shows the effect of temperatures from 10 to 50 C (with 10 C temperature intervals) on different parameters of rheological models for 0.5 vol.% of Al2O3
water nanofluid. Unlike Table 5-1, in Table 5-2, the fitting percentages were found to be higher with an increase in temperature for all the models. Table 5-3 shows the effect of temperatures from 10 to 50 C (with 10 C temperature intervals) on different parameters of rheology models for 0.5 wt.% of graphene oxide
water nanofluid. Unlike Table 5-1 and Table 5-2, in Table 5-3, the fitting percentages were found to be independent of the variation in temperature for all the models.

5.3.4 Effect of Ultrasonication on Rheogram Rheograms of 0.5 vol.% of Al2O3
water nanofluid prepared by different ultrasonication durations (0
5 h) were analyzed using Power law (Ostwald, 1925), Herschel
Bulkley (Herschel and Bulkley, 1926), Bingham (Bingham, 1922), and Casson (Casson, 1959) models.

Chapter 5 • Rheological Behavior of Nanofluid

205

FIGURE 5-8 Rheogram analysis of 0.5 wt.% of graphene oxide
water nanofluid at 30 C: (A) Power law, (B) Bingham, (C) Herschel Bulkley, and (D) Casson.

5.3.4.1 Analyses by Power Law Model The flow characteristics of the nanofluids prepared by 0, 1, 2, 3, 4, and 5 h of ultrasonication duration were analyzed by the Power law rheological model (Ostwald, 1925). A very good agreement with the model was observed as the average confidence of fit was 98.77% (R2 in %), which was found to be 97.77% as the lowest. The details of the fitting parameters are reported in Table 5-4. The flow index values are plotted in Fig. 5-9. The parameters were calculated for the experimental values at 10, 20, 30, 40, and 50 C temperature. It is noted that the types of fluid depend on the value of this Power law index n; as n , 1 means pseudoplastic or shear thinning, n 5 1 means Newtonian fluid, and n . 1 means dilatant or shear thickening behavior. It is found in Fig. 5-9 that the flow index value increased with the increase of temperature, which indicates that the nanofluids were strong non-Newtonian with shear thickening behavior with increasing temperature. It was also found that at a lower temperature (10 C), the values of n were lower for the nanofluid prepared without ultrasonication (0 h). It is observed from Fig. 5-9 that the flow behavior index varies for the nanofluid

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Table 5-1 Curve-Fitting Parameters of Water
Ethylene Glycol Mixture (50:50 by Volume) at Different Temperatures for Different Rheological Models Model

Temperature ( C)

Power law 10 20 30 40 50 Herschel
Bulkley 10 20 30 40 50 Bingham 10 20 30 40 50 Casson 10 20 30 40 50

Confidence of Fit (%)

Parameters

τ 0 (N/m2) 0.010
0.005 0.008 0.035 0.056 τ 0 (N/m2) 0.002 0.005
0.005
0.017
0.055 τ 0 (N/m2) 0.000 0.000 0.000 0.000 0.004

K (mPa  s) 6.86 4.48 3.30 2.49 1.54 K (mPa  s) 5.16 5.01 2.41 0.58 0.04 η (mPa  s) 5.96 4.12 3.23 2.69 2.71 η (mPa  s) 5.82 4.08 3.22 2.69 2.85

n 0.97 0.98 0.99 1.00 1.07 n 1.03 0.96 1.05 1.27 1.76

98.7 99.2 98.3 97.0 91.2 100 100 100 99.2 99.3 98.9 99.0 98.1 92.7 77.1 99.5 99.6 99.3 98.0 94.1

prepared by 0 and 1 h of ultrasonication. However, in the case of the nanofluids prepared by 2, 3, 4, and 5 h of ultrasonication, the values of n were almost identical. (This paragraph is adapted from Mahbubul, Saidur, Amalina, and Niza (2016b), copyright (2016), with permission from Elsevier.) The effect of ultrasonication duration of nanofluid on the consistency index (k) was determined using the Power law model (Ostwald, 1925) and portrayed in Fig. 5-10 from Mahbubul, Saidur, Amalina, and Niza (2016b). It can be seen from Fig. 5-10 that the consistency index was decreased with increasing temperature. This is because flow consistency index k is proportional to viscosity and viscosity decreased with an increase in temperature. It is also observed that the consistency index decreased with an increase in ultrasonication duration. The values of k were found to be higher for the nanofluid prepared without ultrasonication and it rapidly decreased with an increase in the ultrasonication period. A very slow decrement rate of k was observed after 1 h of ultrasonication. (This paragraph is adapted from Mahbubul, Saidur, Amalina, and Niza (2016b), copyright (2016), with permission from Elsevier.)

