J. Cent. South Univ. Technol. (2009) 16: 0926-0930
DOI: 10.1007/s11771-009-0154-8
Shear-thickening rheological response of PCC/PEG suspensions
YANG Hai-lin(杨海林), RUAN Jian-ming(阮建明), ZHOU Zhong-cheng(周忠诚), ZOU Jian-peng(邹俭鹏),
WU Qiu-mei(伍秋美), XIE Yuan-yan(谢元彦)
(State Key Laboratory of Powder Metallurgy, Central South University, Changsha 410083, China)
Abstract: The steady and dynamic rheological behaviors of precipitated calcium carbonate (PCC) suspension in polyethylene glycol (PEG) were investigated on a TA AR2000ex rheometer. Under steady shear consistency index K and flow exponent N of suspensions with different volume fractions were determined. The shear-thinning and the discontinuous shear-thickening behavior were observed at different constant frequencies from 10 to 100 rad/s. The relationship between the complex viscosity and the constant frequency were determined. As the volume fraction increases, flow exponent N shows a rapid increase, and it increases dramatically when the discontinuous shear-thickening takes place, while consistency index K decreases. Dynamic oscillatory shear experiments were conducted at constant strain amplitude and constant frequency, respectively. For the frequency sweep, the system shows viscous property in entire range of the frequency investigated, and the complex viscosity shows discontinuous jump at a critical frequency of 10 rad/s. For the strain sweep, on the other hand, at low strain the elastic modulus is strongly dependent on the strain, and the viscous modulus is independent of the strain. But at the critical strain point both of the moduli show an abrupt jump and the system transits from elastic to viscous at a strain of 0.1.
Key words: precipitated calcium carbonate (PCC) suspension; rheological response; shear-thickening; steady shear; dynamic shear; frequency
1 Introduction
Many colloidal suspensions, such as paints, coatings, and lubricants, are subjected to steeply shearing during processing. In some instances the shear force can be strong enough to drive shear-thickening, which is marked by a rapid, sometimes discontinuous increase in viscosity with small increase in shear rate. Generally, shear- thickening refers to that the viscosity of a fluid increases with increasing rates or stress of shear. This behavior is unacceptable because the steep increase in viscosity can damage processing equipment. The change in microstructure leads to poor fluid and coating qualities. Many aspects play an important role in the occurrence of shear-thickening of the fluid, such as the polarity of the continuous phase[1], considerable volume fraction[2-3], particle size[4] and medium of dispersed phase[5-6]. On the other hand, the shear-thickening behavior could be exploited to design the damping and controlling devices[7]. Interestingly, some researchers in USA took advantage of the shear-thickening behavior under stress or strain of the silica suspensions in ethylene glycol[8], polyethylene glycol (PEG)[9] and water[10] to make novel advanced body armor materials. It was reported that these novel materials could not only offer equivalent ballistic performance of existing body armor materials but also be more compact and flexible.
Calcium carbonate is a mineral widely applied in paper industry, cosmetics, medicine, catalyst, ceramics, rubber and paint. The precipitated calcium carbonate (PCC) suspensions subjected to macroscopic stresses are involved in many industrial processes such as paper, filler and ceramic industries[11-13]. The rheologicial properties play an important role in these processes. Just mentioned above, the PCC suspension in polar liquid can also be utilized to make the shear-thickening fluid (STF). The fabric impregnated with STF can be dramatic improvement in puncture resistance (spike threat) [14-15]. But few investigations have been done on the rheologicial properties of PCC in polar liquid[16-17]. In this work, steady rheologicial properties and the relationships between different volume fractions of PCC were focused. On the other hand, the oscillatory rheologicial properties were investigated through frequency sweeps at constant strain and strain sweeps at constant frequencies.
2 Experimental
2.1 Materials
The raw materials used in this work were commercial. XRD analysis revealed that calcite was the only crystalline phase. It can also be observed by a Jeol-6360LV SEM in Fig.1 that the morphology of PCC is cuboidal and the particle sizes are ranged from 80 to 100 nm. The particles can irreversibly aggregate due to high surface energy, and the pure PCC powders can easily be wetted by polar liquid. The density of the PCC particles obtained by solution density measurement assuming ideal mixing in PEG at 25 ℃ and various mass fractions was 2.6 g/cm3.
Fig.1 SEM image of PCC powders
The continuous polar phase in the experiment was PEG with an average relative molecular mass of 200 supplied by Sinopharm Chemical Reagent Co Ltd. The viscosity of PEG at ambient temperature (25 ℃) was 0.03 Pa?s.
