Rheological Properties of Paraffin-based Co3O4 Nano-Ferrofluid

In: Advances in Nanotechnology. Volume 11 ISBN: 978-1-62948-732-8

Editors: Zacharie Bartul and Jérôme Trenor © 2014 Nova Science Publishers, Inc.

Chapter 8

RHEOLOGICAL PROPERTIES OF PARAFFIN-BASED

CO3O4 NANO-FERROFLUID

Alireza Fazlali,1,*

Saba Lashkarara1 and Amir H. Mohammadi

2,3, 1Department of Chemical Engineering, Faculty of Engineering,

Arak University, Arak, Iran 2Institut de Recherche en Génie Chimique et Pétrolier (IRGCP), Paris Cedex, France

3Thermodynamics Research Unit, School of Engineering, University of KwaZulu-Natal,

Howard College Campus, Durban, South Africa

ABSTRACT

The rheological properties of Co3O4 ferrofluid (F.F.) nanoparticles in paraffin base

have been investigated for wide concentration range. For preparing this ferrofluid, ball

mill and ultrasonic bath were used. The experimental results show that these magnetic

fluids show approximately Newtonian behavior in very low concentrations, whereas they

seem to act as a non-Newtonian fluid by increasing concentration. The viscosity of this

ferrofluid is falling with shear rate increasing, especially for high concentrations; thus

this phenomenon shows shear thinning behavior. The viscosity of the ferrofluid is

increasing with claiming up in the Co3O4 nanoparticles concentrations in a constant shear

rate. The experimental data have been compared with some existing models.

Keywords: Co3O4; nanoparticle; ferrofluid; viscosity; nanoparticle interaction; model.

1. INTRODUCTION

A magnetic fluid (ferrofluid or F.F.) is a stable suspension of magnetic nanoparticles such

as Fe3O4 [1], CoFe2O4 [2], Mn–Zn [3], Co–Zn [4], Lithium ferrite [5] in a base liquid. The

base liquid can be polar or nonpolar compound [6]. In order to avoid nanoparticles

Corresponding authors: Alireza Fazlali, Email: [email protected] & Amir H. Mohammadi, E-mail:

[email protected]

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Alireza Fazlali, Saba Lashkarara and Amir H. Mohammadi 170

agglomerations, the magnetic particles must be coated with a shell of a surfactant [7]. This

coating causes F.F.s stability even in magnetic fields with very high intensity [8]. F.F.s are

widely used in the industry and the medical science e.g. technological applications (dynamic

sealing, heat dissipation, inertial and viscous damper), materials research (magnetic colloids

used to dope liquid crystals, doping of lyotropic liquid crystals with magnetic particles) and

biomedical applications (magnetic drug targeting, hyperthermia, contrast enhancement for

magnetic resonance imaging (MRI), magnetic separation of cells) [9, 10].

Rheology is a part of science in order to understanding the effects of external forces on

flow and deformation of materials. Therefore, the rheological and magnetorheological

properties of F.F.s are very important in the basic researches of F.F.s, and have significant

effect on their applications.

Regarding the researches performed on the properties of F.F., the shear thinning behavior

for F.F. has been demonstrated [11] e.g. their viscosity decreases with shear rate. In addition,

it has been found that the ferrofluid viscosity increases with the intensity of the magnetic field

[12]. Recent researches on the magnetoviscos effect of F.F. show that the strong magnetic

fields form chains and aggregates of nanoparticles which can seriously affect the macroscopic

properties of F.F.s even for low nanoparticle concentration [13-18]. Moreover, one of the

important parameters that influences the rheological properties of F.F.s is the interaction of

magnetic particles, in which the size and distribution of particles are of significance [19,20].

Normally, the propounded theories at this field do not consider the particle interactions

because of their complication [18, 19, 21-23].

In this work, the rheological properties of Co3O4 F.F.s suspended in the paraffin base

have been investigated.

2. MATERIAL AND METHOD

2.1. Materials

Co3O4 magnetic nanoparticles powder (size 50 nm) (Aldrich co.).

Pure liquid paraffin (Arman Sina co. Iran) as base fluid synthesis grade.

Oleic acid (OA) (Merch co.) as surfactant of nanoparticles analytical grade.