Chapter 5 • Rheological Behavior of Nanofluid

207

Table 5-2 Curve-Fitting Parameters of 0.5 vol.% of Al2O3
Water Nanofluid at Different Temperatures for Different Rheological Models Model

Temperature ( C)

Power law 10 20 30 40 50 Herschel
Bulkley 10 20 30 40 50 Bingham 10 20 30 40 50 Casson 10 20 30 40 50

Confidence of Fit (%)

Parameters

τ 0 (N/m2) 0.059 0.027 0.008 0.001
0.003 τ 0 (N/m2)
0.122
0.125
0.117
0.106
0.101 τ 0 (N/m2) 0.032 0.045 0.047 0.045 0.046

K (mPa  s) 0.52 0.27 0.18 0.14 0.11 K (mPa  s) 0.01 0.03 0.07 0.10 0.11 η (mPa  s) 2.94 2.73 2.50 2.29 2.18 η (mPa  s) 3.61 3.60 3.41 3.18 3.06

n 1.27 1.38 1.44 1.47 1.51 n 1.91 1.75 1.60 1.53 1.50

90.6 91.0 93.5 95.3 96.7 99.8 99.9 99.9 99.9 100 79.5 78.1 79.7 81.5 82.3 93.7 93.6 94.7 95.5 96.2

Garg et al. (2009) used the Power law model to analyze the effect of the sonication period on the flow behavior of multiwalled carbon nanotubes (MWCNTs) with deionized water (DIW) and gum arabic. The results are reprinted in Fig. 5-11. It can be seen in Fig. 5-11A that the flow consistency index was increased for the addition of nanoparticles and decreased with an increase in temperature. Moreover, the highest flow consistency index was observed for 40 min of ultrasonication and then it was decreased with further ultrasonication. The flow behavior index was found to be increased with an increase in temperature and decreased with the addition of nanoparticles, as shown in Fig. 5-11B.

5.3.4.2 Analyses by Herschel
Bulkley Model The yield stress for the 0.5 vol.% of Al2O3
water nanofluids prepared by different ultrasonication durations was analyzed with the Herschel
Bulkley rheological model (Herschel and Bulkley, 1926). A very good agreement with the model has been observed as the average confidence of fit was found to be 99.87% (R2 in %), which was within the confidence probability between 99.55% to 99.96%. The details of the fitting parameters are reported in

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Table 5-3 Curve-Fitting Parameters of 0.5 wt.% of Graphene Oxide
Water Nanofluid at Different Temperatures for Different Rheological Models Model

Temperature ( C)

Power law 10 20 30 40 50 Herschel
Bulkley 10 20 30 40 50 Bingham 10 20 30 40 50 Casson 10 20 30 40 50

Confidence of Fit (%)

Parameters

τ 0 (N/m2) 0.042 0.025 0.014 0.007 0.005 τ 0 (N/m2)
0.088
0.091
0.083
0.072
0.064 τ 0 (N/m2) 0.013 0.018 0.019 0.018 0.016

K (mPa  s) 1.06 0.69 0.50 0.42 0.36 K (mPa  s) 0.04 0.04 0.06 0.09 0.10 η (mPa  s) 2.74 2.54 2.28 2.06 1.88 η (mPa  s) 3.04 2.95 2.72 2.49 2.29

n 1.13 1.19 1.23 1.25 1.26 n 1.75 1.70 1.63 1.53 1.50

87.4 86.2 86.3 87.3 88.8 99.7 99.9 99.9 99.9 99.9 65.8 60.4 59.7 62.3 64.0 91.6 90.6 90.6 91.2 91.8

Table 5-5. Fig. 5-12 shows the effect of the ultrasonication periods (used to prepare nanofluid) on yield stress point. It is found that yield stress rapidly decreased with the start of ultrasonication (as the variation of yield stress point significantly decreased from 0 to 1 h). The clusters of nanoparticles do not take part in the flow, making resistance to flow and higher yield stress was observed for the nanofluid prepared by 0 h of ultrasonication. As with the start of ultrasonication, there is less aggregation of particles for ultrasonication, therefore, the nanoparticles take part in the flow and create less resistance to the spindle and lower yield stress was observed for the sample prepared by 1 h of ultrasonication. Again, with further ultrasonication after 1 h, yield stress slowly decreased with the increase of ultrasonication duration. Moreover, yield stress decreased with an increase in temperature. With increase in temperature, the interparticle adhesion forces become weak and yield stress point was decreased. (This paragraph is adapted from Mahbubul, Saidur, Hepbasli, and Amalina (2016a), copyright (2015), with permission from Elsevier.) The flow behavior and consistency index values are plotted in Fig. 5-13A and B, respectively, from Mahbubul, Saidur, Hepbasli, and Amalina (2016a). The parameters were

Table 5-4 Curve-Fitting Parameters of 0.5 vol.% of Al2O3
Water Nanofluid at Different Temperatures for Power Law Rheological Model Temperature ( C)

Ultrasonic Duration (h)

K (mPa  s)

n

Confidence of Fit (%)

10

0 1 2 3 4 5 0 1 2 3 4 5 0 1 2 3 4 5 0 1 2 3 4 5 0 1 2 3 4 5

0.7570 0.5640 0.6170 0.5970 0.6020 0.5940 0.3470 0.2470 0.2770 0.2780 0.2730 0.2590 0.1920 0.1720 0.1800 0.1800 0.1800 0.1650 0.1430 0.1520 0.1330 0.1420 0.1400 0.1240 0.1260 0.1160 0.1120 0.1080 0.1200 0.1110

1.2002 1.2492 1.2327 1.2389 1.2379 1.2398 1.3319 1.3904 1.3694 1.3690 1.3723 1.3817 1.4280 1.4409 1.4354 1.4353 1.4317 1.4501 1.4673 1.4494 1.4746 1.4659 1.4635 1.4869 1.4764 1.4867 1.4937 1.5061 1.4798 1.4947

98.08 97.79 97.73 97.79 97.74 97.96 98.00 98.35 98.09 98.27 98.13 98.35 98.87 98.87 98.82 98.89 98.84 98.95 99.25 99.35 99.40 99.36 99.32 99.45 99.55 99.61 99.55 99.65 99.52 99.59

20

30

40

50

FIGURE 5-9 Effect of ultrasonication duration on flow behavior index for the Al2O3
water nanofluid. Adapted from Mahbubul, I. M., Saidur, R., Amalina, M. A., and Niza, M. E. (2016b). Influence of ultrasonication duration on rheological properties of nanofluid: An experimental study with alumina
water nanofluid. International Communications in Heat and Mass Transfer 76, 33
40, copyright (2016), with permission from Elsevier.