2.2 Sample preparation
In order to remove the absorbed water, the PCC powders were kept in vacuum at 100 ℃ for 1 h prior to the experiments. The suspensions were prepared by adding the powders into the liquid in a blender and mixing for about 60 min, and then homogenized by ultrasonic for 10 min. The samples (100 mL) were made in batches and placed in vacuum at room temperature for more than 24 h to remove air bubbles. Because of high hydrophile on the particle surfaces, when the powders were dispersed in polar liquid PEG, the powders could preferentially be wetted by PEG. On the other hand, the absorbed polar liquid interacted with other suspending molecules through hydrogen bonds, which resulted in nonflocculated suspension.
2.3 Rheological experiments
A stress (strain)-controlled rheometer AR2000ex (USA: TA Company) was used to measure the rheological properties. A cone-and-plate fixture having a cone angle of 1? and a diameter of 40 mm was used. All the measurements were conducted at ambient temperature (25 ℃). In order to erase any previous shear histories and ensure the equilibrium structure, a steady preshear was applied at a shear rate of 1 s-1 for 60 s, followed by a 120 s rest period before any dynamic experiments.
3 Results
3.1 Steady rheological behavior
Fig.2 shows the steady apparent viscosity as a function of the shear rate for the PCC suspension in PEG at different volume fractions ranging from 32% to 42%. As can be seen from Fig.2, at low shear rate the shear-thinning can be easily observed. The low level of viscosity at the shear rates reflects that the system is not flocculated. But with the increase of the shear rate, when the critical shear rate
is obtained, the apparent viscosity shows a rapidly increase. On the other hand, with the increase of the volume fraction of PCC powders the initial apparent viscosity increases and the shear-thickening effect gets more and more notable. Especially for the volume fraction of 42%, the apparent viscosity shows a discontinuous jump. Note that in the shear-thickening region for the volume fraction of 42% the apparent viscosity gets the maximum and then begins to drop again. The magnitude of the shear-thickening effect progressively increases with the increase of PCC concentration. At the same time the critical shear rate (
) shifts toward lower shear rates.
Fig.2 Apparent viscosity (η) as function of shear rate (
) of PCC/PEG suspensions at different volume fractions of PCC powders
The shear-thickening behavior can be fitted by the Ostwald-de Weale model with the following equation:
η=K(
)N-1 (1)
where K is the consistency index; and N is the shear flow exponent that indicates the departure from Newtonian liquid. The fitting parameters are given in Table 1. It can be obtained from Table 1 that with the increase of the volume fraction of PCC powders the shear flow exponent N increases and the consistency index K decreases, which means that the system gets departure from Newtonian liquid more and more obviously and becomes non-Newtonian flow. At the same time the fluidness of the system gets slow.
Table 1 Critical shear rates and fitting parameters using Ostwald-de Weale model for shear-thickening behavior in Fig.2
3.2 Dynamic frequency sweep rheological behavior
Typically, for PCC (volume fraction of 42%) suspension in PEG the moduli (elastic modulus G′ and viscous modulus G″) and the complex viscosity (η*) as a function of sweep frequency (ω) are plotted in Fig.3. The experiment was performed from low to high sweep frequency at a constant strain of 7.5. It can be observed from Fig.3 that viscous modulus G″ exceeds elastic modulus G′ in the entire frequency range, with both moduli depending strongly on frequency, which means that the system is viscous and dissipated. The system is a nonflocculated suspension. In the entire frequency range investigated the moduli (G′ and G″) are monotone increasing functions of sweep frequency. In the narrow range of the sweep frequency (10-13 rad/s) the moduli show a rapid increase, but at high frequency the increase trend of the moduli gets slow. On the other hand, for the complex viscosity at the sweep frequency less than 10 rad/s the obvious shear-thinning effect can be observed with the increase of the sweep frequency; but at frequency of approximately 10 rad/s, an abrupt transition to a high level of the complex viscosity is observed. In addition, it is also noteworthy pointing out that the maximum complex viscosity is obtained; thereafter it begins to drop, corresponding to that the modulus increase trend gets slow at high sweep frequency.
Fig.3 Moduli (G′ and G″) and complex viscosity (η*) of 42% PCC suspension in PEG as function of sweep frequency (ω) at constant strain of 7.5
3.3 Dynamic strain sweep rheological behavior
Fig.4 shows the relationship between the complex viscosity and the strain at different constant frequencies for PCC/PEG suspension with a volume faction of 42%. It can be observed from Fig.4 at the considerable lower strain the complex viscosity reaches a plateau; but with the increase of strain the obvious shear-thinning occurs; once the critical strain is obtained the abrupt shear-thickening takes place and the complex viscosity dramatically increases to high level. It can also be observed from Fig.4 that the initial complex viscosity decreases with the increase of constant frequency and the dynamic shear-thickening critical strain shifts to lower value strain. It should also be pointed out that with the decrease of the constant frequency the dynamic shear-thinning gets more and more notable and the shear-thickening trend becomes no more notable than that at high constant frequency.