2.2. Rheometery Equipment

The rheological properties of Co3O4 nanoparticles F.F. were measured by a MCR300

Rheometer from Physica Anton Paar GmbH with a special plate-plate spindle MRD 180

(Figure 1). The various magnetic fields were induced at horizontal direction relative to the

sample during the test. The samples volume used in the tests were smaller than 0.5 ml.


Rheological Properties of Paraffin-Based Co3O4 Nano-Ferrofluid 171

2.3. Preparation of Ferrofluids Samples

For preparing the suspensions, Co3O4 nanoparticles powder was mixed with paraffin and

oleic acid (as surfactant) in a ball mill (Pulversisette model, Fritsch co.) (Figure 2.a and 2.b).

All samples were mixed in the ball mill at 150 rpm for 1 hour.

Figure 1. Rheometer set.

Figure 2a. Ball mill set.



Figure 2b. Agate container and its balls for mixture.

Thus, the suspensions became completely homogeneous. Later, suspensions were put into

ultrasonic bath (FRITSCH Ultrasonic, laborette 17, Frequency: 50-60 HZ) for better

distribution of nanoparticles and destroying the probable agglomerations wrought from

nanoparticles and better covering of particles by OA. After one hour intensive sonication, the

stable suspensions were obtained. Percentage of OA for all samples was 5 % by weight

relative to solid powder.

Generally, suspensions had very good stability during the tests. For comparing the

concentration effect, the samples were prepared in wide range of concentrations.

Figure 3a. Flow curve for Co3O4 ferrofluids weight fractions of 5 and 10%.



Figure 3b. Flow curve for Co3O4 ferrofluids weight fractions of 15 - 25%.

Figure 3c. Flow curve for Co3O4 ferrofluids weight fractions of 30 and 40%.

3. RESULTS AND DISCUSSION

Figure 3 (a-c) show the shear stress vs. shear rate for different concentrations of F.F. The

F.F.s exhibit almost Newtonian fluid characteristics in low concentrations (5% w) (Figure

3a), as shear stress increases almost linearly with shear rate increasing. However, they have

the non-Newtonian behavior by increasing the concentration. For weight fractions more than

10%, at low shear rates (smaller than 200 s-1

), the shear stress rises nonlinearly vs. shear rate,



whereas this rise is linear for higher shear rates (more than 200 s-1

) (Figures 3a-3c). The flow

curves for concentrated F.F.s (15% - 40%) included a yield stress too (Figures 3). The

existence of yield stress can be related to nanoparticles interaction. The nanoparticles

interactions are increased by rising in their weight fraction. Therefore, the interaction forces

become stronger and lead to an initial resistance against fluid motion in concentrated F.F.s.

However, this resistance is destroyed by increasing the shear rate and fluid can start flowing.

One of the theories that represents fairly good flow curves of the suspensions is Bingham

model: 0 y where denotes the shear stress, y is yield stress, η0 represents

viscosity at zero field and stands for the shear rate [24]. In Figure 4, it has been shown that

Bingham model is in good agreement with Co3O4 F.F.s in low concentrations, whereas this

agreement becomes unsatisfactory by increasing the concentration. Another proposed model

for flow curve which includes yield point is the Casson model: 2/12/1

0

2/12/1 y [24],

which has been reported for magnetic fluids [25]. As can be seen in Figure 5, this model

yields good agreement with Co3O4 F.F.s. Another model which can be used for modeling

flow curve of nanofluids, which includes yield point is the Hurschel-Bulkley (H-B) model: n

y K [26], which has been reported for magnetic fluids [25, 26]. In Figure 6, it has

been indicated that H-B model also shows satisfactory agreement for Co3O4 F.F.s.

Table 1 shows the correlation coefficient of these models. It can be seen in Table 1 that

H-B model has the best fitting.

Figure 4. Comparison of the results of Bingham model with experimental data.

Table 1. Regression results for nanoparticle suspension

Empirical models H-B model Bingham model Casson model

0.991 0.9897 0.9735



Figure 5. Comparison of the results of Casson model with experimental data.

Figure 6. Comparison of the results of H-B model with experimental data.