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PREPARATION, CHARACTERIZATION, PROPERTIES, AND APPLICATION OF NANOFLUID

Flow consistency index (k), mPa.s

0.80 10°C

20°C

30°C

40°C

50°C

0.60

0.40

0.20

0.00

0

1

2

3

4

5

Ultrasonication duration, h FIGURE 5-10 Effect of ultrasonication duration on flow consistency index for the Al2O3
water nanofluid. Adapted from Mahbubul, I. M., Saidur, R., Amalina, M. A., and Niza, M. E. (2016b). Influence of ultrasonication duration on rheological properties of nanofluid: An experimental study with alumina
water nanofluid. International Communications in Heat and Mass Transfer 76, 33
40, copyright (2016), with permission from Elsevier.

calculated for the experimental values at 10, 20, 30, 40, and 50 C. It is noted that the types of fluid depend on the value of this flow behavior index n as n , 1 means pseudoplastic or shear thinning, n 5 1 means Newtonian fluid, and n . 1 means dilatant or shear thickening behavior. It is found from Fig. 5-13A that the flow behavior index values were decreased with an increase in the temperature. From Fig. 5-13B, it is found that the consistency index (k) was increased with increasing temperature. The increase is also observed when the samples prepared by 0 and 5 h ultrasonication were compared. (This paragraph is adapted from Mahbubul, Saidur, Hepbasli, and Amalina (2016a), copyright (2015), with permission from Elsevier.)

5.3.4.3 Analyses by Bingham Model Table 5-6 shows the curve-fitting parameter of 0.5 vol.% of Al2O3
water nanofluid (prepared by different ultrasonication durations) at different temperatures from 10 to 50 C (with 10 C temperature intervals) on different parameters of the Bingham rheological model (Bingham, 1922). The poor confidence of fit percentages of Table 5-6 reflect that the fitting parameters of the nanofluid are not good matches with the Bingham model.

5.3.4.4 Analyses by Casson Model Table 5-7 shows the curve-fitting parameter of 0.5 vol.% of Al2O3
water nanofluid (prepared by different ultrasonication durations) at different temperatures from 10 to 50 C (with 10 C temperature intervals) on different parameters of the Casson rheological model (Casson, 1959). The Al2O3
water nanofluid is better fitted with the Casson model than the Bingham model. The minimum confidence of fit was found to be 90%. It can be seen in Table 5-7 that

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211

FIGURE 5-11 Variation of: (A) flow consistency index with ultrasonication time and (B) flow behavior index with ultrasonication time. Reprinted from Garg, P., Alvarado, J. L., Marsh, C., Carlson, T. A., Kessler, D. A., and Annamalai, K. (2009). An experimental study on the effect of ultrasonication on viscosity and heat transfer performance of multi-wall carbon nanotube-based aqueous nanofluids. International Journal of Heat and Mass Transfer 52, 5090
5101, copyright (2009), with permission from Elsevier.

yield stress and plastic viscosity were increased with an increase in ultrasonic duration until 3 h. For further ultrasonication after 3 h, those parameters were found to be decreased. In most cases, the highest yield stress and plastic viscosity were observed for the nanofluid prepared by 3 h of ultrasonication. Therefore, 3 h of ultrasonication could be the optimum required ultrasonication duration for 0.5 vol.% of Al2O3
water nanofluid.

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PREPARATION, CHARACTERIZATION, PROPERTIES, AND APPLICATION OF NANOFLUID

Table 5-5 Curve-Fitting Parameters of 0.5 vol.% of Al2O3
Water Nanofluid at Different Temperatures for the Herschel
Bulkley Rheological Model Temperature ( C)

Ultrasonic Duration (h)

τ 0 (N/m2)

K (mPa  s)

n

Confidence of Fit (%)

10

0 1 2 3 4 5 0 1 2 3 4 5 0 1 2 3 4 5 0 1 2 3 4 5 0 1 2 3 4 5

0.0498 0.0439 0.0459 0.0450 0.0446 0.0445 0.0306 0.0237 0.0243 0.0235 0.0236 0.0224 0.0128 0.0098 0.0097 0.0098 0.0088 0.0090 0.0063 0.0071 0.0033 0.0055 0.0060 0.0036 0.0042 0.0020 0.0016 0.0014 0.0029 0.0006

0.0283680 0.0229870 0.0227740 0.0232390 0.0244410 0.0250220 0.0294500 0.0385030 0.0387350 0.0421970 0.0401090 0.0421390 0.0638140 0.0739200 0.0736590 0.0775530 0.0810920 0.0724320 0.0808560 0.0895780 0.0984730 0.0895760 0.0850350 0.0918220 0.0902560 0.1103800 0.1093300 0.1005600 0.0998320 0.1135400