Fig.4 Complex viscosity (η*) as function of sweep strain (γ)
The plot of the critical strain (g*c) vs the constant frequency for PCC/PEG suspension with the volume fraction ranging from 32% to 42% is shown in Fig.5. As can be seen, the critical strain is in a reverse proportion to the constant frequency, at a very high constant frequency the critical strain gets to a plateau. Interestingly, in this experiment the samples with different volume fractions of PCC powders at very high constant frequency nearly have the same critical strain. The results also agree with those obtained by YANG et al[18].
The moduli (G′ and G”) as a function of sweep strain at a constant frequency of 10 rad/s are shown in Fig.6. Viscous modulus G″, is nearly independent of the strain until the strain reaches the critical point and thereafter a steep increase in G″ occurs. But elastic modulus G′ reaches a plateau at the strain less than 0.1 and then obviously decreases. Once the critical strain point is obtained, a dramatical increase will occur. This is different from the frequency sweep mentioned above that at lower strain (γ＜0.1) elastic modulus G′ dominates viscous modulus G″. But at higher strain (γ＞0.1) viscous modulus G″ becomes dominative, which indicates that the system is elastic at low strain and gets viscous at high strain.
Fig.5 Critical strain (γc*) as function of constant sweep frequency for PCC suspension in PEG
Fig.6 Moduli (G′ and G″) as function of sweep strain at constant frequency of 10 rad/s for sample with volume fraction of 42% PCC suspension
4 Discussion
The viscosity change of the PCC suspension in PEG is related to the microstructure change. There are two theories for the shear-thickening. One is the order- disorder transition (ODT)[19-21]. The disruption of an ordered structure results in the increase of particle interaction, which leads to the increase of viscosity of the suspension. The other is the cluster theory[22-25]. In this experiment the cluster theory can be applied to explaining the phenomena above. Because of the high hydrophile for PCC powders aggregates are formed easily. If the ordered structure is formed, it will be visualized. But in this experiment no visualized ordered structure appears. It seems unlikely that these irregular aggregates can be arranged into ordered structures at low shear rates. On the contrary, the cluster theory can be applied to accounting for the complex rheological phenomena reasonably. At low shear rates, PCC powders in the suspension are prevented from further association by weak steric repulsive forces and Brownian forces. As the shear rate increases, the hydrodynamic force increases; and at the critical transition, it exceeds the repulsive interaction. At this point, clusters of the aggregates or particles are formed, as a result of the increase of the viscosity (η or η*). The clusters composed of compacted groups of particles or aggregates, when shear forces drive particles nearly into contact, are formed, which block the flow of the fluid, and the viscosity shows a dramatic increase, corresponding to the shear-thickening[23, 26]. Meanwhile, the particles concentration takes an important role in the occurrence of the abrupt shear-thickening. If the particle concentration is not high enough, the distance of the particles or aggregates is not close to form the clusters, leading to jamming the flow, and there is no abrupt shear-thickening, which can be observed from Fig.2. The discontinuous shear-thickening only occurs at the volume fraction of 42% PCC powders.
The reasons for the viscosity increase are twofold[25]. Firstly, the formation of clusters results in the effective volume fraction of dispersed phase. Secondly, the shape of the formed clusters takes an important role in the increase in the effective volume fraction of dispersed phase. The elongated clusters contribute much more to viscosity than the aggregates or particles. Thus, the anisotropy of the PCC particle units is expected to play a significant role in the shear-thickening behavior.
5 Conclusions
(1) At the volume fractions of PCC powders varying from 32% to 42% shear flow exponent N and consistency index K are determined through the steady rheological experiments. Shear flow exponent N increases with the increase of PCC suspension concentration, and jumps to a higher level when discontinuous shear-thickening occurs. At the same time consistency index K decreases with the increase of PCC suspension concentration.
(2) For the frequency sweep at constant strain amplitude, moduli (G′ and G″) are strongly dependent on the frequency and the effect of viscous modulus G″ exceeds that of elastic modulus G′ in the entire range of frequency investigated. The complex viscosity shows an abrupt increase at a frequency approaching to 10 rad/s. For the strain sweep at a constant frequency, the dynamic critical strain is reversely proportional to the constant frequency. Elastic modulus G′ dominates viscous modulus G″ when the stain is less than 0.1, thereafter G″ becomes dominative.
(3) The clusters theory on the formation of metastable, flow induced clusters due to the hydrodynamic force predominating over repulsive force is reasonable. The clusters that block the flow of the fluid cause the occurrence of shear-thickening under steady shear and dynamic oscillatory shear. The clusters and the shape of the clusters play an important role in the occurrence of continuous and discontinuous shear-thickening.
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(Edited by CHEN Wei-ping)
Foundation item: Projects (50774096, 50606017) supported by the National Natural Science Foundation of China
Received date: 2009-01-11; Accepted date: 2009-05-08
Corresponding author: RUAN Jian-ming, Professor, PhD; Tel: +86-731-88876644; E-mail: jianming@mail.csu.edu.cn