Figure 7. Shear thinning behavior for various weight fractions of Co3O4 ferrofluids.

Figure 8. Increasing of ferrofluids viscosity with weight fraction for different shear rate.

Figures 7 and 8 indicate the F.F.s viscosity changes with shear rate and weight fraction of

Co3O4 nanoparticles, respectively. As can be seen, the F.F.s at all concentrations have shear

thinning behavior, as their viscosities decrease by increasing shear rate, particularly as by



increasing the shear rate, the agglomerates are progressively destroyed, consequently the

F.F.s viscosity decreases [27]. The shear thinning behavior is more convenience in high

concentration of F.F.s, relative to their low concentrations.

For the particles interactions, contacts and instance of particles are very effective as well

as their size. Therefore, solid particles concentration is important for determining the rate of

particles interaction and consequently rheological properties of suspension.

The dependence of viscosity on solid particle volume fraction has been determined by

some models. The first theory for viscosity of the dilute colloids and one size, presented by

Einstein as following:

(1 )s l HK (1)

where, ηs, η1, KH and φ are viscosity of the suspension, viscosity of base fluid, shape factor of

particle and solid particle volume fraction, respectively. This model indicates that the iscosity

is not function of particle size, but depends on particle shape and concentration. For spherical

particles, shape factor is 2.5 [28, 29]. Of course, equation (1) is for the colloids that their

particles do not have any interactions. For F.F.s, particle concentration is considered as

hydrodynamic volume fraction (φh). The solid particle concentration with surfactant layer, φh

can be obtained as following:

3

2

d

sdh (2)

where, d and s are particle size and thickness of surfactant layer. According to presented

information, normally approximate amount for surfactant layer has been considered [29]. In

order to measure the thickness of this layer, limited attempts have been performed [30, 31].

By increasing the concentration of the solid particles, the interactions would increase.

Thus, the Einstein equation is corrected as follow [32]:

)2.65.21( 2

1 hhs (3)

This relation has been extended for spherical silica particles as shown in equation (4). In

concentration 18%, this model is in good agreement with equation (3) with b=5 and c=53

[32].

2 3

1(1 2.5 )s h h hb c (4)

It is possible to increase solid particles up to 15% vol., but this does not show any raise in

the viscosity of the suspension. Even this amount for spherical particles has been reported up

to 30% vol. However, by increasing more than this amount, the viscosity increases strongly

[33].

Chow [33] presented a theoretical analysis of concentrated suspensions by taking into

account the particle interactions on the effective viscosity which was limited to the low-shear

viscosity as expressed in the following equation:



Figure 9. Comparison of constitutive equations with experimental data.

mh

h

h

h

A

A

2

2

0 11

5.2exp

(5)

where, φm is the maximum hydrodynamic volume fraction and A is the coupling coefficient.

Without considering interactions between particles, the theoretical value of A was determined

to be 4.67 [33].

Also, Krieger-Dougherty model [34,35] indicates changes of viscosity vs. concentration

in concentrated suspensions as expressed by the following equation:

m

mhs

][)/1(

(6)

where η is the intrinsic viscosity. For spherical particles, different amounts obtained for η i.e.

2.5 and 2.925.

As indicated in the Figure 9, the experimental data are compared with Einstein, Chow

and Krieger-Dougherty (K-D) models in a shear rate of 129 (1/s). It can be seen that the

results of these models are not in good agreement with experimental data of Co3O4-Paraffin

F.F.s.

CONCLUSION

In this study, the rheological properties of Paraffin- Co3O4 nanoparticles ferrofluid are

investigated. The experimental results demonstrate that ferroluids are approximately

Newtonian in very low concentrations, whereas they have non-Newtonian characterization in

higher concentrations. By increasing the shear rate, ferrofluids viscosity decreases which



shows the shear thinning behavior. Thus, their viscosity increases with nanoparticle weight

fraction in a constant shear rate. The experimental data obtained in the present work are not in

good agreement with the results of the models investigated.

ACKNOWLEDGMENT

The authors would like to acknowledge the financial support from the Arak University

and research support from Institute for Colorants, Paint and Coating (ICPC), Tehran/Iran.

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Rheological Properties of Paraffin-based Co3O4 Nano-Ferrofluid

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