1.7997 1.8360 1.8370 1.8335 1.8251 1.8197 1.7840 1.7314 1.7293 1.7141 1.7231 1.7136 1.6292 1.5962 1.5976 1.5903 1.5787 1.6012 1.5725 1.5451 1.5305 1.5500 1.5547 1.5429 1.5374 1.4956 1.4980 1.5190 1.5128 1.4905

99.55 99.75 99.68 99.72 99.72 99.71 99.86 99.90 99.89 99.87 99.88 99.86 99.92 99.91 99.90 99.91 99.89 99.92 99.94 99.94 99.94 99.95 99.94 99.94 99.96 99.93 99.96 99.96 99.95 99.94

20

30

40

50

5.4 Rheology Analyses 5.4.1 Effect of Nanoparticles Mostafizur et al. (2014) studied the rheological behavior of Al2O3
methanol and TiO2
methanol nanofluids, as shown in Figs. 5-14 and 5-15, respectively. They studied shear stress and viscosity of the nanofluids having 0.01
0.15 vol.% of nanoparticle concentrations and for the temperature range of 1
20 C at different shear rates (61.15
305.8 s21) for the corresponding spindle rotation of 50
250 rpm. They used an LVDV-III ultra-programmable rheometer (Brookfield, USA) and this very similar process was followed as stated in Section 5.2. However, during the measurement and data collection, they waited at specific

Chapter 5 • Rheological Behavior of Nanofluid

213

0.06 10°C 20°C 30°C 40°C 50°C

Yield stress, N/m2

0.05 0.04 0.03 0.02 0.01 0.00

0

1

2 3 4 Ultrasonication duration, h

5

6

FIGURE 5-12 Effect of ultrasonication duration on yield stress point of Al2O3
water nanofluid. Reprinted from Mahbubul, I. M., Saidur, R., Hepbasli, A., & Amalina, M. A. (2016a). Experimental investigation of the relation between yield stress and ultrasonication period of nanofluid. International Journal of Heat and Mass Transfer 93, 1169
1174, copyright (2015), with permission from Elsevier.

(B) Flow behavior index

1.9 10°C 1.8

20°C

1.7

30°C 40°C

1.6

50°C

1.5 1.4 0

1

2

3

4

5

Ultrasonication duration, h

6

Flow consistency index, mPa⋅s

(A)

0.12

50°C

0.10

40°C

0.08

30°C

0.06

20°C

0.04

10°C

0.02 0.00 0

1

2

3

4

5

6

Ultrasonication duration, h

FIGURE 5-13 Effect of ultrasonication duration on: (A) flow behavior index and (B) flow consistency index for the Al2O3
water nanofluid. Reprinted from Mahbubul, I. M., Saidur, R., Hepbasli, A., & Amalina, M. A. (2016a). Experimental investigation of the relation between yield stress and ultrasonication period of nanofluid. International Journal of Heat and Mass Transfer 93, 1169
1174, copyright (2015), with permission from Elsevier.

spindle rotations of 50, 100, 150, 200, and 250 rpm until it reached a steady-state shear stress and viscosity. They observed non-Newtonian shear thickening behavior (increasing viscosity with increasing shear rates) for all the fluids. They found that shear stress and viscosity were increased with an increase in nanoparticle concentrations. Again, those properties were decreased with an increase in temperature. Comparatively higher shear stress and viscosity were observed for TiO2
methanol in comparison to Al2O3
methanol nanofluids, however, the differences were not very significant.

214

PREPARATION, CHARACTERIZATION, PROPERTIES, AND APPLICATION OF NANOFLUID

Table 5-6 Curve-Fitting Parameters of 0.5 vol.% of Al2O3
Water Nanofluid at Different Temperatures for the Bingham Rheological Model Temperature ( C)

Ultrasonic Duration (h)

τ 0 (N/m2)

η (mPa  s)

Confidence of Fit (%)

10

0 1 2 3 4 5 0 1 2 3 4 5 0 1 2 3 4 5 0 1 2 3 4 5 0 1 2 3 4 5


0.085
0.096
0.100
0.103
0.098
0.090
0.099
0.119
0.126
0.123
0.133
0.100
0.095
0.115
0.118
0.119
0.116
0.090
0.084
0.107
0.106
0.111
0.102
0.081
0.077
0.094
0.100
0.110
0.095
0.072

2.84 2.82 2.76 2.76 2.77 2.83 2.72 2.72 2.73 2.71 2.80 2.67 2.49 2.45 2.50 2.54 2.47 2.41 2.26 2.27 2.27 2.35 2.24 2.17 2.09 2.08 2.15 2.28 2.08 1.98

67.6 62.0 81.4 81.2 82.6 65.8 57.3 81.5 77.6 78.7 77.3 56.1 53.1 80.0 79.7 80.2 79.7 55.4 54.1 81.0 81.1 81.1 82.5 56.8 55.3 83.7 82.4 79.8 83.0 58.8

20

30

40

50

Kumar and Sharma (2018) studied rheological behavior of 0.5 wt.% of SiO2 (B15 nm) termed SN nanofluid, 0.5 wt.% of TiO2 (B50 nm) termed TN nanofluid, 0.5 wt.% of SiO2 1 0.05 wt.% of TiO2 termed STN-1 nanofluid, and 0.5 wt.% of SiO2 1 0.1 wt.% of TiO2 termed STN-2 nanofluid, where the base solution was 1 g of polyacrylamide (PAM) in 1000 mL of DIW. The effects of shear rates on the viscosity of the fluids are shown in Fig. 5-16. It can be seen in Fig. 5-16 that very similar non-Newtonian shear thinning flow behavior (decreasing viscosity with increasing shear rates) was observed for all the fluids. Viscosity values were found to be higher for the nanofluids in comparison to those of the base fluid. For the addition of TiO2 nanoparticles in SiO2 nanoparticles (STN nanofluids), viscosity values were decreased in comparison to only SiO2 nanofluids (SN) and TiO2 nanofluids (TN).

Chapter 5 • Rheological Behavior of Nanofluid

215

Table 5-7 Curve-Fitting Parameters of 0.5 vol.% of Al2O3
Water Nanofluid at Different Temperatures for the Casson Rheological Model Temperature ( C)

Ultrasonic Duration (h)

τ 0 (N/m2)

η (mPa  s)

Confidence of Fit (%)

10

0 1 2 3 4 5 0 1 2 3 4 5 0 1 2 3 4 5 0 1 2 3 4 5 0 1 2 3 4 5

0.012 0.017 0.022 0.026 0.022 0.014 0.020 0.042 0.045 0.045 0.050 0.021 0.025 0.050 0.048 0.050 0.048 0.023 0.023 0.050 0.045 0.049 0.044 0.022 0.023 0.041 0.044 0.051 0.042 0.020

3.16 3.21 3.29 3.37 3.31 3.17 3.17 3.59 3.60 3.60 3.73 3.13 3.05 3.42 3.44 3.51 3.39 2.94 2.78 3.22 3.15 3.29 3.11 2.68 2.63 2.91 3.01 3.24 2.91 2.46

92.4 91.1 94.0 94.1 94.3 91.8 90.6 94.9 93.4 93.9 93.6 90.0 90.3 95.2 94.6 94.8 94.7 90.4 90.8 96.1 95.4 95.6 95.8 90.7 91.1 96.9 96.2 96.0 96.3 91.3

20

30

40

50

Li, Zou, Wang, and Lei (2015) studied the rheological behavior as dynamic viscosity of the 0.2
1.0 vol.% of spherical SiC
ethylene glycol (EG) nanofluids at 25 C by using a HAAKE MARS III rheometer (Thermo Scientific, Karlsruhe, Germany) under continuous changed shear rates from 0.1 to 1000 s21. The results are shown in Fig. 5-17. Two groups of rheological behaviors were observed for the SiC
EG nanofluids. For dilute nanofluids (ϕ # 0.6 vol.%) with well-dispersed nanoparticles, Newtonian behavior was observed. For concentrated nanofluids (ϕ . 0.6 vol.%), non-Newtonian with clear shear thinning behavior was observed at the low shear rates (0.1
94.3 s21); however, at higher shear rates, almost Newtonian behavior was observed (Li et al., 2015).

FIGURE 5-14 Shear stress (solid line) and viscosity (dash line) of Al2O3
methanol nanofluids for (A) 0.01 vol.%, (B) 0.05 vol.%, (C) 0.10 vol.%, and (D) 0.15 vol.% as a function of shear rate and temperature. Reprinted from Mostafizur, R.M., Abdul Aziz, A.R., Saidur, R., Bhuiyan, M.H.U., and Mahbubul, I.M. (2014). Effect of temperature and volume fraction on rheology of methanol based nanofluids. International Journal of Heat and Mass Transfer 77, 765
769, copyright (2014), with permission from Elsevier.

FIGURE 5-15 Shear stress (solid line) and viscosity (dash line) of TiO2
methanol nanofluids for (A) 0.01 vol.%, (B) 0.05 vol.%, (C) 0.10 vol.%, and (D) 0.15 vol.% as a function of shear rate and temperature. Reprinted from Mostafizur, R.M., Abdul Aziz, A.R., Saidur, R., Bhuiyan, M.H.U., and Mahbubul, I.M. (2014). Effect of temperature and volume fraction on rheology of methanol based nanofluids. International Journal of Heat and Mass Transfer 77, 765
769, copyright (2014), with permission from Elsevier.

218

PREPARATION, CHARACTERIZATION, PROPERTIES, AND APPLICATION OF NANOFLUID

10

Viscosity (mPa.s)

PAM phase SN nanofluid TN nanofluid STN-1 nanofluid STN-2 nanofluid

1

0.1 100 Shear rate (s–1)

10

1000

FIGURE 5-16 Effect of high temperature (90 C) on viscosity results of polyacrylamide (PAM) phase without nanoparticles and nanofluids (SN, TN, STN-1, and STN-2). Reprinted from Kumar, R. S., and Sharma, T. (2018). Stability and rheological properties of nanofluids stabilized by SiO2 nanoparticles and SiO2-TiO2 nanocomposites for oilfield applications. Colloids and Surfaces A: Physicochemical and Engineering Aspects 539, 171
183, copyright (2017), with permission from Elsevier.

(A)

(B) 26

1.0 vol% NF 0.8 vol% NF 0.6 vol% NF

20 18 16 14

1.0 vol% NF 0.8 vol% NF 0.6 vol% NF

24

0.4 vol% NF 0.2 vol% NF EG

22

0.4 vol% NF 0.2 vol% NF

22 Viscosity/mPa.s

Viscosity/mPa.s

24

26

20 18 16 14

12 0

200

400

600

Shear rate/s–1

800

1000

0

20

40

60

80

100

120

Shear rate/s–1

FIGURE 5-17 (A) Viscosity as a function of shear rate on different volume fractions SiC
ethylene glycol nanofluids; (B) viscosity curves of SiC
ethylene glycol nanofluids on lower shear rates. Reprinted from Li, X., Zou, C., Wang, T., and Lei, X. (2015). Rheological behavior of ethylene glycol-based SiC nanofluids. International Journal of Heat and Mass Transfer 84, 925
930, copyright (2015), with permission from Elsevier.

Chapter 5 • Rheological Behavior of Nanofluid

219

5.4.2 Effect of Ultrasonication Leong et al. (1993) reported that aggregate size of particles proportionally affects the shear stress and viscosity of a sample. Therefore, the effects of cluster size on rheological properties are needed to be studied and the cluster size relates to the preparation process. The effect of ultrasonication and dispersion properties on rheological behavior, like Newtonian or nonNewtonian (shear thinning or thickening) behavior, was not reported in most cases. Yang, Grulke, Zhang, and Wu (2006) analyzed the influence of ultrasonication on rheology of the CNT
oil dispersions for 0.3
8 wt.% of dispersant concentrations. They found decreased viscosity and yield stress for the CNT
oil dispersions by an increase in the dispersing energy. They observed clear shear thinning behavior at very low and high concentrations of dispersant. However, in the case of 3 wt.% dispersant, a nearly Newtonian trend was observed. Again, for higher applied shear stress, almost identical and Newtonian flow curves was observed. The authors indicated that prolonged ultrasonication breaks the CNT, as a result, agglomeration size and viscosity were decreased (Yang et al., 2006). Kabir, Saha, and Jeelani (2007) studied the effect of ultrasound sonication (up to 40 min) on the compressive yield strength of carbon nanofiber-doped polymer. They reported that the optimum sonication time depended on the sonicator power, the nanoparticle concentration, and the amount of base fluid. It was emphasized that the sonication period should be controlled to get a better mechanical performance from composites. Garg et al. (2009) studied the effect of the sonication time on the rheological behavior of MWCNTs with DIW and gum arabic for limited shear rates (up to 75 s21). They found a non-Newtonian trend with the shear thinning or pseudoplastic style as the viscosity decreased with the increase in shear rate, especially at 15 C, as shown in Fig. 5-18. Almost unique flow characteristics were observed for the nanofluid prepared by 20, 40, 60, and 80 min ultrasonication. The unique flow characteristics may be due to the lower applied shear rate ranges throughout the study, which were up to 75 s21 of shear rate. They suggested more related studies to understand these criteria. They also reported that viscosity was increased until 40 min of ultrasonication and, after that, it declined with increasing ultrasonication time. Ruan and Jacobi (2012) also studied rheological properties of MWCNTs but with the base fluid ethylene glycol and a shear thinning behavior was observed. However, they found various flow behaviors for the nanofluids. For example, the viscosity of nanofluid prepared by 40, 140, and 520 min showed high viscosity and they rapidly decreased with increasing shear rates. In contrast, nanofluid prepared by 1355 min showed slower viscosity variation with shear rates. Even at higher shear rates, viscosity values were found to be near to the viscosity of the base fluid. Conversely, nanofluid prepared without sonication (0 min) showed various flow characteristics as, initially, viscosity decreased with the increase in shear rate then it increased and finally unchanged with shear rates. Here are some discussions of the ultrasonication effect on rheological properties of 0.5 vol.% of Al2O3
water nanofluid from the studies of Mahbubul, Saidur, Hepbasli, and Amalina (2016a) and Mahbubul, Saidur, Amalina, and Niza (2016b). Figs. 5-19 and 5-20 show the trend of shear stress and viscosity, respectively, at different shear rates from 12.23 to 305.75 s21. To give a clear understanding of Figs. 5-19 and 5-20,

220

PREPARATION, CHARACTERIZATION, PROPERTIES, AND APPLICATION OF NANOFLUID

FIGURE 5-18 Variation of viscosity with shear rate at: (A) 15 C and (B) 30 C. Reprinted from Garg, P., Alvarado, J. L., Marsh, C., Carlson, T. A., Kessler, D. A., and Annamalai, K. (2009). An experimental study on the effect of ultrasonication on viscosity and heat transfer performance of multi-wall carbon nanotube-based aqueous nanofluids. International Journal of Heat and Mass Transfer 52, 5090
5101, copyright (2009), with permission from Elsevier.

only the data for 10, 30, and 50 C temperatures are plotted. Flow behavior for the specific temperatures is indicated by circles. It is observed from Figs. 5-19 and 5-20 that initially the nanofluid showed Newtonian behavior at 10 C temperature and the trend continued almost up to 150 s21 shear rates. Nanofluid prepared without ultrasonication (0 h) showed higher viscosity compared with others and exhibited Newtonian behavior for the longer range of shear rates (up to 170 s21). That is why, in Fig. 5-9, the flow behavior index (n) was found to be lower for the nanofluids at 10 C, especially for the nanofluid prepared by 0 h. After that, at a higher shear rate, the nanofluid was found to be non-Newtonian (dilatant and shear

Chapter 5 • Rheological Behavior of Nanofluid

221

0.80 10°C

Shear stress, N/m2

0.70

30°C

0.60 0.50

50°C

0.40

0h 1h

0.30

2h 0.20

3h 4h

0.10

5h 0.00

0

40

80

120

160

Shear rate,

200

240

280

320

s–1

FIGURE 5-19 Relation of shear stress of Al2O3
water nanofluid with shear rates. Reprinted from Mahbubul, I.M., Saidur, R., Hepbasli, A., Amalina, M.A. (2016a). Experimental investigation of the relation between yield stress and ultrasonication period of nanofluid. International Journal of Heat and Mass Transfer 93, 1169
1174, copyright (2015), with permission from Elsevier.

thickening fluid). It is also observed from Figs. 5-19 and 5-20 that at 30 C, initially the nanofluid showed Newtonian behavior and existed up to 100 s21 shear rates. Then it became non-Newtonian as dilatant and shear thickening fluid. The almost identical trend of rheological behavior was observed at 50 C. However, in the case of 50 C, the Newtonian behavior continued up to 73.38 s21 shear rates only. For a better understanding of flow, the behavior of nanofluids prepared by different ultrasonication durations are again presented. Figs. 5-21 and 5-22 represent shear stress and viscosity at different shear rates, respectively, of nanofluids (0.5 vol.% of Al2O3
water) prepared by different ultrasonication periods, wherein both Figs. 5-21 and 5-22, (A
F) represent nanofluids prepared by 0 (without ultrasonication), 1, 2, 3, 4, and 5 h of ultrasonication, respectively. It is clear from Figs. 5-21 and 5-22 that almost identical flow behavior was observed for the nanofluid prepared by different durations of ultrasonication. It is observed that at the start of ultrasonication, shear stress and viscosity of nanofluids were found to be decreased by an increase of ultrasonication periods. The shear stresses and viscosities values (Y-axis) of Figs. 5-21B and 5-22B, which are the values for 1 h of ultrasonication, were found to be lower than the values of Figs. 5-21A and 5-22A (for 0 h of ultrasonication). Initially, without ultrasonication, the nanoparticles were in highly clustered form and aggregated. These clusters do not take part in the flow, rather making resistance to flow; as a result, shear stress and viscosity were found to be higher for 0 h. However, further ultrasonication after 1 h, the shear stress and viscosity values (Y-axis) of Figs. 5-21 and 5-22 were found to be almost identical (very small changes were observed) as seen in Figs. 5-21B
F and 5-22B
F. Again, flow

222

PREPARATION, CHARACTERIZATION, PROPERTIES, AND APPLICATION OF NANOFLUID

2.85

2.60 10°C 2.35 30°C

Viscosity, mPa·s

2.10

1.85

1.60

0h

50°C

1h

1.35

2h 1.10

3h 4h

0.85

5h 0.60 30

70

110

150

190

230

270

310

Shear rate, s–1 FIGURE 5-20 Viscosity of Al2O3
water nanofluid at different shear rates. Reprinted from Mahbubul, I. M., Saidur, R., Amalina, M. A., and Niza, M. E. (2016b). Influence of ultrasonication duration on rheological properties of nanofluid: An experimental study with alumina
water nanofluid. International Communications in Heat and Mass Transfer 76, 33
40, copyright (2016), with permission from Elsevier.

behavior was changed by increases in temperature and shear rate. It is also found from Figs. 5-21 and 5-22 that there are interactions between temperature and sonication period with the shear stress and viscosity of nanofluid. At the lower temperatures, the decrease of viscosity with the increase of ultrasonication duration was found to be higher in comparison to a higher temperature. This phenomenon is due to the effect of Brownian motion and van der Waals force. From Figs. 5-21 and 5-22, it is clear that the shear stresses and viscosities of the nanofluid were significantly decreased by the increase of temperature from 10 to 50 C. This is because of the weakening of interparticle adhesion forces that decrease with an increase in temperature (Murshed et al., 2008). It is found that shear stress and viscosity of nanofluid decreased by the increase of ultrasonication duration. A similar trend has also been observed by Yang et al. (2006). (Subsection 5.4.2 is adapted from Mahbubul, Saidur, Hepbasli, and Amalina (2016a), copyright (2015), and from Mahbubul, Saidur, Amalina, and Niza (2016b), copyright (2016), with permission from Elsevier.)

Chapter 5 • Rheological Behavior of Nanofluid

223

FIGURE 5-21 Shear stresses at different shear rates for the Al2O3
water nanofluid prepared by (A) 0, (B) 1, (C) 2, (D) 3, (E) 4, and (F) 5 h of ultrasonication. Reprinted from Mahbubul I.M., Saidur R., Hepbasli A. and Amalina M.A. (2016a). Experimental investigation of the relation between yield stress and ultrasonication period of nanofluid, International Journal of Heat and Mass Transfer 93, 1169
1174, copyright (2015), with permission from Elsevier.

224

PREPARATION, CHARACTERIZATION, PROPERTIES, AND APPLICATION OF NANOFLUID

FIGURE 5-22 Viscosity at different shear rates for the Al2O3
water nanofluid prepared by (A) 0, (B) 1, (C) 2, (D) 3, (E) 4, and (F) 5 h of ultrasonication. Reprinted from Mahbubul I.M., Saidur R., Amalina M.A. and Niza M.E. (2016b). Influence of ultrasonication duration on rheological properties of nanofluid: An experimental study with alumina
water nanofluid, International Communications in Heat and Mass Transfer 76, 33
40, copyright (2016), with permission from Elsevier.

5.4.3 Effect of Microstructure The relation of microstructures of colloids with rheological behavior could be seen in the study of Mueller, Llewellin, and Mader (2010), according to Fig. 5-23. Mueller et al. (2010) stated that in the case of very low volume concentrations of nanoparticles, where the particles are sufficiently well separated, the interactions among the nanoparticles are negligible.

Chapter 5 • Rheological Behavior of Nanofluid

225

FIGURE 5-23 Relations of microstructure of colloids with rheology. Reprinted from Mahbubul, I. M., Saidur, R., Amalina, M. A., and Niza, M. E. (2016b). Influence of ultrasonication duration on rheological properties of nanofluid: An experimental study with alumina
water nanofluid. International Communications in Heat and Mass Transfer 76, 33
40, copyright (2016), with permission from Elsevier.

226

PREPARATION, CHARACTERIZATION, PROPERTIES, AND APPLICATION OF NANOFLUID

By applying, and increasing shear rates, viscosity does not change and a Newtonian flow characteristic is observed in such cases, and the yield stress is supposed to be zero. Nevertheless, the addition of particles will increase the viscosity of the suspension. For adding a very low concentration of particles, viscosity increases linearly, however, for slightly higher particle concentration, viscosity increases nonlinearly (Mueller et al., 2010). Fig. 5-23A shows a pictorial example of the addition of low concentration of particles in a fluid. For intermediate or higher particle concentration, non-Newtonian fluid is observed. However, the flow behavior can be shear thinning or shear thickening. With the increase of applied shear rates, particles can be organized in the fluid and viscosity will be decreased (Wagner & Brady, 2009). In some cases, particles become separated, although it is very small, the applied force (shear rate) squeezed the fluid to pass through the gaps and viscosity decreases. Such an approach is called shear thinning behavior, as shown in Fig. 5-23B. Even the increase of shear rate can form chains and networks among neighboring particles. In such cases, particles face difficulties in flowing, and viscosity is abruptly increased, and yield stress is also developed. The above condition is called shear thickening, which is shown in Fig. 5-23C. The blue particles in Fig. 5-23C show an example of the network. (This paragraph is adapted from Mahbubul, Saidur, Amalina, and Niza (2016b), copyright (2016), with permission from Elsevier.)

5.5 Concluding Remarks • The impact of nanoparticle type is not significant in rheology, rather particle shape and concentration are important. • Base fluid types or properties are the most important in rheology. • The Herschel
Bulkley model was found to be the best-fitting model for nanofluids. • The rapid decreases in yield stresses were observed for increases in temperature for all the nanofluids prepared by different durations of ultrasonication. The yield stress decreased rapidly with the start of ultrasonication. However, it decreased slowly with further ultrasonication. • Flow index values were found to be increased with increasing temperatures. An irregular trend of flow index with ultrasonication duration was observed. The consistency indexes were found to be decreased with increasing ultrasonication durations and temperatures. • The shear stress values were found to be decreased with increasing temperatures, and the decrement was more significant at higher shear rates. At lower temperatures and lower shear rates, the nanofluids were found to be Newtonian. • The shear stresses were slowly decreased with the start of ultrasonication. However, with further ultrasonication, no significant changes to the shear stresses were observed. • The viscosity of nanofluids was found to be decreased with an increase in temperature. At lower temperatures, nanofluids showed Newtonian behavior at lower shear rates, but they showed non-Newtonian behavior at higher shear rates. At higher temperatures, nanofluids showed almost non-Newtonian behavior.

Chapter 5 • Rheological Behavior of Nanofluid

227

• The viscosity values of nanofluids were found to be decreased with increasing ultrasonication. With the start of ultrasonication, the decrements of viscosity values were significant. However, further prolonged ultrasonication did not show a major difference in viscosity values. (Section 5.5 is adapted from Mahbubul, Saidur, Hepbasli, and Amalina (2016a), copyright (2015), and from Mahbubul, Saidur, Amalina, and Niza (2016b), copyright (2016), with permission from Elsevier.)

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1402. Casson, N. (1959). A flow equation for pigment-oil suspensions of the printing ink type. In C. Mill (Ed.), Rheology of disperse systems London: Pergamon Press. Chen, H., Witharana, S., Jin, Y., Kim, C., & Ding, Y. (2009). Predicting thermal conductivity of liquid suspensions of nanoparticles (nanofluids) based on rheology. Particuology, 7, 151
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306. Elias, M. M., Miqdad, M., Mahbubul, I. M., Saidur, R., Kamalisarvestani, M., Sohel, M. R., . . . Amalina, M. A. (2013). Effect of nanoparticle shape on the heat transfer and thermodynamic performance of a shell and tube heat exchanger. International Communications in Heat and Mass Transfer, 44, 93
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